Evaluating ChatGPT-4o’s Performance in Construction of Q-Matrix for a Cognitive Diagnostic Assessment

Evaluating ChatGPT-4o’s Performance in Construction of Q-Matrix for a Cognitive Diagnostic Assessment | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Evaluating ChatGPT-4o’s Performance in Construction of Q-Matrix for a Cognitive Diagnostic Assessment Semih Aşiret, Seçil Ömür Sünbül This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6235063/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 8 You are reading this latest preprint version Abstract This study evaluates the performance of ChatGPT-4o in constructing Q-matrices for cognitive diagnostic assessments by comparing its outputs with those constructed by researchers and human experts. The research examines the overlap rates among these Q-matrices and assesses their validity using empirical methods. Two distinct mathematics datasets were used, and the Q-matrices were validated through statistical techniques to determine their model-data fit. The results indicate that ChatGPT-4o can generate Q-matrices with a high degree of overlap rate to those specified by human experts, demonstrating its potential as a tool for cognitive diagnostic assessments. The study highlights that AI-generated Q-matrices can be a valuable supplement to traditional methods, but expert validation remains essential to ensure theoretical accuracy and practical applicability. The findings suggest that a hybrid approach—integrating AI-based Q-matrix construction with expert refinement—can enhance the accuracy and efficiency of cognitive diagnostic assessments. Social science/Education Social science/Psychology Q-matrix ChatGPT-4o Generative Artificial Intelligence Cognitive Diagnostic Model Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 1. Introduction 1.1. Generative Artificial Intelligence The integration of computers and the Internet into education has greatly advanced technology-enhanced learning. This development has been further facilitated by innovations in artificial intelligence (AI). Specifically, AI is a subfield of computer science that focuses on simulating human intelligence 1 . As an interdisciplinary field, AI seeks to build systems and algorithms that mimic human cognitive functions, including learning, problem-solving, perception, language understanding, and decision-making 2 . Generative AI, a subset of AI, includes sophisticated models capable of producing various forms of content, such as images, text, code, audio, and music. Utilizing advanced techniques such as deep learning and large language models, generative AI has gained widespread adoption in industries such as manufacturing, healthcare, information technology, the arts, finance, and education. One of the leading models in this field is ChatGPT, a multimodal AI system developed by OpenAI and made publicly available in November 2022. The recently released ChatGPT-4o processes text-based responses as well as visual and auditory inputs 3 . It works faster and more efficiently than its predecessors while providing enhanced natural language understanding and generation capabilities that improve the fluidity of human-computer interaction. This model is particularly relevant to content creation, training, coding, and creative processes, providing innovative solutions that improve access to information through generative AI. In recent years, ChatGPT has gained significant traction in educational settings and has become the focus of numerous academic studies. 1.2 Cognitive Diagnostic Models Currently, most psychometric studies focus on tests that measure unidimensional latent traits. These tests are often used in summative assessments such as selection and placement. DiBello et al. 4 recently noted that teachers and educational administrators are increasingly requesting measurement tools for formative assessments. In such formative assessments, it is critical to provide quick and accurate feedback in the classroom to improve instructional effectiveness. In order to provide effective and accurate feedback, it is essential to accurately and reliably identify an individual's strengths and weaknesses. Cognitive Diagnostic Models (CDMs) can be particularly useful in this context. CDMs classify examinees into attribute profiles that reveal their mastery or non-mastery of a set of latent abilities 5 . More generally, CDMs identify the latent skills and attributes that an individual must possess in order to answer an item correctly 4 , 6 . These attributes encompass a range of latent characteristics, including cognitive processes, operations, skills, or trait states 7 . CDMs are particularly useful in educational and psychological assessments because they allow for targeted interventions by identifying specific skill gaps 8 . This detailed diagnostic feedback makes CDMs particularly valuable in educational assessment, where understanding learners' specific strengths and weaknesses is critical for targeted interventions 9 . The Q-matrix is a key element for all CDMs. The Q-matrix is a fundamental tool that defines the relationship between test items and the latent skills or attributes they are intended to measure 10 , 6 , 11 . The Q-matrix introduced by Tatsuoka 11 is a binary J×K matrix, where J represents the number of items and K represents the number of attributes. Each entry q jk in the matrix is either 1 or 0, indicating whether a particular attribute k is required (q jk = 1) or not required (q jk =0) to correctly answer item j. An example of a Q-matrix in a cognitive diagnostic assessment can be seen in a mathematics test that measures three attributes: A1 (addition), A2 (subtraction), and A3 (multiplication). Suppose there are four items in the test. The Q-matrix might look like this: $$\:Q=\left[\begin{array}{c}1\:\:\:\:0\:\:\:\:0\\\:1\:\:\:\:1\:\:\:\:0\\\:0\:\:\:\:1\:\:\:\:1\\\:0\:\:\:\:0\:\:\:\:1\end{array}\right]$$ Each row corresponds to an item, and each column represents an attribute. For example, item 1 (q1) requires only A1 (addition), so the q-vector for this item is [1,0,0]. Item 2 (q2) requires both A1 (addition) and A2 (subtraction), represented by [1,1,0]. The Q-matrix explicitly outlines the cognitive demands of each item and serves as the structural framework for diagnosing examinees' mastery of these attributes. It provides the structural basis for estimating model parameters and classifying examinees into attribute mastery profiles 8 . A properly specified Q-matrix ensures that the model accurately represents the cognitive processes involved in responding to each item 12 . Traditionally, Q-matrices are constructed based on expert judgment and theoretical foundations regarding the attributes and the relationship between these attributes and the test items. Subject matter experts, such as teachers or psychologists, determine which attributes are necessary to solve each test item. This process involves identifying the key cognitive skills or attributes that each item assesses. Experts often rely on a combination of theoretical frameworks, curriculum standards, and item content analysis to construct the Q-matrix. While this expert-driven approach is essential, it can be subjective, and therefore, the construction of the Q-matrix requires careful consideration of potential biases and misinterpretations 13 , 14 , 6 , 8 . Studies have shown that misspecification of the Q-matrix can significantly affect parameter estimation and classification of examinees 14 , 15 . To address these challenges, researchers have developed empirical methods for Q-matrix validation. Empirical methods such as the delta method 16 , the GDI methods 14 , the Wald method 17 , the Hull method 18 , the multiple logistic regression-based (MLR-B) method 19 , the β method 20 have been proposed in the literature to validate and refine the Q-matrix with the aim of improving its accuracy and reducing subjectivity. These methods allow the identification of potential misclassifications in the Q-matrix by comparing the estimated item responses with the actual observed responses. Among the Q-matrix validation methods, two techniques stand out: the Hull method 18 and the MLR-B method 19 . These techniques were used in the present study because of their robust performance and their ready availability within the ‘ Qval’ package 21 . 1.3 Aim of this study The main purpose of this research is to evaluate the performance of ChatGPT-4o in constructing Q-matrices used in cognitive diagnostic assessments. The study examines the overlap rates between Q-matrices obtained from three different sources and asks whether AI-based approaches can be an alternative to traditional methods. To this end, the study addresses the following research questions: RQ1: What are the overlap rates between the Q-matrices constructed by the researcher, human experts, and ChatGPT-4o? RQ2: How does the performance of Q-matrices vary according to empirical validation methods? RQ3: What are the strengths and limitations of ChatGPT-4o in the Q-matrix construction process? RQ4: How can AI-based Q-matrix generation approaches be effectively integrated with traditional methods in cognitive diagnostic assessments? 2. Method 2.1 Datasets In this study, two different binary datasets were used to evaluate the Q-matrix construction process. In Study 1, the dataset developed by de la Torre 12 was derived from Tatsuoka's 22 study. This dataset contained responses from 536 middle school students to 12 fraction subtraction items. The Q-matrix for this dataset included four attributes: (a) performing basic fraction subtraction operations, (b) simplified/reduced fractions, (c) separating whole numbers from fractions, and (d) borrowing from whole numbers to fractions. In Study 2, the dataset was taken from the TIMSS 2007 Grade 4 mathematics assessment, as analysed by Park and Lee 23 . This dataset included responses from 825 participants from the US national sample to 25 dichotomized mathematics items from Booklet 4. The Q-matrix was adapted from the work of Lee et al. 24 , where the original 15 attributes were consolidated into seven attributes through domain-specific grouping. These attributes included: (a) whole numbers, (b) fractions and decimals, (c) number sets, patterns, and relationships, (d) lines and angles, (e) two- and three-dimensional shapes, (f) location and motion, and (g) reading, interpreting, organizing, and representing. The data and Q-matrices from these two studies were obtained from the CDM package 25 in R. 2.2 Automatic Q-Matrix Construction A customized GPT model (Q-Matrix Construction for CDM) was developed to automate the Q-matrix construction process for CDM ( https://chatgpt.com/g/g-673d9a33dbe481919b849c62fa1d61f3-q-matrix-construction-for-cdm ). The customized GPT model was trained on foundational literature, incorporating both theoretical insights and practical methodologies for Q-matrix construction. The pre-training process focused on defining the purpose and features of Q-matrices and outlining the construction steps. Detailed explanations of the attributes were added to ensure that the model's outputs remain clear and consistent. Before uploading test items, the customized model needed to understand the purpose of the test as well as detailed information about the intended audience, including age and grade level. Users were asked to provide the names and detailed explanations of the attributes that represent the skills or knowledge components to be measured in the assessment. In the next step, users were prompted for test items. For items that contained visuals or tables, the model required that the input be formatted as JSON to ensure that it could process the information correctly. To validate the model's understanding, it had to provide the correct answers and demonstrate the solution steps for each test item. If any answers were incorrect, additional prompts were used to guide the model to the correct solution, ensuring that it accurately understood the item content and cognitive requirements. Once the model's understanding of the test items was confirmed, it generated a Q-matrix for each item, assigning binary codes (1 or 0) to each attribute level. The model also provided detailed justifications for these assignments, explaining the reasoning behind the binary coding for each attribute. All prompts and outputs of ChatGPT-4o and explanations of attributes for Study 2 are available in the Supplemental Material ( https://osf.io/5arv8/ ). 2.3 Human-Expert Evaluation The Q-matrices generated by ChatGPT-4o were compared with those constructed by the researcher for two datasets, separately. A group of seven experts, including academics and teachers with advanced degrees in mathematics education, educational measurement, and evaluation, participated in the review process. Experts who were not familiar with Cognitive Diagnostic Models (CDMs) first received a brief introduction to CDMs and the Q-matrix construction process. After this introduction, the experts analysed Q-matrices with discrepancies, reviewing the attributes and test items without knowing whether they were mapped by the researchers or ChatGPT-4o. They carefully reviewed the differences, assigned binary codes (1 or 0), and provided justifications for their decisions. Following their evaluations, a follow-up meeting was held where experts discussed their reasoning and reached a consensus. Since all panellists agreed on the final Q-matrix after this discussion, inter-rater reliability was not calculated. A final Q-matrix was created based on the panel’s consensus. However, for the fraction subtraction dataset, the Q-matrices generated by ChatGPT-4o and the human experts were identical, so an additional Q-matrix was not needed. 2.4 Data Analysis The analysis was conducted in several steps to assess the quality and validity of the Q-matrices. The overlap rate of the Q-matrices has been calculated at the attribute and attribute vector levels. Hull and MLR-B validation methods were used to examine the validity of the Q-matrices. Since the true Q-matrix is unknown, the Q-matrix recovery rate (QRR) has been calculated by comparing the suggested Q-matrices from the validation method. Model-data fit was evaluated for the researcher’s and ChatGPT-4o’s Q-matrices as well as estimated Q-matrices by MLR-B and Hull methods using both relative indices (− 2LL, AIC, BIC) and absolute indices (M2, RMSEA2, SRMSR). Relative fit indices identify the best-fitting model among competing models, while absolute fit indices assess how well the model’s predictions align with the observed values 13 . These analyses were conducted using R 4.1 27 , specifically the 'GDINA' package 17 for model-data fit assessment and the 'Qval' package 21 for Q-matrix validation. The Q-matrices constructed by the researcher, ChatGPT-4o, human experts, and those suggested by the validation procedures were compared. Differences in the Q-matrices were analysed at the attribute level, and the justifications provided by human-experts and ChatGPT-4o were discussed to evaluate the reasons for these differences. All codes and Q-matrices for data analysis are available in OSF ( https://osf.io/5arv8/ ) 3. Results For conciseness, only the results directly relevant to the discussion are included in this article. The complete set of results is available upon request from the first author. 3.1 Results of Study 1 In Study 1, the Q-matrices derived from the researcher and ChatGPT-4o for fraction-subtraction items were compared. Using the GDINA model for fit analysis, differences between these matrices and those obtained via the MLR-B and Hull methods were evaluated (see Table 1 ) and QRRs were computed. Table 1 shows that the only discrepancy between the researcher’s and ChatGPT-4o’s Q-matrices concerns attribute A2 in items 2, 11, and 12 (the researcher marked these as 1, whereas ChatGPT-4o marked them as 0). The overlap rates between the researchers' and ChatGPT-4o's Q-matrices were 0.938 at the attribute level and 0.75 at the attribute vector level. Additionally, the MLR-B and Hull methods suggested 10 and 11 q-entry modifications for the researcher’s Q-matrix and 7 and 6 for ChatGPT-4o’s Q-matrix, respectively. Notably, while both original Q-matrices assign a value of 1 to attribute A1, the validation methods recommend a 0 for certain items. The researcher’s Q-matrix achieved a QRR of 0.771 using both Hull and MLR-B methods. In contrast, the ChatGPT-4o’s Q-matrix obtained a higher QRR of 0.896 with the Hull method than 0.875 with MLR-B. However, as the true Q-matrix is unknown, these results should be interpreted with caution. Table 1 Q-Matrices for fraction-subtraction data Items Researcher ChatGPT-4o/Human Expert A1 A2 A3 A4 A1 A2 A3 A4 Item 1 \(\:\frac{3}{4}-\frac{3}{8}\) 1 0 0 0 1 0* 0 0 Item 2 \(\:3\frac{1}{2}-2\frac{3}{2}\) 1 1* 1* 1 1 0^ 1 1 Item 3 \(\:\frac{6}{7}-\frac{4}{7}\) 1 0 0 0 1 0 0 0 Item 4 \(\:3\frac{7}{8}-2\) 1* 0 1 0 1 0 1* 0 Item 5 \(\:4\frac{4}{12}-2\frac{7}{12}\) 1* 1* 1 1 1* 1 1* 1* Item 6 \(\:4\frac{1}{3}-2\frac{4}{3}\) 1* 1 1 1 1 1* 1 1 Item 7 \(\:\frac{11}{8}-\frac{1}{8}\) 1 1 0 0 1 1 0 0 Item 8 \(\:3\frac{4}{5}-3\frac{2}{5}\) 1 0 1 0 1 0 1 0 Item 9 \(\:5\frac{5}{7}-1\frac{4}{7}\) 1 0 1 0 1 0 1 0 Item 10 \(\:7\frac{3}{5}-\frac{4}{5}\) 1* 0 1 1 1 0 1 1* Item 11 \(\:4\frac{1}{10}-2\frac{8}{10}\) 1 1* 1 1 1 0^ 1 1 Item 12 \(\:4\frac{1}{3}-1\frac{5}{3}\) 1* 1* 1 1 1 0^ 1 1 Notes : Entries suggested for modification by the MLR-B method are underlined (_). Modifications suggested by the Hull method are indicated by an asterisk (*). Entries in the Q-matrix generated by ChatGPT-4o that differ from those constructed by the researcher are marked with a caret (^). A1, perform basic operations of subtraction of fractions; A2, simplify/reduce fractions; A3, separate whole numbers from fractions; A4, borrow from whole numbers to fractions. The fit indices are summarized in Table 2 . Lower RMSEA 2 (excellent fit 0.045) and SRMSR (< 0.05) values indicate superior fit 28 , 29 , 30 . Analysis of the absolute goodness-of-fit statistics indicated computational limitations in deriving M 2 statistics and RMSEA 2 values for the original Q-matrices due to low degrees of freedom. According to the results of the SMRSR, ChatGPT-4o Q-matrix (SRMSR = 0.027) has a better fit than the researcher Q-matrix and Q-matrices estimated by the two methods. The results of the absolute fit statistics indicate that the M 2 statistics of the Q-matrices suggested by validation methods based on the researcher Q-matrix (M 2-Res-Hull =89.19, p < 0.05; M 2-Res-MLR-B = 95.23, p < 0.05) were found to be significant, thereby failing to achieve model-data fit. In contrast, the Q-matrices estimated based on the ChatGPT-4o Q-matrix yielded adequate model-data fit (M 2-Chat-Hull =3.66, p > 0.05; M 2-Chat-MLR-B = 1.37, p > 0.05). According to the RMSEA 2 with MLR-B, the ChatGPT-4o Q-matrix and the corresponding Q-matrices suggested by the validation methods provided a better fit than the researcher's. In terms of relative model fit indices (AIC, BIC, and − 2LL), the ChatGPT-4o Q-matrix provided a better model-data fit than the researcher's Q-matrix. However, Hull and MLR-B modifications to the ChatGPT-4o Q-matrix ultimately provided an even better fit. These empirical results indicate that model predictions based on the ChatGPT-4o and human-experts Q-matrices performed a better fit with the observed data, leading to a higher model-data fit. Table 2 Model Fit Indices of Q-Matrices for Fraction-Subtraction data Absolute Fit İndices Relative Fit İndices Q-Matrix M 2 Statistics RMSEA 2 SRMSR AIC BIC -2LL M 2 df p Researcher Original * * * * 0.087 5739.85 6266.80 5493.84 Hull 89.19 17 0 0.089 0.085 5626.79 5888.12 5504.78 MLR-B 95.23 15 0 0.099 0.071 5597.71 5867.61 5471.70 ChatGPT-4o Original * * * * 0.027 5559.05 5974.61 5365.04 Hull 3.66 5 0.598 0 0.035 5549.19 5861.94 5403.19 MLR-B 1.37 3 0.711 0 0.036 5545.15 5866.46 5395.15 Notes : *, M 2 statistic cannot be calculated - Degrees of freedom are too low. To explore the reasons behind the discrepancies between the researcher and ChatGPT-4o Q-matrices, we examined item 11 ("4 1/10 − 2 8/10"). The researcher's q-vector (1111) included attribute A2, while ChatGPT-4o's q-vector (1011) excluded it. This difference may stem from alternative problem-solving strategies: the researcher's approach required converting integers to fractions (requiring A2), while ChatGPT-4o employed a different yet valid method (Fig. 1 ) problem-solving. Notably, ChatGPT-4o's q-vector aligns with MLR-B and Hull method estimations, supporting its validity. Similar patterns were observed for items 2 and 12, where ChatGPT-4o's q-entries differed from the researcher's proposals. 3.2 Results of Study 2 In Study 2, the capability of ChatGPT-4o in Q-matrix generation was examined using a more complex dataset than in Study 1. We analysed three distinct Q-matrices: researcher-constructed, ChatGPT-4o-generated, and human expert-constructed ( Table 3 ). Additionally, the suggested Q-matrices through MLR-B and Hull methods are available as supplementary materials ( https://osf.io/5arv8/ ). Table 3 Q-Matrices for TIMSS 2007 Mathematics Items Item Researchers ChatGPT-4o Human-Expert N1 N2 N3 G4 G5 G6 D7 N1 N2 N3 G4 G5 G6 D7 N1 N2 N3 G4 G5 G6 D7 M041052 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 M041056 0^ 1 0 0 0 0 0 1* 1 0 0 0 0 0 1* 1 0 0 0 0 0 M041069 1^ 1 0 0 0 0 0 0* 1 0 0 0 0 0 0* 1 0 0 0 0 0 M041076 1^ 1 0 0 0 0 0 0* 1 0 0 0 0 0 1^ 1 0 0 0 0 0 M041281 1 0 1 0 0 0 0 1 0 1 0 0 0 0 1 0 1 0 0 0 0 M041164 0 0 0 0^ 1 1^ 0 0 0 0 1* 1 0* 0 0 0 0 0^ 1 1^ 0 M041146 0 0 0 1 1 1 0 0 0 0 1 1 1 0 0 0 0 1 1 1 0 M041152 1 0 0 0 1 0 0 1 0 0 0 1 0 0 1 0 0 0 1 0 0 M041258A 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 M041258B 0 0 0 1 1 0 0 0 0 0 1 1 0 0 0 0 0 1 1 0 0 M041131 1 0 0 1^ 0 0 0^ 1 0 0 0* 0 0 1* 1 0 0 1^ 0 0 1* M041275 1 0 0 0 0 0 1 1 0 0 0 0 0 1 1 0 0 0 0 0 1 M041186 1 0 0 0 0 0 1 1 0 0 0 0 0 1 1 0 0 0 0 0 1 M041336 1 1 0 0 0 0 1 1 1 0 0 0 0 1 1 1 0 0 0 0 1 M031303 1 0 0^ 0 0 0 0 1 0 1* 0 0 0 0 1 0 1* 0 0 0 0 M031309 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 M031245 1 0 1 0 0 0 0 1 0 1 0 0 0 0 1 0 1 0 0 0 0 M031242A 1 0 1 0 0 0 0^ 1 0 1 0 0 0 1* 1 0 1 0 0 0 1* M031242B 1 0 0^ 0 0 0 1 1 0 1* 0 0 0 1 1 0 1* 0 0 0 1 M031242C 1 0 1 0 0 0 1 1 0 1 0 0 0 1 1 0 1 0 0 0 1 M031247 1 0 1 0 0 0 0 1 0 1 0 0 0 0 1 0 1 0 0 0 0 M031219 0 0 0 0 1 1 0 0 0 0 0 1 1 0 0 0 0 0 1 1 0 M031173 1 0 0^ 0 0 0 0 1 0 1* 0 0 0 0 1 0 1* 0 0 0 0 M031085 0 0 0 0^ 1 0 0 0 0 0 1* 1 0 0 0 0 0 1* 1 0 0 M031172 1 0 0 0 0 0 1 1 0 0 0 0 0 1 1 0 0 0 0 0 1 Notes : Entries that differ according to the ChatGPT-4o-based Q-matrix are indicated with ^, whereas those that differ according to the researcher-based Q-matrix are indicated with *. N1, Whole Numbers; N2, Fractions and Decimals; N3, Number Sentences, Patterns, & Relationships; G4, Lines and Angles; G5, Two- and Three-Dimensional Shapes; G6, Location and Movement; D7, Reading, Interpreting, Organizing, & Representing. Compared to the human-expert Q-matrix, experts were presented with 12 q-entries, with variations in items and attributes between the two Q-matrices. The experts accepted 8 q-entries from ChatGPT-4o and 4 from the researchers. The overlap rates between the researchers' and ChatGPT-4o's Q-matrices were 0.931 at the attribute level and 0.60 at the attribute vector level, with 12 differences (6.86%) in 10 items (40%) (Fig. 3 ). In addition, the overlap between the researcher and human-expert Q-matrices was 0.954 (attribute level) and 0.68 (attribute vector level), whereas the ChatGPT-4o and human-expert Q-matrices were higher, with rates of 0.977 and 0.842, respectively. Using the Hull method, the Q-matrices constructed by researchers and human-experts were identical, with a QRR of 0.926, which was higher than that of ChatGPT-4o (Table 4 ). Similarly, the MLR-B method yielded the highest QRR of 0.926 for the researchers’ Q-matrix. As a result, the highest QRR values, according to the Q-matrices suggested by the validation methods, were obtained from the researchers' Q-matrix, followed by the human-expert and ChatGPT-4o Q-matrices, respectively. Table 4 QRR results for Q-matrices for Study 2 Q-matrix QRR HULL MLR-B Researchers 0.926 0.926 ChatGPT-4o 0.851 0.863 Human Expert 0.926 0.909 Table 5 presents absolute and relative model fit results for all nine Q-matrices. Each demonstrated acceptable fit with non-significant M 2 statistics (p > 0.05) and excellent absolute model-data fit (RMSEA 2 < 0.03). Additionally, the SRMSR indicated a good fit for the human-expert Q-matrix and the suggested Q-matrix by Hull method (SRMSR < 0.05), while the remaining Q-matrices also showed acceptable fit, suggesting strong overall model performance. Among the original Q-matrices, the highest absolute fit index was achieved by the model based on the human-expert Q-matrix, followed by the models using the ChatGPT-4o and researchers' Q-matrices, respectively. For the relative model fit, the MLR-B-based human-expert’s Q-matrix showed the best fit with the lowest AIC (AIC = 9192.27). Among the original Q-matrices, the human-expert ’s Q-matrix had the lowest relative goodness-of-fit statistics (-2LL = 8731.96, AIC = 9217.96, BIC = 10151.24), followed by the ChatGPT-4o ’s Q-matrix (-2LL = 8746.79, AIC = 9220.80, BIC = 10131.03) and the researcher s’ Q-matrix (-2LL = 8807.91, AIC = 9257.92, BIC = 10122.06). Based on the empirical analysis, these findings suggest that the human experts ’ Q-matrix provides the best overall model fit, both in absolute and relative fit evaluations , followed closely by the ChatGPT-4o and researchers’ Q-matrices. Table 5 Model-fit indices for Q-Matrices in Study 2 Absolute Fit Indices Relative Fit Indices Q-Matrix M 2 Statistic RMSEA 2 SRMSR AIC BIC -2LL M 2 df p Researcher Original 122.16 100 0.065 0.025 0.053 9257.92 10122.06 8807.91 Hull 108.72 116 0.671 0.000 0.053 9259.05 10061.75 8841.05 MLR-B 115.78 115 0.641 0.000 0.052 9239.81 10019.46 8833.81 ChatGPT-4o Original 94.46 88 0.299 0.014 0.051 9220.80 10131.03 8746.79 Hull 123.48 108 0.072 0.024 0.051 9221.51 10077.97 8775.51 MLR-B 138.08 118 0.099 0.022 0.054 9226.84 10021.86 8812.84 Human Expert Original 88.32 82 0.296 0.015 0.045 9217.96 10151.24 8731.96 Hull 65.56 76 0.797 0.000 0.047 9225.60 10181.92 8727.59 MLR-B 94.33 102 0.692 0.000 0.052 9192.27 10048.73 8746.26 As shown in Fig. 2 , the N2 and G5 attributes in the ChatGPT-4o’s Q-matrix are identical to those in the researchers’ Q-matrix. However, discrepancies exist in three items for attributes N1, N3, and G4, one item for G6, and two items for D7. Figure 3 illustrates that among the ten misaligned items, two (M041131 and M041164) have discrepancies in two attributes, while eight have discrepancies in only one attribute. The remaining 13 items show no discrepancies between the Q-matrices. For item M041164 (Fig. 4 ), discrepancies arise between ChatGPT-4o's and the researchers' q-vectors in attributes G4 and G6. ChatGPT-4o proposed the q-vector (0001100), while the researchers used (0000110). Notably, human experts aligned with the researchers' q-vector. Table 6 shows ChatGPT-4o's rationale for assigning a 1 to attribute G4 and 0 to attribute G6. Table 6 ChatGPT-4o's Justifications for Attribute G4 and G6 Assignments for Item M041164 Item Attribute G4 (assigned 1) Attribute G6 (assigned 0) M041164 “This problem involves understanding the concept of symmetry, which is a property of lines and shapes. The concept of symmetry is directly tied to understanding the properties of lines and their relationships within shapes. The task requires analyzing the properties of the dotted line and its relationship to the figures. Understanding symmetry—a key concept tied to lines—falls squarely under Attribute 4. " " The problem asks the student to identify the line of symmetry for different shapes. This involves analyzing static properties of the given shapes (symmetry), not locating points or analyzing movement. The dotted line is already provided, and the student does not need to locate specific points on a grid or map. The task does not involve moving or transforming shapes (e.g., rotating, translating, or reflecting the figure). It focuses only on determining whether the dotted line creates symmetry. " As shown in Table 6 , ChatGPT-4o assigned a value of 1 to attribute G4 based on its interpretation that analysing symmetry involves understanding line properties and their relationships within shapes. While this interpretation aligns with the definition of attribute G4, subject matter experts assigned a value of 0 due to their more nuanced understanding of the task requirements. The experts stated that the task doesn't explicitly require measuring, estimating, or drawing lines and angles—the essential components of attribute G4. Instead, they classified determining lines of symmetry under attribute G6, which focuses on analysing static properties of shapes. The experts explained that although a symmetry line exists in the problem, the cognitive process required involves understanding shapes' reflective characteristics rather than the technical manipulation of lines. Therefore, while symmetry involves lines, the primary cognitive engagement aligns more closely with G6's emphasis on analysing geometric properties rather than G4's focus on line measurement and construction. When examining the estimated Q-matrices (see Supplementary Materials), the human-expert q-vector for item M041164 is identical to the one estimated by validation methods. However, the researchers’ q-vector differ from the estimated q-vectors. Since validation methods derive the Q-matrix completely through data-driven approaches, these results should be interpreted with caution. Item M031242A (Fig. 5 ) requires interpreting pricing data from two bike rental service posters (Mountain Bike Rentals and Roadrace Bike Rentals). Students must complete tables showing rental costs across multiple hours. For this item, the researchers proposed a q-vector of (1010000), while both ChatGPT-4o and human-experts suggested (1010001). The sole difference lies in attribute D7, where researchers assigned 0 while ChatGPT-4o and experts assigned 1. Table 8 outlines ChatGPT-4o's rationale for assigning 1 to attribute D7. Table 8 ChatGPT-4o's Justifications for Attribute D7 for Item M031242A Item ChatGPT-4o's Justifications for Attribute D7 M031242A Attribute D7 is assigned a value of 1 because the task explicitly requires the interpretation, organization, and representation of structured data. The pricing rules provided in the posters are presented visually, and students must extract and interpret this information, such as the base costs for the first hour and the incremental costs for each additional hour. This aligns with D7's focus on interpreting structured data. After interpreting the data, students are required to calculate cumulative costs and systematically organize these values into structured tables. This process reflects the attribute's emphasis on organizing and representing numerical data in a clear and logical format. Additionally, the tables created by the students allow for further analysis and comparisons between the two rental options, demonstrating the ability to use structured data for reasoning and decision-making. The task, therefore, directly assesses the essential components of Attribute D7, making it central to the problem's solution. Item M031242A requires students to transform rental cost information from two posters into organized tables. The researchers assigned 0 to attribute D7, likely focusing on arithmetic operations related to attributes N1 (Whole Numbers) and N3 (Number Sentences, Patterns, and Relationships). However, as shown in Table 7, ChatGPT-4o's rationale—supported by expert opinions—aligns with attribute D7's definition. The task requires students to read and interpret data from textual and numerical sources, organize information across multiple periods, and represent it in structured tables. This corresponds directly with attribute D7: reading data from tables, understanding data utilization, and organizing information in tabular form. At this point, both ChatGPT-4o and human experts constructed their q-entries based solely on the given attributes and their explanations, recognizing that the item requires students to go beyond basic calculations to interpret and organize data. 4. Discussion This study evaluates the performance of the generative artificial intelligence model, ChatGPT-4o, in constructing Q-matrices for CDMs. The study employs the Q-matrices developed by de la Torre 12 for the fraction subtraction test items and dataset, as well as those constructed by Park and Lee 23 for the TIMSS 2007 Grade 4 Mathematics Test. The overlap rates between ChatGPT-4o and researchers’ Q-matrices was 0.938 for the fraction-subtraction test and 0.931 for the TIMSS 2007 mathematics test, demonstrating ChatGPT-4o's capability to generate Q-matrices closely resembling those constructed by researchers. However, the differences in the two studies stems from different reasons. In Study 1, discrepancies were limited to attribute A2, likely due to variations in problem-solving strategies. In Study 2, discrepancies of varying degrees appeared across five of seven attributes. These differences may arise from conceptual overlaps between attributes (e.g., G6 intersects with G4 and G5 through shared elements of spatial reasoning and geometric transformations) and from ChatGPT-4o's reliance on textual and conceptual associations rather than deep analysis of mathematical content and cognitive processes. For effective use of generative AI in Q-matrix construction, minimizing conceptual overlaps among attributes, defining them clearly, and involving human experts to ensure accuracy is essential. The empirical results of this study show that the best performance in both relative and absolute fit evaluations was observed in models based on the human-expert Q-matrix, followed by those using the ChatGPT-4o and researcher Q-matrices, respectively. In terms of QRR, Study 1 showed a higher QRR value for the ChatGPT-4o Q-matrix compared to the researcher Q-matrix, while the opposite was observed in Study 2. The QRR values for the human-expert Q matrices were consistently high in both studies. One possible explanation for the performance of ChatGPT-4o is that Study 2 included a more complex dataset with item types containing visual and graphical elements and a greater number of attributes. The differences between the original and suggested Q-matrices may stem from factors beyond our investigation's scope, such as Q-matrix incompleteness 31 , small sample sizes, attribute correlations, or test length limitations. Importantly, Chen and de la Torre 32 caution that Q-matrices determined solely from estimated q-vectors might show acceptable fit statistics yet remain theoretically flawed. Therefore, results from Q-matrix validation methods should be thoroughly discussed by subject matter experts to refine the final Q-matrix based on item characteristics 32 , 33 . Consequently, it is recommended that subject-matter experts evaluate Q-matrix specifications whether empirically suggested or generated by ChatGPT-4o, to ensure they accurately reflect and theoretically sound item-attribute relationships. The fraction subtraction and TIMSS 2007 mathematics test items differ structurally, with twenty-one TIMSS items incorporating visuals and graphics. ChatGPT-4o's performance on image-based items requires improvement 34 , 35 due to difficulties in interpreting diagrams and spatial relationships 36 , 37 . To overcome these issues, all items in this study were provided in both image and JSON formats, leading to more accurate interpretations and solutions. Thus, including JSON codes alongside visual items may enhance the accuracy of Q-matrices generated by ChatGPT-4o. The empirical and qualitative findings of this study show that ChatGPT-4o specified more effectively, possibly due to its ability to detect latent item-attribute structures without introducing human bias. However, some discrepancies between q-vectors for items indicate that ChatGPT-4o struggled to capture deeper conceptual dependencies. Unlike human experts, ChatGPT-4o operates based on probabilistic textual associations rather than domain-specific reasoning, which may explain its reduced performance in modelling complex cognitive constructs. These findings suggest that while AI-assisted Q-matrix generation can enhance efficiency, expert validation remains essential for ensuring conceptual accuracy. Chen and de la Torre 32 noted that recent CDM advancements allow adaptation of non-diagnostic assessments for diagnostic purposes. In Study 2, large-scale assessments with TIMSS mathematics items, originally designed for unidimensional item response models were used. However, this adaptation may yield suboptimal results since these items were not initially designed to provide diagnostic information. Additionally, in large-scale assessments, Q-matrices are typically constructed after item development, whereas in CDM studies, they're created before 31 —thus increasing misspecification risks. Therefore, when adapting diagnostic models to existing assessments, ensuring the Q-matrix accurately represents required cognitive skills without influence from irrelevant item characteristics is crucial 32 . Consequently, this issue requires careful consideration when developing AI-assisted Q-matrices for large-scale assessments. To mitigate the challenge of hallucinations and inaccuracies in LLM-generated outputs, effective prompt engineering strategies should be employed to enhance precision and reliability 38 . Future studies should systematically evaluate whether the model accurately understands the attributes and integrate ChatGPT-4o’s reasoning with researcher expertise to construct more precise Q-matrices. This study presents several important limitations that should be considered. First, it focuses solely on ChatGPT-4o’s performance in generating Q-matrices for mathematical data. Future research should expand its scope to examine its effectiveness in other domains. Additionally, this study only utilizes datasets with four and seven attributes. However, many educational assessments require Q-matrices for items with a greater number of attributes, raising questions about how ChatGPT-4o would adapt to more complex scenarios. Furthermore, the rapid advancements in AI technologies highlight the need for continuous research on the stability and reliability of AI-generated outputs. 5. Conclusion This study demonstrates that ChatGPT-4o can effectively construct Q-matrices for cognitive diagnostic assessments, showing high overlap rate with those constructed by researchers and human experts. However, while ChatGPT-4o performs well in identifying conceptual associations, expert validation remains crucial to ensure theoretical soundness and accuracy. The findings emphasize the importance of combining AI-assisted methods with expert input to enhance the validity of the Q-matrix. The justifications provided by ChatGPT-4o can also be considered in the Q-matrix specification process to improve accuracy. Ultimately, while generative AI can be leveraged for Q-matrix construction, ensuring the validity of these matrices necessitates empirical methods alongside expert evaluation. Future studies should explore the model’s robustness and generalizability in diagnostic assessment settings by examining its applicability across various assessment contexts and more complex attributes. Declarations The authors report there are no competing interests to declare. Author Contribution S.A. conducted the literature review, performed the analyses, conducted focus group interviews with experts, prepared figures, contributed to writing the main manuscript reviewed it.S.Ö.S. conducted the literature review, conducted focus group interviews with experts, designed the methodology and writing the main manuscript, and reviewed the manuscript. All authors reviewed and approved the final version of the manuscript. Data availability The data that support the findings of this study are openly available in OSF at https://osf.io/5arv8 Supplemental material Supplemental materials are available at https://osf.io/5arv8 References Broussard M et al (2019) Artificial intelligence and journalism. J Mass Commun Q 96:673–695. https://doi.org/10.1177/1077699019859901 Russell S, Norvig P (2021) Artificial intelligence: A modern approach, 4th edn. Pearson Education, Inc. OpenAI (2023) GPT-4 technical report. https://cdn.openai.com/papers/gpt-4.pdf DiBello L, Roussos LA, Stout WF (2007) Review of cognitively diagnostic assessment and a summary of psychometric models. In Handbook of Statistics (eds. Rao, C. R. & Sinharay, S.) 26, 979–1030 de la Torre J (2009) A cognitive diagnosis model for cognitively based multiple-choice options. 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Lawrence Erlbaum Associates, Inc., pp 453–488 Park YS, Lee Y-S (2014) An extension of the DINA model using covariates: Examining factors affecting response probability and latent classification. Appl Psychol Meas 38:376–390. https://doi.org/10.1177/0146621614523830 Lee Y-S, Park YS, Taylan D (2011) A cognitive diagnostic modeling of attribute mastery in Massachusetts, Minnesota, and the U.S. national sample using the TIMSS 2007. Int J Test 11:144–177. https://doi.org/10.1080/15305058.2010.534571 Robitzsch A, Kiefer T, George AC, Uenlue A (2022) CDM: Cognitive diagnosis modeling . R package version 8.2-6. https://CRAN.R-project.org/package=CDM Chen J, de la Torre J, Zhang Z (2013) Relative and absolute fit evaluation in cognitive diagnosis modeling. J Educ Meas 50:123–140. https://doi.org/10.1111/j.1745-3984.2012.00185.x R Core Team (2024) R: A language and environment for statistical computing . R Foundation for Statistical Computing, Vienna, Austria. https://www.R-project.org Ma W (2020) Evaluating the fit of sequential G-DINA model using limited-information measures. Appl Psychol Meas 44:167–181. https://doi.org/10.1177/0146621619843829 Liu R, Huggins-Manley AC, Bulut O (2018) Retrofitting diagnostic classification models to responses from IRT-based assessment forms. Educ Psychol Meas 78:357–383. https://doi.org/10.1177/0013164416685599 Maydeu-Olivares A, Joe H (2014) Assessing approximate fit in categorical data analysis. Multivar Behav Res 49:305–328. https://doi.org/10.1080/00273171.2014.911075 Köhn H, Chiu C (2018) How to build a complete Q-matrix for a cognitively diagnostic test. J Classif 35:273–299. https://doi.org/10.1007/s00357-018-9255-0 Chen J, de la Torre J (2014) A procedure for diagnostically modeling extant large-scale assessment data: The case of the Programme for International Student Assessment in reading. Psychology 5:1967–1978. https://doi.org/10.4236/psych.2014.518200 Shi Q, Ma W, Robitzsch A, Sorrel MA, Man K (2021) Cognitively diagnostic analysis using the G-DINA model in R. Psych 3:812–835. https://doi.org/10.3390/psych3040052 Massey PA, Montgomery C, Zhang AS (2023) Comparison of ChatGPT-3.5, ChatGPT-4, and orthopaedic resident performance on orthopaedic assessment examinations. J Am Acad Orthop Surg 31:1173–1179. https://doi.org/10.5435/JAAOS-D-23-00396 Sawamura S et al (2024) Performance of ChatGPT 4.0 on Japan's National Physical Therapist Examination: A comprehensive analysis of text and visual question handling. Cureus 16, e67347 https://doi.org/10.7759/cureus.67347 Polverini G, Gregorcic B (2023) Performance of ChatGPT on the test of understanding graphs in kinematics. Phys Rev Phys Educ Res 20:010109. https://doi.org/10.1103/physrevphyseducres.20.010109 Wei X (2024) Evaluating ChatGPT-4 and ChatGPT-4o: Performance insights from NAEP mathematics problem solving. Front Educ 9. https://doi.org/10.3389/feduc.2024.1452570 Zheng Z, Zhang O, Borgs C, Chayes J, Yaghi O (2023) ChatGPT chemistry assistant for text mining and prediction of MOF synthesis. J Am Chem Soc. https://doi.org/10.1021/jacs.3c05819 Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 12 Nov, 2025 Reviews received at journal 02 Jul, 2025 Reviewers agreed at journal 05 Apr, 2025 Reviewers invited by journal 03 Apr, 2025 Editor invited by journal 27 Mar, 2025 Editor assigned by journal 27 Mar, 2025 Submission checks completed at journal 25 Mar, 2025 First submitted to journal 15 Mar, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. 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2","display":"","copyAsset":false,"role":"figure","size":14114,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cem\u003eOverlap\u003c/em\u003e Rates at the Attribute Level\u003c/p\u003e","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-6235063/v1/fa72297f71595f165c5778d4.png"},{"id":81309630,"identity":"245999bd-836c-49c1-9115-4d964001011d","added_by":"auto","created_at":"2025-04-24 15:12:12","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":15876,"visible":true,"origin":"","legend":"\u003cp\u003eItem-level Differentiating Attributes\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eNotes\u003c/strong\u003e: The red line denotes identical attribute vectors across all Q-matrices, while the blue line indicates at least one attribute-level difference.\u003c/p\u003e","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-6235063/v1/31db316180314e58e7543f3a.png"},{"id":81309641,"identity":"277410ea-2331-4036-ab82-112d66f50202","added_by":"auto","created_at":"2025-04-24 15:12:13","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":117285,"visible":true,"origin":"","legend":"\u003cp\u003eItem M041164 of the TIMSS 2007 Fourth Grade Mathematics Test\u003c/p\u003e","description":"","filename":"floatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-6235063/v1/7a740a3621fadbe5562f638d.png"},{"id":81310128,"identity":"9dd601a9-5fcd-47cc-8bc8-1fad2d1608c8","added_by":"auto","created_at":"2025-04-24 15:20:12","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":110042,"visible":true,"origin":"","legend":"\u003cp\u003eItem M031242A of the TIMSS 2007 Fourth Grade Mathematic\u003c/p\u003e","description":"","filename":"floatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-6235063/v1/835d2a7755d1e0af37c6db19.png"},{"id":81695971,"identity":"46e50f67-6778-4247-bcf2-996b8d18dc1b","added_by":"auto","created_at":"2025-04-30 12:07:48","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1546369,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6235063/v1/0409c73d-9f76-4737-80df-8dfab6f4ce5f.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Evaluating ChatGPT-4o’s Performance in Construction of Q-Matrix for a Cognitive Diagnostic Assessment","fulltext":[{"header":"1. Introduction","content":"\u003cdiv id=\"Sec2\" class=\"Section2\"\u003e \u003ch2\u003e1.1. Generative Artificial Intelligence\u003c/h2\u003e \u003cp\u003eThe integration of computers and the Internet into education has greatly advanced technology-enhanced learning. This development has been further facilitated by innovations in artificial intelligence (AI). Specifically, AI is a subfield of computer science that focuses on simulating human intelligence\u003csup\u003e\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u003c/sup\u003e. As an interdisciplinary field, AI seeks to build systems and algorithms that mimic human cognitive functions, including learning, problem-solving, perception, language understanding, and decision-making\u003csup\u003e\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/sup\u003e. Generative AI, a subset of AI, includes sophisticated models capable of producing various forms of content, such as images, text, code, audio, and music. Utilizing advanced techniques such as deep learning and large language models, generative AI has gained widespread adoption in industries such as manufacturing, healthcare, information technology, the arts, finance, and education. One of the leading models in this field is ChatGPT, a multimodal AI system developed by OpenAI and made publicly available in November 2022. The recently released ChatGPT-4o processes text-based responses as well as visual and auditory inputs\u003csup\u003e\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e\u003c/sup\u003e. It works faster and more efficiently than its predecessors while providing enhanced natural language understanding and generation capabilities that improve the fluidity of human-computer interaction. This model is particularly relevant to content creation, training, coding, and creative processes, providing innovative solutions that improve access to information through generative AI. In recent years, ChatGPT has gained significant traction in educational settings and has become the focus of numerous academic studies.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e1.2 Cognitive Diagnostic Models\u003c/h2\u003e \u003cp\u003eCurrently, most psychometric studies focus on tests that measure unidimensional latent traits. These tests are often used in summative assessments such as selection and placement. DiBello et al.\u003csup\u003e\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e\u003c/sup\u003e recently noted that teachers and educational administrators are increasingly requesting measurement tools for formative assessments. In such formative assessments, it is critical to provide quick and accurate feedback in the classroom to improve instructional effectiveness. In order to provide effective and accurate feedback, it is essential to accurately and reliably identify an individual's strengths and weaknesses. Cognitive Diagnostic Models (CDMs) can be particularly useful in this context. CDMs classify examinees into attribute profiles that reveal their mastery or non-mastery of a set of latent abilities\u003csup\u003e\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e\u003c/sup\u003e. More generally, CDMs identify the latent skills and attributes that an individual must possess in order to answer an item correctly\u003csup\u003e\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e,\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e\u003c/sup\u003e. These attributes encompass a range of latent characteristics, including cognitive processes, operations, skills, or trait states\u003csup\u003e\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e\u003c/sup\u003e. CDMs are particularly useful in educational and psychological assessments because they allow for targeted interventions by identifying specific skill gaps\u003csup\u003e\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e\u003c/sup\u003e. This detailed diagnostic feedback makes CDMs particularly valuable in educational assessment, where understanding learners' specific strengths and weaknesses is critical for targeted interventions\u003csup\u003e\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eThe Q-matrix is a key element for all CDMs. The Q-matrix is a fundamental tool that defines the relationship between test items and the latent skills or attributes they are intended to measure\u003csup\u003e\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e,\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e,\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e\u003c/sup\u003e. The Q-matrix introduced by Tatsuoka\u003csup\u003e\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e\u003c/sup\u003e is a binary \u003cem\u003eJ\u0026times;K\u003c/em\u003e matrix, where J represents the number of items and K represents the number of attributes. Each entry q\u003csub\u003ejk\u003c/sub\u003e in the matrix is either 1 or 0, indicating whether a particular attribute k is required (q\u003csub\u003ejk\u003c/sub\u003e = 1) or not required (q\u003csub\u003ejk\u003c/sub\u003e=0) to correctly answer item j. An example of a Q-matrix in a cognitive diagnostic assessment can be seen in a mathematics test that measures three attributes: A1 (addition), A2 (subtraction), and A3 (multiplication). Suppose there are four items in the test. The Q-matrix might look like this:\u003cdiv id=\"Equa\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equa\" name=\"EquationSource\"\u003e\n$$\\:Q=\\left[\\begin{array}{c}1\\:\\:\\:\\:0\\:\\:\\:\\:0\\\\\\:1\\:\\:\\:\\:1\\:\\:\\:\\:0\\\\\\:0\\:\\:\\:\\:1\\:\\:\\:\\:1\\\\\\:0\\:\\:\\:\\:0\\:\\:\\:\\:1\\end{array}\\right]$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eEach row corresponds to an item, and each column represents an attribute. For example, item 1 (q1) requires only A1 (addition), so the q-vector for this item is [1,0,0]. Item 2 (q2) requires both A1 (addition) and A2 (subtraction), represented by [1,1,0]. The Q-matrix explicitly outlines the cognitive demands of each item and serves as the structural framework for diagnosing examinees' mastery of these attributes. It provides the structural basis for estimating model parameters and classifying examinees into attribute mastery profiles\u003csup\u003e\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e\u003c/sup\u003e. A properly specified Q-matrix ensures that the model accurately represents the cognitive processes involved in responding to each item\u003csup\u003e\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e\u003c/sup\u003e. Traditionally, Q-matrices are constructed based on expert judgment and theoretical foundations regarding the attributes and the relationship between these attributes and the test items. Subject matter experts, such as teachers or psychologists, determine which attributes are necessary to solve each test item. This process involves identifying the key cognitive skills or attributes that each item assesses. Experts often rely on a combination of theoretical frameworks, curriculum standards, and item content analysis to construct the Q-matrix. While this expert-driven approach is essential, it can be subjective, and therefore, the construction of the Q-matrix requires careful consideration of potential biases and misinterpretations\u003csup\u003e\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e,\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e,\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e\u003c/sup\u003e. Studies have shown that misspecification of the Q-matrix can significantly affect parameter estimation and classification of examinees\u003csup\u003e\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e,\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e\u003c/sup\u003e. To address these challenges, researchers have developed empirical methods for Q-matrix validation. Empirical methods such as the delta method\u003csup\u003e\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e\u003c/sup\u003e, the GDI methods\u003csup\u003e\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e\u003c/sup\u003e, the Wald method\u003csup\u003e\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e\u003c/sup\u003e, the Hull method\u003csup\u003e\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e\u003c/sup\u003e, the multiple logistic regression-based (MLR-B) method\u003csup\u003e\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e\u003c/sup\u003e, the β method\u003csup\u003e\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e\u003c/sup\u003e have been proposed in the literature to validate and refine the Q-matrix with the aim of improving its accuracy and reducing subjectivity. These methods allow the identification of potential misclassifications in the Q-matrix by comparing the estimated item responses with the actual observed responses. Among the Q-matrix validation methods, two techniques stand out: the Hull method\u003csup\u003e\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e\u003c/sup\u003e and the MLR-B method\u003csup\u003e\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e\u003c/sup\u003e. These techniques were used in the present study because of their robust performance and their ready availability within the \u0026lsquo;\u003cem\u003eQval\u0026rsquo;\u003c/em\u003e package\u003csup\u003e\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e1.3 Aim of this study\u003c/h2\u003e \u003cp\u003eThe main purpose of this research is to evaluate the performance of ChatGPT-4o in constructing Q-matrices used in cognitive diagnostic assessments. The study examines the overlap rates between Q-matrices obtained from three different sources and asks whether AI-based approaches can be an alternative to traditional methods. To this end, the study addresses the following research questions:\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003eRQ1: What are the overlap rates between the Q-matrices constructed by the researcher, human experts, and ChatGPT-4o?\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eRQ2: How does the performance of Q-matrices vary according to empirical validation methods?\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eRQ3: What are the strengths and limitations of ChatGPT-4o in the Q-matrix construction process?\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eRQ4: How can AI-based Q-matrix generation approaches be effectively integrated with traditional methods in cognitive diagnostic assessments?\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"2. Method","content":"\u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003e2.1 Datasets\u003c/h2\u003e \u003cp\u003eIn this study, two different binary datasets were used to evaluate the Q-matrix construction process. In Study 1, the dataset developed by de la Torre\u003csup\u003e\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e\u003c/sup\u003e was derived from Tatsuoka's\u003csup\u003e\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e\u003c/sup\u003e study. This dataset contained responses from 536 middle school students to 12 fraction subtraction items. The Q-matrix for this dataset included four attributes: (a) performing basic fraction subtraction operations, (b) simplified/reduced fractions, (c) separating whole numbers from fractions, and (d) borrowing from whole numbers to fractions. In Study 2, the dataset was taken from the TIMSS 2007 Grade 4 mathematics assessment, as analysed by Park and Lee\u003csup\u003e\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e\u003c/sup\u003e. This dataset included responses from 825 participants from the US national sample to 25 dichotomized mathematics items from Booklet 4. The Q-matrix was adapted from the work of Lee et al.\u003csup\u003e\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e\u003c/sup\u003e, where the original 15 attributes were consolidated into seven attributes through domain-specific grouping. These attributes included: (a) whole numbers, (b) fractions and decimals, (c) number sets, patterns, and relationships, (d) lines and angles, (e) two- and three-dimensional shapes, (f) location and motion, and (g) reading, interpreting, organizing, and representing. The data and Q-matrices from these two studies were obtained from the \u003cem\u003eCDM\u003c/em\u003e package\u003csup\u003e\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e\u003c/sup\u003e in R.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003e2.2 Automatic Q-Matrix Construction\u003c/h2\u003e \u003cp\u003eA customized GPT model (Q-Matrix Construction for CDM) was developed to automate the Q-matrix construction process for CDM (\u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://chatgpt.com/g/g-673d9a33dbe481919b849c62fa1d61f3-q-matrix-construction-for-cdm\u003c/span\u003e\u003cspan address=\"https://chatgpt.com/g/g-673d9a33dbe481919b849c62fa1d61f3-q-matrix-construction-for-cdm\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e). The customized GPT model was trained on foundational literature, incorporating both theoretical insights and practical methodologies for Q-matrix construction. The pre-training process focused on defining the purpose and features of Q-matrices and outlining the construction steps. Detailed explanations of the attributes were added to ensure that the model's outputs remain clear and consistent. Before uploading test items, the customized model needed to understand the purpose of the test as well as detailed information about the intended audience, including age and grade level. Users were asked to provide the names and detailed explanations of the attributes that represent the skills or knowledge components to be measured in the assessment. In the next step, users were prompted for test items. For items that contained visuals or tables, the model required that the input be formatted as JSON to ensure that it could process the information correctly. To validate the model's understanding, it had to provide the correct answers and demonstrate the solution steps for each test item. If any answers were incorrect, additional prompts were used to guide the model to the correct solution, ensuring that it accurately understood the item content and cognitive requirements. Once the model's understanding of the test items was confirmed, it generated a Q-matrix for each item, assigning binary codes (1 or 0) to each attribute level. The model also provided detailed justifications for these assignments, explaining the reasoning behind the binary coding for each attribute. All prompts and outputs of ChatGPT-4o and explanations of attributes for Study 2 are available in the Supplemental Material (\u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://osf.io/5arv8/\u003c/span\u003e\u003cspan address=\"https://osf.io/5arv8/\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003e2.3 Human-Expert Evaluation\u003c/h2\u003e \u003cp\u003eThe Q-matrices generated by ChatGPT-4o were compared with those constructed by the researcher for two datasets, separately. A group of seven experts, including academics and teachers with advanced degrees in mathematics education, educational measurement, and evaluation, participated in the review process. Experts who were not familiar with Cognitive Diagnostic Models (CDMs) first received a brief introduction to CDMs and the Q-matrix construction process. After this introduction, the experts analysed Q-matrices with discrepancies, reviewing the attributes and test items without knowing whether they were mapped by the researchers or ChatGPT-4o. They carefully reviewed the differences, assigned binary codes (1 or 0), and provided justifications for their decisions. Following their evaluations, a follow-up meeting was held where experts discussed their reasoning and reached a consensus. Since all panellists agreed on the final Q-matrix after this discussion, inter-rater reliability was not calculated. A final Q-matrix was created based on the panel\u0026rsquo;s consensus. However, for the fraction subtraction dataset, the Q-matrices generated by ChatGPT-4o and the human experts were identical, so an additional Q-matrix was not needed.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec9\" class=\"Section2\"\u003e \u003ch2\u003e2.4 Data Analysis\u003c/h2\u003e \u003cp\u003eThe analysis was conducted in several steps to assess the quality and validity of the Q-matrices. The overlap rate of the Q-matrices has been calculated at the attribute and attribute vector levels. Hull and MLR-B validation methods were used to examine the validity of the Q-matrices. Since the true Q-matrix is unknown, the Q-matrix recovery rate (QRR) has been calculated by comparing the suggested Q-matrices from the validation method. Model-data fit was evaluated for the researcher\u0026rsquo;s and ChatGPT-4o\u0026rsquo;s Q-matrices as well as estimated Q-matrices by MLR-B and Hull methods using both relative indices (\u0026minus;\u0026thinsp;2LL, AIC, BIC) and absolute indices (M2, RMSEA2, SRMSR). Relative fit indices identify the best-fitting model among competing models, while absolute fit indices assess how well the model\u0026rsquo;s predictions align with the observed values\u003csup\u003e\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e\u003c/sup\u003e. These analyses were conducted using R 4.1\u003csup\u003e27\u003c/sup\u003e, specifically the \u003cem\u003e'GDINA'\u003c/em\u003e package\u003csup\u003e\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e\u003c/sup\u003e for model-data fit assessment and the \u003cem\u003e'Qval'\u003c/em\u003e package\u003csup\u003e\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e\u003c/sup\u003e for Q-matrix validation. The Q-matrices constructed by the researcher, ChatGPT-4o, human experts, and those suggested by the validation procedures were compared. Differences in the Q-matrices were analysed at the attribute level, and the justifications provided by human-experts and ChatGPT-4o were discussed to evaluate the reasons for these differences. All codes and Q-matrices for data analysis are available in OSF (\u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://osf.io/5arv8/\u003c/span\u003e\u003cspan address=\"https://osf.io/5arv8/\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e)\u003c/p\u003e \u003c/div\u003e"},{"header":"3. Results","content":"\u003cp\u003eFor conciseness, only the results directly relevant to the discussion are included in this article. The complete set of results is available upon request from the first author.\u003c/p\u003e \u003cdiv id=\"Sec11\" class=\"Section2\"\u003e \u003ch2\u003e3.1 Results of Study 1\u003c/h2\u003e \u003cp\u003eIn Study 1, the Q-matrices derived from the researcher and ChatGPT-4o for fraction-subtraction items were compared. Using the GDINA model for fit analysis, differences between these matrices and those obtained via the MLR-B and Hull methods were evaluated (see Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e) and QRRs were computed. Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e shows that the only discrepancy between the researcher\u0026rsquo;s and ChatGPT-4o\u0026rsquo;s Q-matrices concerns attribute A2 in items 2, 11, and 12 (the researcher marked these as 1, whereas ChatGPT-4o marked them as 0). The overlap rates between the researchers' and ChatGPT-4o's Q-matrices were 0.938 at the attribute level and 0.75 at the attribute vector level. Additionally, the MLR-B and Hull methods suggested 10 and 11 q-entry modifications for the researcher\u0026rsquo;s Q-matrix and 7 and 6 for ChatGPT-4o\u0026rsquo;s Q-matrix, respectively. Notably, while both original Q-matrices assign a value of 1 to attribute A1, the validation methods recommend a 0 for certain items. The researcher\u0026rsquo;s Q-matrix achieved a QRR of 0.771 using both Hull and MLR-B methods. In contrast, the ChatGPT-4o\u0026rsquo;s Q-matrix obtained a higher QRR of 0.896 with the Hull method than 0.875 with MLR-B. However, as the true Q-matrix is unknown, these results should be interpreted with caution.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eQ-Matrices for fraction-subtraction data\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"13\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c10\" colnum=\"10\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c11\" colnum=\"11\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c12\" colnum=\"12\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c13\" colnum=\"13\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eItems\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colspan=\"5\" nameend=\"c7\" namest=\"c3\"\u003e \u003cp\u003eResearcher\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c9\" namest=\"c8\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colspan=\"4\" nameend=\"c13\" namest=\"c10\"\u003e \u003cp\u003eChatGPT-4o/Human Expert\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eA1\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eA2\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eA3\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eA4\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c8\" namest=\"c7\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c10\" namest=\"c9\"\u003e \u003cp\u003eA1\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c11\"\u003e \u003cp\u003eA2\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c12\"\u003e \u003cp\u003eA3\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c13\"\u003e \u003cp\u003eA4\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eItem 1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\frac{3}{4}-\\frac{3}{8}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c8\" namest=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c10\" namest=\"c9\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e\u003cspan type=\"BoldUnderline\" class=\"BoldUnderline\" name=\"Emphasis\"\u003e0*\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eItem 2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:3\\frac{1}{2}-2\\frac{3}{2}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cspan type=\"BoldUnderline\" class=\"BoldUnderline\" name=\"Emphasis\"\u003e1*\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cspan type=\"BoldUnderline\" class=\"BoldUnderline\" name=\"Emphasis\"\u003e1*\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c8\" namest=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c10\" namest=\"c9\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e\u003cb\u003e0^\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e\u003cspan type=\"BoldUnderline\" class=\"BoldUnderline\" name=\"Emphasis\"\u003e1\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eItem 3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\frac{6}{7}-\\frac{4}{7}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c8\" namest=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c10\" namest=\"c9\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eItem 4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:3\\frac{7}{8}-2\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cspan type=\"BoldUnderline\" class=\"BoldUnderline\" name=\"Emphasis\"\u003e1*\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c8\" namest=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c10\" namest=\"c9\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e\u003cspan type=\"BoldUnderline\" class=\"BoldUnderline\" name=\"Emphasis\"\u003e1*\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eItem 5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:4\\frac{4}{12}-2\\frac{7}{12}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cspan type=\"BoldUnderline\" class=\"BoldUnderline\" name=\"Emphasis\"\u003e1*\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cspan type=\"BoldUnderline\" class=\"BoldUnderline\" name=\"Emphasis\"\u003e1*\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c8\" namest=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c10\" namest=\"c9\"\u003e \u003cp\u003e\u003cb\u003e1*\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e\u003cb\u003e1*\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e\u003cspan type=\"BoldUnderline\" class=\"BoldUnderline\" name=\"Emphasis\"\u003e1*\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eItem 6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:4\\frac{1}{3}-2\\frac{4}{3}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003e1*\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cspan type=\"BoldUnderline\" class=\"BoldUnderline\" name=\"Emphasis\"\u003e1\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c8\" namest=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c10\" namest=\"c9\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e\u003cspan type=\"BoldUnderline\" class=\"BoldUnderline\" name=\"Emphasis\"\u003e1*\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eItem 7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\frac{11}{8}-\\frac{1}{8}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cspan type=\"BoldUnderline\" class=\"BoldUnderline\" name=\"Emphasis\"\u003e1\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c8\" namest=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c10\" namest=\"c9\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eItem 8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:3\\frac{4}{5}-3\\frac{2}{5}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c8\" namest=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c10\" namest=\"c9\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eItem 9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:5\\frac{5}{7}-1\\frac{4}{7}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c8\" namest=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c10\" namest=\"c9\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eItem 10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:7\\frac{3}{5}-\\frac{4}{5}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cspan type=\"BoldUnderline\" class=\"BoldUnderline\" name=\"Emphasis\"\u003e1*\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c8\" namest=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c10\" namest=\"c9\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e\u003cspan type=\"BoldUnderline\" class=\"BoldUnderline\" name=\"Emphasis\"\u003e1*\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eItem 11\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:4\\frac{1}{10}-2\\frac{8}{10}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cspan type=\"BoldUnderline\" class=\"BoldUnderline\" name=\"Emphasis\"\u003e1*\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c8\" namest=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c10\" namest=\"c9\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e\u003cb\u003e0^\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eItem 12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:4\\frac{1}{3}-1\\frac{5}{3}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cspan type=\"BoldUnderline\" class=\"BoldUnderline\" name=\"Emphasis\"\u003e1*\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cspan type=\"BoldUnderline\" class=\"BoldUnderline\" name=\"Emphasis\"\u003e1*\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c8\" namest=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c10\" namest=\"c9\"\u003e \u003cp\u003e\u003cspan type=\"BoldUnderline\" class=\"BoldUnderline\" name=\"Emphasis\"\u003e1\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e\u003cb\u003e0^\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"13\"\u003e\u003cb\u003eNotes\u003c/b\u003e: Entries suggested for modification by the MLR-B method are underlined (_). Modifications suggested by the Hull method are indicated by an asterisk (*). Entries in the Q-matrix generated by ChatGPT-4o that differ from those constructed by the researcher are marked with a caret (^). A1, perform basic operations of subtraction of fractions; A2, simplify/reduce fractions; A3, separate whole numbers from fractions; A4, borrow from whole numbers to fractions.\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eThe fit indices are summarized in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. Lower RMSEA\u003csub\u003e2\u003c/sub\u003e (excellent fit\u0026thinsp;\u0026lt;\u0026thinsp;0.03; good fit 0.03\u0026ndash;0.045; poor fit\u0026thinsp;\u0026gt;\u0026thinsp;0.045) and SRMSR (\u0026lt;\u0026thinsp;0.05) values indicate superior fit\u003csup\u003e\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e,\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e,\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e\u003c/sup\u003e. Analysis of the absolute goodness-of-fit statistics indicated computational limitations in deriving M\u003csub\u003e2\u003c/sub\u003e statistics and RMSEA\u003csub\u003e2\u003c/sub\u003e values for the original Q-matrices due to low degrees of freedom. According to the results of the SMRSR, ChatGPT-4o Q-matrix (SRMSR\u0026thinsp;=\u0026thinsp;0.027) has a better fit than the researcher Q-matrix and Q-matrices estimated by the two methods. The results of the absolute fit statistics indicate that the M\u003csub\u003e2\u003c/sub\u003e statistics of the Q-matrices suggested by validation methods based on the researcher Q-matrix (M\u003csub\u003e2-Res-Hull\u003c/sub\u003e=89.19, p\u0026thinsp;\u0026lt;\u0026thinsp;0.05; M\u003csub\u003e2-Res-MLR-B\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;95.23, p\u0026thinsp;\u0026lt;\u0026thinsp;0.05) were found to be significant, thereby failing to achieve model-data fit. In contrast, the Q-matrices estimated based on the ChatGPT-4o Q-matrix yielded adequate model-data fit (M\u003csub\u003e2-Chat-Hull\u003c/sub\u003e=3.66, p\u0026thinsp;\u0026gt;\u0026thinsp;0.05; M\u003csub\u003e2-Chat-MLR-B\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;1.37, p\u0026thinsp;\u0026gt;\u0026thinsp;0.05). According to the RMSEA\u003csub\u003e2\u003c/sub\u003e with MLR-B, the ChatGPT-4o Q-matrix and the corresponding Q-matrices suggested by the validation methods provided a better fit than the researcher's. In terms of relative model fit indices (AIC, BIC, and \u0026minus;\u0026thinsp;2LL), the ChatGPT-4o Q-matrix provided a better model-data fit than the researcher's Q-matrix. However, Hull and MLR-B modifications to the ChatGPT-4o Q-matrix ultimately provided an even better fit. These empirical results indicate that model predictions based on the ChatGPT-4o and human-experts Q-matrices performed a better fit with the observed data, leading to a higher model-data fit.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eModel Fit Indices of Q-Matrices for Fraction-Subtraction data\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"10\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c10\" colnum=\"10\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colspan=\"5\" nameend=\"c7\" namest=\"c3\"\u003e \u003cp\u003eAbsolute Fit İndices\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"3\" nameend=\"c10\" namest=\"c8\"\u003e \u003cp\u003eRelative Fit İndices\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eQ-Matrix\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c5\" namest=\"c3\"\u003e \u003cp\u003eM\u003csub\u003e2\u003c/sub\u003e Statistics\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eRMSEA\u003csub\u003e2\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eSRMSR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eAIC\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eBIC\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003e-2LL\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eM\u003csub\u003e2\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003edf\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003ep\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003eResearcher\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eOriginal\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e*\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e*\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e*\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e*\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.087\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e5739.85\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e6266.80\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e5493.84\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eHull\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e89.19\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e17\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.089\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.085\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e5626.79\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e5888.12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e5504.78\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMLR-B\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e95.23\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.099\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.071\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e5597.71\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e5867.61\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e5471.70\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003eChatGPT-4o\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eOriginal\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e*\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e*\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e*\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e*\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.027\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e5559.05\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e5974.61\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e5365.04\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eHull\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e3.66\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.598\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.035\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e5549.19\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e5861.94\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e5403.19\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMLR-B\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.37\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.711\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.036\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e5545.15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e5866.46\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e5395.15\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"10\"\u003e\u003cb\u003eNotes\u003c/b\u003e: *, M\u003csub\u003e2\u003c/sub\u003e statistic cannot be calculated - Degrees of freedom are too low.\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eTo explore the reasons behind the discrepancies between the researcher and ChatGPT-4o Q-matrices, we examined item 11 (\"4 1/10\u0026thinsp;\u0026minus;\u0026thinsp;2 8/10\"). The researcher's q-vector (1111) included attribute A2, while ChatGPT-4o's q-vector (1011) excluded it. This difference may stem from alternative problem-solving strategies: the researcher's approach required converting integers to fractions (requiring A2), while ChatGPT-4o employed a different yet valid method (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e) problem-solving. Notably, ChatGPT-4o's q-vector aligns with MLR-B and Hull method estimations, supporting its validity. Similar patterns were observed for items 2 and 12, where ChatGPT-4o's q-entries differed from the researcher's proposals.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec12\" class=\"Section2\"\u003e \u003ch2\u003e3.2 Results of Study 2\u003c/h2\u003e \u003cp\u003eIn Study 2, the capability of ChatGPT-4o in Q-matrix generation was examined using a more complex dataset than in Study 1. We analysed three distinct Q-matrices: researcher-constructed, ChatGPT-4o-generated, and human expert-constructed \u003cem\u003e(\u003c/em\u003eTable\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e). Additionally, the suggested Q-matrices through MLR-B and Hull methods are available as supplementary materials (\u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://osf.io/5arv8/\u003c/span\u003e\u003cspan address=\"https://osf.io/5arv8/\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eQ-Matrices for TIMSS 2007 Mathematics Items\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"25\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c10\" colnum=\"10\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c11\" colnum=\"11\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c12\" colnum=\"12\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c13\" colnum=\"13\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c14\" colnum=\"14\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c15\" colnum=\"15\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c16\" colnum=\"16\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c17\" colnum=\"17\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c18\" colnum=\"18\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c19\" colnum=\"19\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c20\" colnum=\"20\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c21\" colnum=\"21\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c22\" colnum=\"22\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c23\" colnum=\"23\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c24\" colnum=\"24\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c25\" colnum=\"25\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eItem\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"7\" nameend=\"c8\" namest=\"c2\"\u003e \u003cp\u003eResearchers\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colspan=\"7\" nameend=\"c16\" namest=\"c10\"\u003e \u003cp\u003eChatGPT-4o\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c17\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colspan=\"8\" nameend=\"c25\" namest=\"c18\"\u003e \u003cp\u003eHuman-Expert\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eN1\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eN2\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eN3\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eG4\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eG5\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eG6\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003eD7\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c10\"\u003e \u003cp\u003eN1\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c11\"\u003e \u003cp\u003eN2\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c12\"\u003e \u003cp\u003eN3\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c13\"\u003e \u003cp\u003eG4\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c14\"\u003e \u003cp\u003eG5\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c15\"\u003e \u003cp\u003eG6\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c16\"\u003e \u003cp\u003eD7\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c17\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c18\"\u003e \u003cp\u003eN1\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c19\"\u003e \u003cp\u003eN2\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c20\"\u003e \u003cp\u003eN3\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c21\"\u003e \u003cp\u003eG4\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c22\"\u003e \u003cp\u003eG5\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c23\"\u003e \u003cp\u003eG6\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c24\"\u003e \u003cp\u003eD7\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"1\" nameend=\"c25\" namest=\"c25\"\u003e\u0026nbsp;\u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eM041052\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c15\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c16\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c17\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c18\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c19\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c20\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c21\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c22\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c23\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c24\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"1\" nameend=\"c25\" namest=\"c25\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eM041056\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003e0^\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e\u003cb\u003e1*\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c15\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c16\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c17\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c18\"\u003e \u003cp\u003e\u003cb\u003e1*\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c19\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c20\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c21\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c22\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c23\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c24\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"1\" nameend=\"c25\" namest=\"c25\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eM041069\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003e1^\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e\u003cb\u003e0*\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c15\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c16\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c17\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c18\"\u003e \u003cp\u003e\u003cb\u003e0*\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c19\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c20\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c21\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c22\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c23\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c24\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"1\" nameend=\"c25\" namest=\"c25\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eM041076\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003e1^\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e\u003cb\u003e0*\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c15\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c16\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c17\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c18\"\u003e \u003cp\u003e\u003cb\u003e1^\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c19\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c20\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c21\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c22\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c23\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c24\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"1\" nameend=\"c25\" namest=\"c25\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eM041281\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c15\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c16\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c17\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c18\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c19\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c20\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c21\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c22\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c23\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c24\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"1\" nameend=\"c25\" namest=\"c25\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eM041164\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e0^\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cb\u003e1^\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e\u003cb\u003e1*\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c15\"\u003e \u003cp\u003e\u003cb\u003e0*\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c16\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c17\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c18\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c19\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c20\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c21\"\u003e \u003cp\u003e\u003cb\u003e0^\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c22\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c23\"\u003e \u003cp\u003e\u003cb\u003e1^\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c24\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"1\" nameend=\"c25\" namest=\"c25\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eM041146\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c15\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c16\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c17\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c18\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c19\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c20\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c21\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c22\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c23\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c24\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"1\" nameend=\"c25\" namest=\"c25\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eM041152\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c15\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c16\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c17\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c18\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c19\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c20\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c21\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c22\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c23\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c24\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"1\" nameend=\"c25\" namest=\"c25\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eM041258A\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c15\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c16\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c17\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c18\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c19\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c20\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c21\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c22\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c23\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c24\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"1\" nameend=\"c25\" namest=\"c25\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eM041258B\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c15\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c16\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c17\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c18\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c19\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c20\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c21\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c22\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c23\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c24\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"1\" nameend=\"c25\" namest=\"c25\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eM041131\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e1^\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u003cb\u003e0^\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e\u003cb\u003e0*\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c15\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c16\"\u003e \u003cp\u003e\u003cb\u003e1*\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c17\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c18\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c19\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c20\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c21\"\u003e \u003cp\u003e\u003cb\u003e1^\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c22\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c23\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c24\"\u003e \u003cp\u003e\u003cb\u003e1*\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"1\" nameend=\"c25\" namest=\"c25\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eM041275\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c15\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c16\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c17\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c18\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c19\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c20\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c21\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c22\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c23\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c24\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"1\" nameend=\"c25\" namest=\"c25\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eM041186\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c15\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c16\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c17\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c18\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c19\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c20\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c21\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c22\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c23\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c24\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"1\" nameend=\"c25\" namest=\"c25\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eM041336\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c15\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c16\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c17\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c18\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c19\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c20\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c21\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c22\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c23\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c24\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"1\" nameend=\"c25\" namest=\"c25\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eM031303\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e0^\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e\u003cb\u003e1*\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c15\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c16\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c17\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c18\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c19\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c20\"\u003e \u003cp\u003e\u003cb\u003e1*\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c21\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c22\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c23\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c24\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"1\" nameend=\"c25\" namest=\"c25\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eM031309\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c15\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c16\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c17\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c18\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c19\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c20\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c21\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c22\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c23\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c24\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"1\" nameend=\"c25\" namest=\"c25\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eM031245\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c15\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c16\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c17\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c18\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c19\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c20\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c21\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c22\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c23\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c24\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"1\" nameend=\"c25\" namest=\"c25\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eM031242A\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u003cb\u003e0^\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c15\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c16\"\u003e \u003cp\u003e\u003cb\u003e1*\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c17\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c18\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c19\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c20\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c21\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c22\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c23\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c24\"\u003e \u003cp\u003e\u003cb\u003e1*\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"1\" nameend=\"c25\" namest=\"c25\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eM031242B\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e0^\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e\u003cb\u003e1*\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c15\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c16\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c17\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c18\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c19\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c20\"\u003e \u003cp\u003e\u003cb\u003e1*\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c21\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c22\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c23\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c24\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"1\" nameend=\"c25\" namest=\"c25\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eM031242C\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c15\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c16\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c17\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c18\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c19\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c20\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c21\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c22\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c23\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c24\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"1\" nameend=\"c25\" namest=\"c25\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eM031247\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c15\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c16\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c17\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c18\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c19\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c20\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c21\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c22\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c23\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c24\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"1\" nameend=\"c25\" namest=\"c25\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eM031219\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c15\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c16\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c17\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c18\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c19\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c20\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c21\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c22\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c23\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c24\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"1\" nameend=\"c25\" namest=\"c25\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eM031173\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e0^\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e\u003cb\u003e1*\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c15\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c16\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c17\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c18\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c19\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c20\"\u003e \u003cp\u003e\u003cb\u003e1*\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c21\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c22\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c23\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c24\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"1\" nameend=\"c25\" namest=\"c25\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eM031085\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e0^\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e\u003cb\u003e1*\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c15\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c16\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c17\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c18\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c19\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c20\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c21\"\u003e \u003cp\u003e\u003cb\u003e1*\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c22\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c23\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c24\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"1\" nameend=\"c25\" namest=\"c25\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eM031172\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c15\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c16\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c17\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c18\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c19\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c20\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c21\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c22\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c23\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c24\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"1\" nameend=\"c25\" namest=\"c25\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"25\"\u003e\u003cb\u003eNotes\u003c/b\u003e: Entries that differ according to the ChatGPT-4o-based Q-matrix are indicated with ^, whereas those that differ according to the researcher-based Q-matrix are indicated with *. N1, Whole Numbers; N2, Fractions and Decimals; N3, Number Sentences, Patterns, \u0026amp; Relationships; G4, Lines and Angles; G5, Two- and Three-Dimensional Shapes; G6, Location and Movement; D7, Reading, Interpreting, Organizing, \u0026amp; Representing.\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eCompared to the human-expert Q-matrix, experts were presented with 12 q-entries, with variations in items and attributes between the two Q-matrices. The experts accepted 8 q-entries from ChatGPT-4o and 4 from the researchers. The overlap rates between the researchers' and ChatGPT-4o's Q-matrices were 0.931 at the attribute level and 0.60 at the attribute vector level, with 12 differences (6.86%) in 10 items (40%) (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e3\u003c/span\u003e). In addition, the overlap between the researcher and human-expert Q-matrices was 0.954 (attribute level) and 0.68 (attribute vector level), whereas the ChatGPT-4o and human-expert Q-matrices were higher, with rates of 0.977 and 0.842, respectively. Using the Hull method, the Q-matrices constructed by researchers and human-experts were identical, with a QRR of 0.926, which was higher than that of ChatGPT-4o (Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e). Similarly, the MLR-B method yielded the highest QRR of 0.926 for the researchers\u0026rsquo; Q-matrix. As a result, the highest QRR values, according to the Q-matrices suggested by the validation methods, were obtained from the researchers' Q-matrix, followed by the human-expert and ChatGPT-4o Q-matrices, respectively.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eQRR results for Q-matrices for Study 2\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eQ-matrix\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003eQRR\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eHULL\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eMLR-B\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eResearchers\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.926\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.926\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eChatGPT-4o\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.851\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.863\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eHuman Expert\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.926\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.909\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e5\u003c/span\u003e presents absolute and relative model fit results for all nine Q-matrices. Each demonstrated acceptable fit with non-significant M\u003csub\u003e2\u003c/sub\u003e statistics (p\u0026thinsp;\u0026gt;\u0026thinsp;0.05) and excellent absolute model-data fit (RMSEA\u003csub\u003e2\u003c/sub\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.03). Additionally, the SRMSR indicated a good fit for the human-expert Q-matrix and the suggested Q-matrix by Hull method (SRMSR\u0026thinsp;\u0026lt;\u0026thinsp;0.05), while the remaining Q-matrices also showed acceptable fit, suggesting strong overall model performance. Among the original Q-matrices, the highest absolute fit index was achieved by the model based on the human-expert Q-matrix, followed by the models using the ChatGPT-4o and researchers' Q-matrices, respectively. For the relative model fit, the MLR-B-based human-expert\u0026rsquo;s Q-matrix showed the best fit with the lowest AIC (AIC\u0026thinsp;=\u0026thinsp;9192.27). Among the original Q-matrices, the human-expert\u003cem\u003e\u0026rsquo;s\u003c/em\u003e Q-matrix had the lowest relative goodness-of-fit statistics (-2LL\u0026thinsp;=\u0026thinsp;8731.96, AIC\u0026thinsp;=\u0026thinsp;9217.96, BIC\u0026thinsp;=\u0026thinsp;10151.24), followed by the ChatGPT-4o\u003cem\u003e\u0026rsquo;s\u003c/em\u003e Q-matrix (-2LL\u0026thinsp;=\u0026thinsp;8746.79, AIC\u0026thinsp;=\u0026thinsp;9220.80, BIC\u0026thinsp;=\u0026thinsp;10131.03) and the researcher\u003cem\u003es\u0026rsquo;\u003c/em\u003e Q-matrix (-2LL\u0026thinsp;=\u0026thinsp;8807.91, AIC\u0026thinsp;=\u0026thinsp;9257.92, BIC\u0026thinsp;=\u0026thinsp;10122.06). Based on the empirical analysis, these findings suggest that the human experts\u003cem\u003e\u0026rsquo;\u003c/em\u003e Q-matrix provides the best overall model fit, both in absolute and relative \u003cem\u003efit evaluations\u003c/em\u003e, followed closely by the ChatGPT-4o and researchers\u0026rsquo; Q-matrices.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab5\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 5\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eModel-fit indices for Q-Matrices in Study 2\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"10\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c10\" colnum=\"10\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colspan=\"5\" nameend=\"c7\" namest=\"c3\"\u003e \u003cp\u003eAbsolute Fit Indices\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"3\" nameend=\"c10\" namest=\"c8\"\u003e \u003cp\u003eRelative Fit Indices\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eQ-Matrix\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c5\" namest=\"c3\"\u003e \u003cp\u003eM\u003csub\u003e2\u003c/sub\u003e Statistic\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eRMSEA\u003csub\u003e2\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eSRMSR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eAIC\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eBIC\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003e-2LL\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eM\u003csub\u003e2\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003edf\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003ep\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003eResearcher\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eOriginal\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e122.16\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.065\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.025\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.053\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e9257.92\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e10122.06\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e8807.91\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eHull\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e108.72\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e116\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.671\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.053\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e9259.05\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e10061.75\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e8841.05\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMLR-B\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e115.78\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e115\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.641\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.052\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e9239.81\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e10019.46\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e8833.81\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003eChatGPT-4o\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eOriginal\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e94.46\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e88\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.299\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.014\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.051\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e9220.80\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e10131.03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e8746.79\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eHull\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e123.48\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e108\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.072\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.024\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.051\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e9221.51\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e10077.97\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e8775.51\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMLR-B\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e138.08\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e118\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.099\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.022\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.054\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e9226.84\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e10021.86\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e8812.84\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003eHuman Expert\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eOriginal\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e88.32\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e82\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.296\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.015\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.045\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e9217.96\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e10151.24\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e8731.96\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eHull\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e65.56\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e76\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.797\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.047\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e9225.60\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e10181.92\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e8727.59\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMLR-B\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e94.33\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e102\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.692\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.052\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e9192.27\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e10048.73\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e8746.26\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eAs shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e2\u003c/span\u003e, the N2 and G5 attributes in the ChatGPT-4o\u0026rsquo;s Q-matrix are identical to those in the researchers\u0026rsquo; Q-matrix. However, discrepancies exist in three items for attributes N1, N3, and G4, one item for G6, and two items for D7. Figure\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e3\u003c/span\u003e illustrates that among the ten misaligned items, two (M041131 and M041164) have discrepancies in two attributes, while eight have discrepancies in only one attribute. The remaining 13 items show no discrepancies between the Q-matrices.\u003c/p\u003e \u003cp\u003eFor item M041164 (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e), discrepancies arise between ChatGPT-4o's and the researchers' q-vectors in attributes G4 and G6. ChatGPT-4o proposed the q-vector (0001100), while the researchers used (0000110). Notably, human experts aligned with the researchers' q-vector. Table\u0026nbsp;\u003cspan refid=\"Tab6\" class=\"InternalRef\"\u003e6\u003c/span\u003e shows ChatGPT-4o's rationale for assigning a 1 to attribute G4 and 0 to attribute G6.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab6\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 6\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eChatGPT-4o's Justifications for Attribute G4 and G6 Assignments for Item M041164\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eItem\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eAttribute G4 (assigned 1)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eAttribute G6 (assigned 0)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eM041164\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cem\u003e\u0026ldquo;This problem involves understanding the concept of symmetry, which is a property of lines and shapes. The concept of symmetry is directly tied to understanding the properties of lines and their relationships within shapes. The task requires analyzing the properties of the dotted line and its relationship to the figures. Understanding symmetry\u0026mdash;a key concept tied to lines\u0026mdash;falls squarely under Attribute 4.\u003c/em\u003e\"\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\"\u003cem\u003eThe problem asks the student to identify the line of symmetry for different shapes. This involves analyzing static properties of the given shapes (symmetry), not locating points or analyzing movement. The dotted line is already provided, and the student does not need to locate specific points on a grid or map. The task does not involve moving or transforming shapes (e.g., rotating, translating, or reflecting the figure). It focuses only on determining whether the dotted line creates symmetry.\u003c/em\u003e\"\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eAs shown in Table\u0026nbsp;\u003cspan refid=\"Tab6\" class=\"InternalRef\"\u003e6\u003c/span\u003e, ChatGPT-4o assigned a value of 1 to attribute G4 based on its interpretation that analysing symmetry involves understanding line properties and their relationships within shapes. While this interpretation aligns with the definition of attribute G4, subject matter experts assigned a value of 0 due to their more nuanced understanding of the task requirements. The experts stated that the task doesn't explicitly require measuring, estimating, or drawing lines and angles\u0026mdash;the essential components of attribute G4. Instead, they classified determining lines of symmetry under attribute G6, which focuses on analysing static properties of shapes. The experts explained that although a symmetry line exists in the problem, the cognitive process required involves understanding shapes' reflective characteristics rather than the technical manipulation of lines. Therefore, while symmetry involves lines, the primary cognitive engagement aligns more closely with G6's emphasis on analysing geometric properties rather than G4's focus on line measurement and construction. When examining the estimated Q-matrices (see Supplementary Materials), the human-expert q-vector for item M041164 is identical to the one estimated by validation methods. However, the researchers\u0026rsquo; q-vector differ from the estimated q-vectors. Since validation methods derive the Q-matrix completely through data-driven approaches, these results should be interpreted with caution.\u003c/p\u003e \u003cp\u003eItem M031242A (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e) requires interpreting pricing data from two bike rental service posters (Mountain Bike Rentals and Roadrace Bike Rentals). Students must complete tables showing rental costs across multiple hours. For this item, the researchers proposed a q-vector of (1010000), while both ChatGPT-4o and human-experts suggested (1010001). The sole difference lies in attribute D7, where researchers assigned 0 while ChatGPT-4o and experts assigned 1. Table\u0026nbsp;\u003cspan refid=\"Tab7\" class=\"InternalRef\"\u003e8\u003c/span\u003e outlines ChatGPT-4o's rationale for assigning 1 to attribute D7.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab7\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 8\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eChatGPT-4o's Justifications for Attribute D7 for Item M031242A\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"2\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eItem\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eChatGPT-4o's Justifications for Attribute D7\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eM031242A\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cem\u003eAttribute D7 is assigned a value of 1 because the task explicitly requires the interpretation, organization, and representation of structured data. The pricing rules provided in the posters are presented visually, and students must extract and interpret this information, such as the base costs for the first hour and the incremental costs for each additional hour. This aligns with D7's focus on interpreting structured data. After interpreting the data, students are required to calculate cumulative costs and systematically organize these values into structured tables. This process reflects the attribute's emphasis on organizing and representing numerical data in a clear and logical format. Additionally, the tables created by the students allow for further analysis and comparisons between the two rental options, demonstrating the ability to use structured data for reasoning and decision-making. The task, therefore, directly assesses the essential components of Attribute D7, making it central to the problem's solution.\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eItem M031242A requires students to transform rental cost information from two posters into organized tables. The researchers assigned 0 to attribute D7, likely focusing on arithmetic operations related to attributes N1 (Whole Numbers) and N3 (Number Sentences, Patterns, and Relationships). However, as shown in Table\u0026nbsp;7, ChatGPT-4o's rationale\u0026mdash;supported by expert opinions\u0026mdash;aligns with attribute D7's definition. The task requires students to read and interpret data from textual and numerical sources, organize information across multiple periods, and represent it in structured tables. This corresponds directly with attribute D7: reading data from tables, understanding data utilization, and organizing information in tabular form. At this point, both ChatGPT-4o and human experts constructed their q-entries based solely on the given attributes and their explanations, recognizing that the item requires students to go beyond basic calculations to interpret and organize data.\u003c/p\u003e \u003c/div\u003e"},{"header":"4. Discussion","content":"\u003cp\u003eThis study evaluates the performance of the generative artificial intelligence model, ChatGPT-4o, in constructing Q-matrices for CDMs. The study employs the Q-matrices developed by de la Torre\u003csup\u003e\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e\u003c/sup\u003e for the fraction subtraction test items and dataset, as well as those constructed by Park and Lee\u003csup\u003e\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e\u003c/sup\u003e for the TIMSS 2007 Grade 4 Mathematics Test.\u003c/p\u003e \u003cp\u003eThe overlap rates between ChatGPT-4o and researchers\u0026rsquo; Q-matrices was 0.938 for the fraction-subtraction test and 0.931 for the TIMSS 2007 mathematics test, demonstrating ChatGPT-4o's capability to generate Q-matrices closely resembling those constructed by researchers. However, the differences in the two studies stems from different reasons. In Study 1, discrepancies were limited to attribute A2, likely due to variations in problem-solving strategies. In Study 2, discrepancies of varying degrees appeared across five of seven attributes. These differences may arise from conceptual overlaps between attributes (e.g., G6 intersects with G4 and G5 through shared elements of spatial reasoning and geometric transformations) and from ChatGPT-4o's reliance on textual and conceptual associations rather than deep analysis of mathematical content and cognitive processes. For effective use of generative AI in Q-matrix construction, minimizing conceptual overlaps among attributes, defining them clearly, and involving human experts to ensure accuracy is essential.\u003c/p\u003e \u003cp\u003eThe empirical results of this study show that the best performance in both relative and absolute fit evaluations was observed in models based on the human-expert Q-matrix, followed by those using the ChatGPT-4o and researcher Q-matrices, respectively. In terms of QRR, Study 1 showed a higher QRR value for the ChatGPT-4o Q-matrix compared to the researcher Q-matrix, while the opposite was observed in Study 2. The QRR values for the human-expert Q matrices were consistently high in both studies. One possible explanation for the performance of ChatGPT-4o is that Study 2 included a more complex dataset with item types containing visual and graphical elements and a greater number of attributes. The differences between the original and suggested Q-matrices may stem from factors beyond our investigation's scope, such as Q-matrix incompleteness\u003csup\u003e\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e\u003c/sup\u003e, small sample sizes, attribute correlations, or test length limitations. Importantly, Chen and de la Torre\u003csup\u003e\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e\u003c/sup\u003e caution that Q-matrices determined solely from estimated q-vectors might show acceptable fit statistics yet remain theoretically flawed. Therefore, results from Q-matrix validation methods should be thoroughly discussed by subject matter experts to refine the final Q-matrix based on item characteristics\u003csup\u003e\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e,\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e\u003c/sup\u003e. Consequently, it is recommended that subject-matter experts evaluate Q-matrix specifications whether empirically suggested or generated by ChatGPT-4o, to ensure they accurately reflect and theoretically sound item-attribute relationships.\u003c/p\u003e \u003cp\u003eThe fraction subtraction and TIMSS 2007 mathematics test items differ structurally, with twenty-one TIMSS items incorporating visuals and graphics. ChatGPT-4o's performance on image-based items requires improvement\u003csup\u003e\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e,\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e\u003c/sup\u003e due to difficulties in interpreting diagrams and spatial relationships\u003csup\u003e\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e,\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e\u003c/sup\u003e. To overcome these issues, all items in this study were provided in both image and JSON formats, leading to more accurate interpretations and solutions. Thus, including JSON codes alongside visual items may enhance the accuracy of Q-matrices generated by ChatGPT-4o.\u003c/p\u003e \u003cp\u003eThe empirical and qualitative findings of this study show that ChatGPT-4o specified more effectively, possibly due to its ability to detect latent item-attribute structures without introducing human bias. However, some discrepancies between q-vectors for items indicate that ChatGPT-4o struggled to capture deeper conceptual dependencies. Unlike human experts, ChatGPT-4o operates based on probabilistic textual associations rather than domain-specific reasoning, which may explain its reduced performance in modelling complex cognitive constructs. These findings suggest that while AI-assisted Q-matrix generation can enhance efficiency, expert validation remains essential for ensuring conceptual accuracy.\u003c/p\u003e \u003cp\u003eChen and de la Torre\u003csup\u003e\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e\u003c/sup\u003e noted that recent CDM advancements allow adaptation of non-diagnostic assessments for diagnostic purposes. In Study 2, large-scale assessments with TIMSS mathematics items, originally designed for unidimensional item response models were used. However, this adaptation may yield suboptimal results since these items were not initially designed to provide diagnostic information. Additionally, in large-scale assessments, Q-matrices are typically constructed after item development, whereas in CDM studies, they're created before\u003csup\u003e\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e\u003c/sup\u003e\u0026mdash;thus increasing misspecification risks. Therefore, when adapting diagnostic models to existing assessments, ensuring the Q-matrix accurately represents required cognitive skills without influence from irrelevant item characteristics is crucial\u003csup\u003e\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e\u003c/sup\u003e. Consequently, this issue requires careful consideration when developing AI-assisted Q-matrices for large-scale assessments.\u003c/p\u003e \u003cp\u003eTo mitigate the challenge of hallucinations and inaccuracies in LLM-generated outputs, effective prompt engineering strategies should be employed to enhance precision and reliability\u003csup\u003e\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e\u003c/sup\u003e. Future studies should systematically evaluate whether the model accurately understands the attributes and integrate ChatGPT-4o\u0026rsquo;s reasoning with researcher expertise to construct more precise Q-matrices.\u003c/p\u003e \u003cp\u003eThis study presents several important limitations that should be considered. First, it focuses solely on ChatGPT-4o\u0026rsquo;s performance in generating Q-matrices for mathematical data. Future research should expand its scope to examine its effectiveness in other domains. Additionally, this study only utilizes datasets with four and seven attributes. However, many educational assessments require Q-matrices for items with a greater number of attributes, raising questions about how ChatGPT-4o would adapt to more complex scenarios. Furthermore, the rapid advancements in AI technologies highlight the need for continuous research on the stability and reliability of AI-generated outputs.\u003c/p\u003e"},{"header":"5. Conclusion","content":"\u003cp\u003eThis study demonstrates that ChatGPT-4o can effectively construct Q-matrices for cognitive diagnostic assessments, showing high overlap rate with those constructed by researchers and human experts. However, while ChatGPT-4o performs well in identifying conceptual associations, expert validation remains crucial to ensure theoretical soundness and accuracy. The findings emphasize the importance of combining AI-assisted methods with expert input to enhance the validity of the Q-matrix. The justifications provided by ChatGPT-4o can also be considered in the Q-matrix specification process to improve accuracy. Ultimately, while generative AI can be leveraged for Q-matrix construction, ensuring the validity of these matrices necessitates empirical methods alongside expert evaluation. Future studies should explore the model\u0026rsquo;s robustness and generalizability in diagnostic assessment settings by examining its applicability across various assessment contexts and more complex attributes.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003eThe authors report there are no competing interests to declare.\u003c/p\u003e\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eS.A. conducted the literature review, performed the analyses, conducted focus group interviews with experts, prepared figures, contributed to writing the main manuscript reviewed it.S.\u0026Ouml;.S. conducted the literature review, conducted focus group interviews with experts, designed the methodology and writing the main manuscript, and reviewed the manuscript. All authors reviewed and approved the final version of the manuscript.\u003c/p\u003e\n\u003ch3\u003eData availability\u003c/h3\u003e\n\u003cp\u003eThe data that support the findings of this study are openly available in OSF at https://osf.io/5arv8\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eSupplemental material\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eSupplemental materials are available at https://osf.io/5arv8\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eBroussard M et al (2019) Artificial intelligence and journalism. 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J Am Chem Soc. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1021/jacs.3c05819\u003c/span\u003e\u003cspan address=\"10.1021/jacs.3c05819\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"humanities-and-social-sciences-communications","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"palcomms","sideBox":"Learn more about [Humanities \u0026 Social Sciences Communications](http://www.nature.com/palcomms/)","snPcode":"41599","submissionUrl":"https://submission.springernature.com/new-submission/41599/3","title":"Humanities and Social Sciences Communications","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Nature AJ","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Q-matrix, ChatGPT-4o, Generative Artificial Intelligence, Cognitive Diagnostic Model","lastPublishedDoi":"10.21203/rs.3.rs-6235063/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6235063/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis study evaluates the performance of ChatGPT-4o in constructing Q-matrices for cognitive diagnostic assessments by comparing its outputs with those constructed by researchers and human experts. The research examines the overlap rates among these Q-matrices and assesses their validity using empirical methods. Two distinct mathematics datasets were used, and the Q-matrices were validated through statistical techniques to determine their model-data fit. The results indicate that ChatGPT-4o can generate Q-matrices with a high degree of overlap rate to those specified by human experts, demonstrating its potential as a tool for cognitive diagnostic assessments. The study highlights that AI-generated Q-matrices can be a valuable supplement to traditional methods, but expert validation remains essential to ensure theoretical accuracy and practical applicability. The findings suggest that a hybrid approach\u0026mdash;integrating AI-based Q-matrix construction with expert refinement\u0026mdash;can enhance the accuracy and efficiency of cognitive diagnostic assessments.\u003c/p\u003e","manuscriptTitle":"Evaluating ChatGPT-4o’s Performance in Construction of Q-Matrix for a Cognitive Diagnostic Assessment","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-04-24 15:12:08","doi":"10.21203/rs.3.rs-6235063/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2025-11-12T14:41:37+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-07-02T07:45:52+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"170425452366755636108023898859862364269","date":"2025-04-05T07:12:23+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-04-03T05:34:05+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2025-03-27T16:42:34+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-03-27T16:23:53+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-03-25T11:34:19+00:00","index":"","fulltext":""},{"type":"submitted","content":"Humanities and Social Sciences Communications","date":"2025-03-15T23:45:28+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"humanities-and-social-sciences-communications","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"palcomms","sideBox":"Learn more about [Humanities \u0026 Social Sciences Communications](http://www.nature.com/palcomms/)","snPcode":"41599","submissionUrl":"https://submission.springernature.com/new-submission/41599/3","title":"Humanities and Social Sciences Communications","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Nature AJ","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"32efb882-2a4d-4bbe-91fc-4b09c5da51f5","owner":[],"postedDate":"April 24th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[{"id":46828091,"name":"Social science/Education"},{"id":46828092,"name":"Social science/Psychology"}],"tags":[],"updatedAt":"2026-01-22T20:38:11+00:00","versionOfRecord":[],"versionCreatedAt":"2025-04-24 15:12:08","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-6235063","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6235063","identity":"rs-6235063","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}