Heterogeneous Mental Health Trajectories in College Students: A Three-Year Longitudinal Study Using Latent Class Growth Modeling

Heterogeneous Mental Health Trajectories in College Students: A Three-Year Longitudinal Study Using Latent Class Growth Modeling | 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 Research Article Heterogeneous Mental Health Trajectories in College Students: A Three-Year Longitudinal Study Using Latent Class Growth Modeling Yajuan Li, Gang Xiao, Huanbin Xue This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8657826/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 30 Apr, 2026 Read the published version in BMC Psychology → Version 1 posted 15 You are reading this latest preprint version Abstract Background College students face significant mental health challenges during their academic journey, yet the heterogeneity in their psychological adaptation patterns remains poorly understood. Traditional variable-centered approaches fail to capture the diverse trajectories that students may follow. Recent studies indicate that 20–30% of Chinese college students experience clinically significant psychological distress, highlighting the need for person-centered analytical approaches. Methods This longitudinal study employed formal Latent Class Growth Modeling (LCGM) using the Expectation-Maximization algorithm implemented in Python to identify distinct mental health trajectories among 2,562 Chinese college students assessed at enrollment (T1), sophomore year (T2, 18 months), and junior year (T3, 30 months). The Symptom Checklist-90 (SCL-90) Global Severity Index served as the primary outcome. Model selection was based on a composite score integrating BIC, entropy, bootstrap stability, and clinical relevance. Results A four-class solution demonstrated optimal fit (composite score = 0.919, entropy = 0.779, bootstrap stability = 0.940). Four trajectories emerged: Low-Optimal (13.2%; M T1 = 1.04), Low-Stable (29.8%; M T1 =1.19), Moderate-Improving (32.9%; M T1 =1.47), and High-Risk-Improving (24.0%; M T1 =1.98). Between-class differences were substantial (η² = 0.62). The high-risk class showed the steepest decline (slope = − 0.0100/month)but 31.8% remained above clinical threshold at T3.Growth parameters revealed substantial within-class heterogeneity in the high-risk group (σ² = 0.314). Conclusions Approximately one quarter of college students follow a high-risk mental health trajectory requiring targeted intervention.The formal LCGM approach with simultaneous parameter estimation provides robust classification with excellent stability. These findings support implementing tiered early warning systems based on baseline screening. mental health trajectories college students latent class growth modeling SCL-90 longitudinal study early warning system EM algorithm Figures Figure 1 Figure 2 1. Background The transition to higher education represents a critical developmental period characterized by significant psychological challenges.College students face multiple stressors including academic pressure,social adjustment,identity formation, and career uncertainty (Arnett,2015).Research consistently demonstrates elevated rates of mental health problems in this population. According to the World Mental Health Report released by the World Health Organization (WHO), 35% of full-time college students screened positive for at least one common lifetime disorder (Auerbach et al., 2018 ). Recent studies have documented substantial prevalence of psychological distress among Chinese college students, with depression, anxiety, and stress being the most commonly reported problems (Chen, 2024 ; Xin et al., 2024 ). The mental health challenges faced by college students have become a growing concern for educational institutions and public health systems worldwide (Pedrelli et al., 2014 ; Wasil et al., 2022 ). Traditional approaches to studying college mental health have predominantly employed variable-centered methods, examining mean-level changes or correlations between risk factors and outcomes across entire samples. While informative, such approaches assume population homogeneity and may obscure meaningful subgroup differences in developmental trajectories (Nagin & Odgers, 2010 ). A growing body of evidence suggests that students follow heterogeneous pathways through their college years, with some showing resilience, others demonstrating recovery, and a subset experiencing persistent or worsening symptoms (Ma et al., 2025 ; Liu et al., 2024 ). Understanding these diverse patterns is essential for developing targeted intervention strategies that address the specific needs of different student subgroups. Person-centered analytical approaches, particularly Growth Mixture Modeling (GMM) and Latent Class Growth Modeling (LCGM), offer powerful tools for identifying unobserved subpopulations following distinct developmental trajectories (Muthén, 2004 ; Ram & Grimm, 2009 ). These methods can reveal clinically meaningful heterogeneity that would otherwise be masked by aggregate statistics. Recent applications of these approaches in college mental health research have successfully identified three to five distinct trajectory classes (Liu et al., 2023 ; Wang & Fang, 2024 ). For example, Liu and colleagues ( 2023 ) employed piecewise growth mixture modeling to analyze depression, anxiety, and stress trajectories among Chinese college students, identifying four distinct classes with the majority falling into a "low and stable" pattern. Wang and Fang ( 2024 ) used latent growth modeling to examine the developmental trajectory of psychological flexibility among college students, while Zhang et al. ( 2023 ) demonstrated that mental health literacy mediates the relationship between psychological resilience and distress in medical college students. However, methodological challenges persist in trajectory modeling research. Concerns about model identification, classification accuracy, and the stability of extracted classes across different samples and specifications have been raised (Bauer & Curran, 2003 ; Infurna & Luthar, 2018 ). Bootstrap validation has emerged as a valuable approach for assessing classification stability, with recent methodological work demonstrating that bootstrap-based methods can effectively quantify uncertainty in the number of identified groups (Diop et al., 2024 ; Dean & Reiter, 2019). Furthermore, most existing studies have relied on two-step GMM approaches that first estimate individual growth parameters and then cluster individuals, potentially underestimating standard errors and misclassifying borderline cases (Ram & Grimm, 2009 ; Kwon et al., 2021 ). The present study addresses these limitations by employing formal Latent Class Growth Modeling with simultaneous parameter estimation via the Expectation-Maximization (EM) algorithm.This approach properly propagates classification uncertainty to parameter estimates and provides correct standard errors. We examine three-year mental health trajectories in a large sample of Chinese college students, with particular attention to: (1) identifying the optimal number and nature of trajectory classes, (2) characterizing a high-risk subgroup requiring intervention, (3) evaluating classification stability through bootstrap validation, and (4) deriving practical implications for campus mental health services. 2. Methods 2.1 Participants and Procedure Participants were drawn from the 2022 entering cohort at a comprehensive university in southern China. Mental health screening was conducted at three time points: enrollment in Fall 2022 (T1), Spring 2024 (T2; approximately 18 months post-enrollment), and Spring 2025 (T3; approximately 30 months post-enrollment). All enrolled students were invited to complete the assessment during designated class periods. Of the 4,501 students who completed the T1 assessment, 3,418 (75.9%) completed T2 and 3,053 (67.8%) completed T3. The analytic sample comprised 2,562 students (56.9% of baseline) with valid data at all three time points. Attrition analysis comparing completers versus non-completers revealed no significant differences in baseline SCL-90 Global Severity Index scores (t = 1.23, p = .219), though completers were more likely to be female (74.6% vs. 71.2%, χ² = 5.89, p = .015). The final sample (N = 2,562) had a mean age of 18.5 years (SD = 0.8) at enrollment. The majority were female (n = 1,910, 74.6%), of Han ethnicity (94.2%), and from urban backgrounds (62.8%). 2.2 Measures Symptom Checklist-90 (SCL-90). The SCL-90 is a 90-item self-report inventory assessing psychological symptom patterns (Derogatis, 1994). Participants rate each symptom on a 5-point Likert scale from 1 (not at all) to 5 (extremely). The Global Severity Index (GSI), calculated as the mean of all 90 items, served as the primary outcome measure. The Chinese version has demonstrated good psychometric properties in college samples (Zhang et al., 2024 ). In the present study, internal consistency was excellent at all time points (Cronbach's α = .97, .98, .97 for T1, T2, T3, respectively). A GSI score of 2.0 or above was used as the clinical threshold for elevated symptomatology at the individual level, consistent with updated Chinese normative data (Dang et al., 2020 ). Demographic variables. Gender, age, ethnicity, and hometown (urban/rural) were collected at baseline. 2.3 Analytic Strategy Latent Class Growth Modeling. We employed formal LCGM using the Expectation-Maximization(EM) algorithm to simultaneously estimate:(a) class-specific growth parameters (intercept η 0k and slope η 1k ), (b) within-class residual variances (σ² k ), and (c) individual posterior class membership probabilities.This approach differs from two-step GMM methods by properly propagating classification uncertainty to parameter estimates (Muthén, 2004 ; Ram & Grimm, 2009 ). The model specification followed a linear growth framework: Y it = η 0k + η 1k × t + ε it , where ε it ~ N(0, σ² k ) where Y it represents the observed GSI score for individual i at time t, η 0k is the class-specific intercept, η 1k is the class-specific slope, and σ² k is the class-specific residual variance. Time was coded in months from baseline (0, 18, 30). Unlike standard LCGM that constrains residual variances to be equal across classes, we allowed class-specific residual variances to capture potential heteroscedasticity, which proved particularly important for the high-risk class. Rationale for LCGM over GMM. We chose LCGM (which fixes within-class intercept and slope variances to zero) rather than the more flexible Growth Mixture Model (GMM, which allows random effects within classes) for several reasons. First, with only three measurement occasions, estimating both between-class and within-class random effects would likely result in model identification problems and unstable parameter estimates (Infurna & Grimm, 2018 ). Second, our primary interest was in identifying discrete trajectory classes rather than characterizing continuous individual differences within classes. Third, the class-specific residual variances (σ² k ) in our model specification capture substantial within-class heterogeneity, providing an intermediate approach between standard LCGM with equal variances and full GMM with random slopes. As will be shown, the high-risk class exhibited markedly higher residual variance (σ²=0.314) compared to other classes (0.001–0.061), suggesting important within-class variability that would need to be interpreted cautiously. Multiple random initializations (n = 10) were employed to avoid local optima, with convergence defined as change in log-likelihood less than 10 − 5 . Models with 2 to 6 classes were estimated and compared. Software and Implementation. All analyses were conducted using a custom Python implementation (Python 3.12) of the EM algorithm utilizing NumPy 1.26 and SciPy 1.11 libraries. The implementation incorporates numerical stability techniques including log-sum-exp transformations for posterior probability calculations. Visualization was performed with Matplotlib 3.8 and Seaborn 0.13. The complete analysis code is provided in Supplementary Materials S1 and is available upon request from the corresponding author. Model Selection. Optimal class enumeration was determined using a composite score integrating multiple criteria with the following weights: BIC (0.25), entropy (0.20), bootstrap stability (0.20), minimum class size (0.10), parsimony (0.10), and clinical relevance (0.15). Clinical relevance was operationalized as identification of a high-risk class with baseline mean GSI approaching the clinical threshold (≥ 1.90), ensuring identification of the most vulnerable subgroup. This threshold is slightly below the individual-level clinical cutoff of 2.0 to account for within-class variability and ensure that students near the clinical threshold are captured in the high-risk group. We acknowledge that these weights represent informed judgments based on the literature and clinical priorities rather than empirically derived optima. Models with 4–5 classes were prioritized based on theoretical considerations and prior literature (Nagin & Odgers, 2010 ; Liu et al., 2023 ). Bootstrap Validation. Classification stability was assessed via bootstrap resampling (n = 50 samples). While this number is lower than the 500-1,000 samples typically recommended for precise confidence interval estimation (Diop et al., 2024 ; Dean & Reiter, 2019), it was chosen as a balance between computational constraints and obtaining a reasonable estimate of classification stability. For each bootstrap sample, the LCGM was re-estimated with 3 random starts and class labels were matched to the reference solution using the Hungarian algorithm (Kuhn, 1955 ). Individual-level stability was calculated as the proportion of bootstrap samples in which each participant was assigned to their modal class. The Adjusted Rand Index (ARI) quantified overall agreement between bootstrap and reference classifications. Classification Quality. Classification accuracy was evaluated using entropy (target ≥ 0.80) and average posterior probability (AvePP; target ≥ 0.70 for each class). These indices follow recommendations from Celeux and Soromenho ( 1996 ) and Clark and Muthén ( 2009 ). We also examined the distribution of maximum posterior probabilities to identify "borderline cases" (participants with maximum posterior probability < 0.70) who may have uncertain class membership. 3. Results 3.1 Descriptive Statistics Table 1 presents descriptive statistics for SCL-90 GSI scores across the three assessment points. Mean symptom levels showed a declining trend from T1 (M = 1.47, SD = 0.47) to T3 (M = 1.30, SD = 0.40). This overall improvement represented a small-to-medium effect size. Using the average of standard deviations as the denominator (Cohen's d = mean difference / average SD = 0.17 / 0.435 = 0.39), the magnitude of change was comparable to that observed in other longitudinal studies of college mental health (Liu et al., 2024 ). The proportion of students exceeding the clinical threshold (GSI ≥ 2.0) decreased from 14.9% at baseline to 7.7% at T3, indicating that the rate of clinically significant distress was approximately halved over the three-year period. Table 1 Descriptive Statistics for SCL-90 Global Severity Index Across Time Points Time Point N Mean SD 95% CI Range % Clinical (≥ 2.0) T1 (Enrollment) 2,562 1.47 0.47 [1.46, 1.49] 1.00–3.80 14.9% T2 (18 months) 2,562 1.35 0.43 [1.34, 1.37] 1.00–4.50 8.4% T3 (30 months) 2,562 1.30 0.40 [1.29, 1.32] 1.00–4.42 7.7% Note. Clinical threshold (GSI ≥ 2.0) based on updated Chinese normative data (Dang et al., 2020 ). CI = confidence interval. 3.2 Model Comparison and Selection Table 2 presents fit indices for LCGM solutions ranging from 2 to 6 classes. The four-class solution emerged as optimal based on the composite score (0.919), demonstrating acceptable entropy (0.779), excellent bootstrap stability (0.940), and successful identification of a high-risk subgroup. Table 2 Fit Indices for Latent Class Growth Models (2–6 Classes) Classes BIC Log-Likelihood Entropy Min. Class % Min. AvePP Stability ARI High-Risk Composite 2 3320.4 −1632.7 0.859 49.0% 0.958 0.985 0.941 No 0.554 3 1918.3 −916.0 0.823 25.1% 0.905 0.975 0.927 No 0.735 4 1353.4 −617.8 0.779 13.2% 0.844 0.940 0.840 Yes 0.919 5 1173.3 −512.1 0.721 8.6% 0.792 0.839 0.633 Yes 0.894 6 1137.0 −478.3 0.712 6.7% 0.674 0.926 0.803 Yes 0.865 Note. BIC = Bayesian Information Criterion; AvePP = average posterior probability; ARI = Adjusted Rand Index; Stability = bootstrap classification stability. The selected four-class solution is highlighted. High-Risk = identification of class with baseline mean approaching clinical threshold (≥ 1.90). This threshold is used for model selection purposes and differs from the individual-level clinical cutoff of GSI ≥ 2.0. The four-class solution was preferred over the five-class model despite the latter's lower BIC for several reasons: (1) substantially higher bootstrap stability (0.940 vs. 0.839), (2) higher ARI (0.840 vs. 0.633), (3) entropy above the acceptable threshold of 0.70, and (4) adequate minimum class size (13.2% vs. 8.6%). Notably, the five-class model showed a marked decline in both stability and ARI, suggesting that the additional class may represent an artifact of sample-specific variation rather than a reliable subpopulation. This non-monotonic pattern—where the 6-class model recovered somewhat in stability (0.926) but with further reduced entropy and minimum class size—underscores the importance of evaluating multiple fit indices rather than relying on any single criterion. Sensitivity Analysis for Model Selection. To evaluate the robustness of the four-class solution to alternative weight specifications in the composite score, we conducted sensitivity analyses varying each weight by ± 50%. The four-class solution remained optimal under all tested weight combinations, with composite scores ranging from 0.88 to 0.94. The selection was particularly robust to changes in the parsimony and clinical relevance weights, but more sensitive to entropy weighting. When entropy weight was increased to 0.30, the three-class solution became marginally competitive (composite = 0.91 vs. 0.92 for four-class), though the four-class solution still identified the high-risk subgroup that was absent in the three-class model. These results support the robustness of our model selection decision. 3.3 Trajectory Class Characteristics Figure 1 displays the four identified trajectory classes, and Table 3 presents their characteristics. The classes were labeled based on their baseline levels and developmental patterns. Figure 1 . Shows four trajectory lines from T1 to T3, with horizontal reference lines at GSI = 2.0 (clinical threshold) and GSI = 1.5 (moderate-risk threshold). The High-Risk-Improving trajectory (purple) starts near 2.0 and shows the steepest decline. Low-Optimal (red) remains near 1.0 throughout. Mental health trajectories across three years of college (N = 2,562). The four-class LCGM solution shows distinct patterns: Low-Optimal (red, 13.2%), Low-Stable (gray, 29.8%), Moderate-Improving (brown, 32.9%), and High-Risk-Improving (purple, 24.0%). Dashed lines indicate clinical threshold at GSI = 2.0 and moderate-risk threshold at GSI = 1.5. Table 3 Characteristics of the Four Trajectory Classes Trajectory Class N (%) T1 Mean T2 Mean T3 Mean Change Slope/Month T1 Clinical % T3 Clinical % Stability Low-Optimal 338 (13.2%) 1.04 1.03 1.01 −0.03 −0.0010 0.0% 0.0% 0.993 Low-Stable 764 (29.8%) 1.19 1.13 1.09 −0.10 −0.0035 0.0% 0.0% 0.959 Moderate-Improving 844 (32.9%) 1.47 1.36 1.28 −0.19 −0.0063 3.7% 0.0% 0.928 High-Risk-Improving 616 (24.0%) 1.98 1.80 1.68 −0.30 −0.0100 56.8% 31.8% 0.904 Note. Change = T3 minus T1. Slope expressed as GSI change per month. Clinical threshold defined as GSI ≥ 2.0. The High-Risk-Improving class (highlighted) represents the high-risk subgroup. Stability = bootstrap classification stability for each class. Class sizes (N) are based on maximum posterior probability assignment; EM-estimated mixing proportions are reported in Table 4 . Gender distribution did not differ significantly across the four trajectory classes (χ² = 4.87, df = 3, p = .182), with female students comprising 73.4% to 76.1% of each class. Class 1: Low-Optimal (n = 338, 13.2%). This class exhibited the lowest symptom levels across all time points, with scores near the minimum possible (M T1 = 1.04). The trajectory was essentially flat (slope = − 0.0010/month), indicating stable optimal mental health. Classification stability was highest in this class (0.993). Class 2: Low-Stable (n = 764, 29.8%). Students in this class showed low-to-normal symptom levels with a slight declining trend (M T1 = 1.19 to M T3 = 1.09). No students in this class exceeded the clinical threshold at any time point. Stability was excellent (0.959). Class 3: Moderate-Improving (n = 844, 32.9%). The largest class demonstrated moderate baseline symptoms (M T1 = 1.47) with consistent improvement over time (slope = − 0.0063/month). While 3.7% exceeded the clinical threshold at T1, none remained above threshold by T3. This pattern suggests successful adaptation to college life. Class 4: High-Risk-Improving (n = 616, 24.0%). This high-risk class exhibited the highest baseline symptoms (M T1 = 1.98, near the clinical threshold) and, notably, the steepest improvement trajectory (slope = − 0.0100/month). Over half (56.8%) exceeded the clinical threshold at enrollment. Despite substantial improvement (total change = − 0.30), 31.8% (approximately 196 students) remained above the clinical threshold at T3. This class showed the highest within-class heterogeneity, as detailed below. Effect Sizes. The magnitude of change within the high-risk class represented a medium effect. The residual variance in our heteroscedastic LCGM represents the within-class variability around the class-specific trajectory; thus √σ² provides an estimate of the within-class standard deviation. Using this approach (SD = √0.314 = 0.56), Cohen's d = 0.30 / 0.56 = 0.54. Between-class differences at baseline were substantial: a one-way ANOVA on T1 GSI scores across the four classes yielded η² = 0.62, indicating that trajectory class membership explained 62% of variance in baseline symptoms. This large effect size supports the clinical meaningfulness of the identified trajectory classes and is consistent with the group heterogeneity observed in other studies of college student mental health (Ma et al., 2025 ). 3.4 Growth Parameter Estimates Table 4 presents the formal growth parameter estimates from the EM algorithm, including class-specific intercepts, slopes, residual variances, and mixing proportions. Table 4 Growth Parameter Estimates for the Four-Class LCGM Solution Parameter Low-Optimal Low-Stable Moderate-Improving High-Risk-Improving Intercept (η 0 ) 1.043 1.194 1.471 1.983 Slope (η 1 ) −0.0010 −0.0035 −0.0063 −0.0100 Residual Variance (σ²) 0.001 0.011 0.061 0.314 Class Proportion (π) 0.126 0.289 0.328 0.257 Note. Slopes represent GSI change per month. All parameters estimated simultaneously via EM algorithm with 10 random starts. Residual variances are class-specific (heteroscedastic model). Class proportions (π) represent EM-estimated mixing probabilities based on the probabilistic (soft) classification, which may differ slightly from the hard classification percentages in Table 3 (e.g., 25.7% vs. 24.0% for the high-risk class) due to the accumulation of classification uncertainty across participants with posterior probabilities between 0.5 and 1.0. A striking finding was the large residual variance in the High-Risk-Improving class (σ² = 0.314), which was 5 to 314 times larger than in the other classes. This substantial within-class heterogeneity warrants careful interpretation. In our LCGM framework where within-class intercept and slope variances are fixed to zero, the residual variance captures all within-class variability around the class-specific growth curve. The exceptionally high residual variance in the high-risk class suggests that this group may contain distinct subpopulations with different underlying mechanisms or response patterns—some showing rapid recovery, others showing modest improvement, and a subset showing persistent difficulties. This finding points to the need for future research with additional measurement occasions or GMM approaches that can formally model within-class random effects. In contrast, the Low-Optimal class showed minimal residual variance (σ²= 0.001), indicating a highly homogeneous group. 3.5 Classification Quality Figure 2 displays the distributions of classification probabilities and bootstrap stability scores. The majority of participants (approximately 75%) had maximum posterior probabilities exceeding 0.70, indicating confident classification. Bootstrap stability scores were concentrated near 1.0, with over 92% of participants showing stability above 0.80. Approximately 10–15% of participants had maximum posterior probabilities below 0.70, representing "borderline cases" with uncertain class membership. These individuals were primarily located at the boundaries between adjacent classes (e.g., between Low-Stable and Moderate-Improving, or between Moderate-Improving and High-Risk-Improving). The entropy value of 0.779, while slightly below the ideal threshold of 0.80, indicates acceptable overall classification precision given the continuous nature of the underlying construct. Figure 2 . Distributions of classification quality indices. Left: Maximum posterior probability for each participant's most likely class assignment. Right: Bootstrap classification stability (proportion of 50 bootstrap samples with consistent assignment). Vertical dashed lines indicate threshold values (red = 0.70 for posterior probability; red = 0.50 and green = 0.70 for stability). 4. Discussion This study employed formal Latent Class Growth Modeling to identify distinct mental health trajectories among Chinese college students over three years. Four trajectory classes emerged, representing qualitatively different patterns of psychological adaptation to college life. Approximately one quarter of students (24.0%) followed a high-risk trajectory characterized by elevated baseline distress and, despite showing the most rapid improvement, a substantial proportion (31.8%) remained above clinical threshold at the end of the study period. 4.1 Trajectory Heterogeneity The identification of four distinct trajectories confirms that college students are not a homogeneous population with respect to mental health development. This finding aligns with recent research using person-centered approaches in college populations. For example, Liu and colleagues ( 2023 ) identified four classes of depression trajectories among Chinese college students using piecewise growth mixture modeling, with a "low and stable" class comprising approximately 79% of the sample. Wang and Fang ( 2024 ) demonstrated that college students' psychological flexibility follows distinct developmental patterns, while Zhang et al. ( 2023 ) showed that mental health literacy plays a mediating role in the relationship between psychological resilience and distress among medical college students. The largest group in our study (Moderate-Improving, 32.9%) showed the pattern often assumed in traditional analyses: moderate initial symptoms that gradually improve as students adapt to college. However, this pattern characterized only one-third of the sample. The Low-Optimal (13.2%) and Low-Stable (29.8%) groups, comprising 43% of the sample, exhibited consistently low symptom levels throughout college. These students likely possess robust psychological resources or face fewer stressors, and may not require targeted mental health services. Importantly, combining these two groups in a simpler three-class solution would have masked meaningful differences in their baseline levels and trajectories. Most clinically significant is the High-Risk-Improving class (24.0%), which began college with symptoms near the clinical threshold (M = 1.98). These students showed the steepest improvement slope (− 0.0100/month), suggesting that many benefited from natural adaptation processes or existing support systems. However, the finding that 31.8% remained above clinical threshold at T3 indicates that a substantial subset requires more intensive intervention than they are currently receiving. This prevalence is consistent with recent findings documenting the heterogeneity in college student mental health (Ma et al., 2025 ; Seehuus et al., 2019 ). 4.2 The High-Risk Subgroup and Within-Class Heterogeneity The 24.0% prevalence of the high-risk trajectory is higher than some previous estimates but consistent with recent meta-analytic findings (Auerbach et al., 2018 ). The exceptionally large residual variance in this class (σ² = 0.314) warrants particular attention and has important methodological and clinical implications. From a methodological perspective, while our a priori rationale for LCGM over GMM was sound given the measurement design (three time points insufficient for random effects estimation), the unexpectedly large residual variance in the high-risk class (σ² = 0.314 vs. 0.001–0.061 in other classes) suggests that this group may have benefited from a more flexible model specification had additional measurement occasions been available. This heterogeneity raises questions about whether a Growth Mixture Model allowing within-class random effects might better characterize this subgroup. However, with only three measurement occasions, estimating such models would likely result in identification problems. The high residual variance in our LCGM can be interpreted as capturing the combined effect of: (a) true individual differences in trajectories within the class, (b) measurement error, and (c) potential model misspecification. Future research with more intensive longitudinal designs (e.g., 5 + waves) could employ GMM to formally distinguish these sources of variance. From a clinical perspective, this heterogeneity suggests that "high-risk" students are not a uniform group but may include: (a) students with transient stress reactions who recover fully, (b) students with moderate chronic symptoms that improve partially, and (c) students with persistent severe symptoms requiring clinical intervention. The 31.8% remaining above threshold at T3 likely represents this latter subgroup. Future research using more intensive longitudinal designs or qualitative methods could illuminate these subpopulations and identify differential predictors of recovery versus persistence (Selvaraj & Bhat, 2018 ; Nogueira & Sequeira, 2024 ). 4.3 Methodological Contributions This study makes several methodological contributions to the trajectory modeling literature. First, the use of formal LCGM with simultaneous EM estimation addresses concerns raised about two-step GMM approaches (Ram & Grimm, 2009 ; Kwon et al., 2021 ). By estimating growth parameters and class membership probabilities jointly, our approach properly propagates classification uncertainty and provides appropriate standard errors. Second, the comprehensive model selection strategy integrating multiple criteria (BIC, entropy, stability, clinical relevance) moves beyond reliance on any single fit index. While we acknowledge that the specific weights used (e.g., clinical relevance = 0.15) reflect our priorities and could be adjusted by other researchers, making these weights explicit improves transparency and replicability. Notably, we did not have access to the Lo-Mendell-Rubin likelihood ratio test (LMR-LRT) or Bootstrap Likelihood Ratio Test (BLRT) in our Python implementation, which are commonly used in Mplus-based analyses. Future implementations could incorporate these tests for more comprehensive model comparison (Kwon et al., 2021 ; Nylund et al., 2007 ). Third, bootstrap validation with Hungarian algorithm label matching provides a rigorous test of classification stability. Although our use of 50 bootstrap samples is lower than methodological recommendations of 500-1,000 samples (Diop et al., 2024 ), the excellent stability observed (0.940) and the strongly right-skewed distribution of individual stability scores (with > 92% above 0.80) give confidence that the identified classes are reproducible. Future studies with greater computational resources could employ larger bootstrap samples to obtain more precise stability estimates and confidence intervals. Fourth, our finding that the 5-class model showed anomalous declines in both stability (0.839) and ARI (0.633) while the 6-class model partially recovered (stability = 0.926) highlights the complexity of model selection in mixture modeling. This non-monotonic pattern underscores the importance of evaluating classification stability alongside traditional fit indices, as overfitting can manifest in unstable solutions that fail to replicate across bootstrap samples. 4.4 Clinical and Practical Implications These findings support the implementation of tiered early warning systems in college mental health services (Gao, 2022 ; Kalkbrenner et al., 2021 ). Based on the observed trajectory class boundaries—with the high-risk class averaging GSI = 1.98 at baseline and the moderate-improving class averaging 1.47—we propose a three-tier framework with thresholds that require independent validation before clinical implementation: Proposed Three-Tier Early Warning System Tier 1 (High Priority) Students with baseline GSI ≥ 2.0 (~ 24% of entering students) → Proactive outreach within first month; individual counseling assessment; peer support programs Tier 2 (Moderate Priority) Students with baseline GSI 1.4–2.0 (~ 33% of students) → Invitation to stress management workshops; periodic check-ins; psychoeducational materials Tier 3 (Universal) Students with baseline GSI < 1.4 (~ 43% of students) → Standard orientation programming; awareness campaigns; available but not mandated services We note that the proposed thresholds (1.4 and 2.0) are derived from the observed distribution of trajectory class means. Formal ROC curve analysis with follow-up outcomes (e.g., service utilization, academic difficulties, clinical diagnoses) would provide empirical support for optimal cutpoints. Researchers and practitioners should validate these thresholds in their own populations before implementation (Du, 2025 ; Xu, 2024 ). Critically, the finding that nearly one-third of high-risk students remain above clinical threshold after three years suggests that current university mental health resources may be insufficient for this population. Enhanced services might include increased counseling capacity, evidence-based group interventions targeting specific symptoms (e.g., anxiety, interpersonal sensitivity), and systematic follow-up protocols for students identified as high-risk at enrollment (Chen et al., 2020 ; Wasil et al., 2022 ). 4.5 Limitations and Future Directions Several limitations should be noted. First, the sample was drawn from a single Chinese university, limiting generalizability to other cultural contexts or institutional types. Cross-cultural replication is needed to determine whether similar trajectory patterns emerge in Western or more diverse samples. Recent research has documented both similarities and differences in college mental health patterns across cultural contexts (Auerbach et al., 2018 ; Wei, 2024 ; Cheng et al., 2016 ). Second, reliance on self-report measures introduces potential biases including social desirability and recall effects. Future studies might incorporate clinical interviews, informant reports, or physiological markers to provide multi-method validation (Zhang, 2021 ; Han, 2023 ). Third, with only three measurement occasions, we could only model linear trajectories. Important non-linear patterns—such as initial deterioration followed by recovery, or early improvement followed by plateau—cannot be captured with this design. Future studies should incorporate more frequent assessments, particularly during the critical first semester of college (Liu et al., 2023 ). Fourth, the entropy value (0.779) fell slightly below the ideal threshold of 0.80, indicating some classification uncertainty, particularly for participants at the boundaries between adjacent classes. However, the excellent bootstrap stability (0.940) and ARI (0.840) suggest that this limitation does not substantially compromise the validity of the identified classes. Researchers interpreting individual-level classifications should consider posterior probabilities rather than treating class assignments as deterministic. Fifth, this study focused on describing trajectories without examining predictors or outcomes. Future research should identify risk and protective factors that differentiate trajectory classes (e.g., family support, coping styles, prior mental health history) and examine downstream consequences such as academic performance, social functioning, and mental health service utilization (Dong et al., 2024 ; Xin et al., 2024 ). The large within-class heterogeneity observed in the high-risk class suggests that identifying predictors of recovery versus persistence within this group would be particularly valuable for intervention targeting. Sixth, given the predominantly female sample (74.6%), future research should specifically investigate potential gender differences in mental health trajectories. Although gender distribution did not differ significantly across trajectory classes in our sample, prior research has documented gender effects on mental health symptoms and help-seeking behaviors among college students (Seehuus et al., 2019 ; Kalkbrenner et al., 2021 ). 4.6 Conclusions Using formal Latent Class Growth Modeling with simultaneous parameter estimation implemented in Python, this study identified four distinct mental health trajectories among Chinese college students. Approximately one quarter followed a high-risk pattern characterized by elevated baseline symptoms and, despite significant improvement, persistent clinical concerns for a substantial subset. The excellent classification stability achieved through bootstrap validation supports the robustness of these findings, although the high within-class heterogeneity in the high-risk group suggests that this class may contain meaningful subpopulations warranting further investigation. Results highlight the importance of person-centered approaches for understanding mental health development and inform the design of tiered early intervention programs in college settings. Declarations Ethics approval and consent to participate: All procedures involving human participants were performed in accordance with the ethical standards of the Ethics Committee of Hanshan Normal University and with the 1964 Helsinki Declaration and its later amendments. This study was approved by the aforementioned committee (Approval No. 2026010804). Informed consent was obtained from all individual participants included in the study. Consent for publication: Not applicable. Competing interests: The authors declare no competing interests. Author’ Contributions Yajuan Li contributed to data collection and interpretation, supervised the project, and revised the manuscript. Gang Xiao conceptualized the study, developed the Python implementation, conducted analyses, and drafted the manuscript.Huanbin Xue conducted analyses, and drafted the manuscript. All authors approved the final version. Acknowledgments We thank the students who participated in this study and the university counseling center staff who facilitated data collection. Funding: This research was supported by the the National Natural Science Foundation(NSF) of China ( Grant12372009), supported by the NSF of Guangdong (Grant 2022A1515011971), Education Science Planning Project of Guangdong Province (Grant No.2023GXJK385), Hanshan Normal University Institutional Projects (Grant Nos.QD2024111 and E24035), the Collaborative Innovation Research Center for East Guangdong Educational Region at Hanshan Normal University, and the Natural Science Foundation of Hanshan Normal University (Grant No. PNB221103). Author Contribution Yajuan Li contributed to data collection and interpretation, supervised the project, and revised the manuscript. Gang Xiao conceptualized the study, developed the Python implementation, conducted analyses, and drafted the manuscript.Huanbin Xue conducted analyses, and drafted the manuscript. All authors approved the final version. Acknowledgement We thank the students who participated in this study and the university counseling center staff who facilitated data collection. Data Availability De-identified data are available from the corresponding author upon reasonable request, subject to institutional data sharing agreements. The Python analysis code is provided in Supplementary Materials S1 and will be deposited in a public repository upon publication. References Arnett JJ. Emerging adulthood: The winding road from the late teens through the twenties. 2nd ed. Oxford University Press; 2015. Auerbach RP, Mortier P, Bruffaerts R, Alonso J, Benjet C, Cuijpers P, Kessler RC, WHO World Mental Health Surveys International College Student Project. Prevalence and distribution of mental disorders. J Abnorm Psychol. 2018;127(7):623–38. 10.1037/abn0000362 . Bauer DJ, Curran PJ. Distributional assumptions of growth mixture models: Implications for overextraction of latent trajectory classes. Psychol Methods. 2003;8(3):338–63. 10.1037/1082-989X.8.3.338 . Celeux G, Soromenho G. An entropy criterion for assessing the number of clusters in a mixture model. J Classif. 1996;13(2):195–212. 10.1007/BF01246098 . Chen J. Study on factors influencing college students’ mental health. Int J Soc Sci Public Adm. 2024;3(2):482–8. 10.62051/ijsspa.v3n2.60 . Chen W, Zheng Q, Liang C, Xie Y, Gu D. Factors influencing college students’ mental health promotion: The mediating effect of online mental health information seeking. Int J Environ Res Public Health. 2020;17(13):4783. 10.3390/ijerph17134783 . Cheng AW, Chang J, O’Brien J, Budgazad MS, Tsai J. Model minority stereotype: Influence on perceived mental health needs of Asian Americans. J Immigr Minor Health. 2016;19(3):572–81. 10.1007/s10903-016-0440-0 . Clark SL, Muthén B. Relating latent class analysis results to variables not included in the analysis. Unpublished manuscript. 2009. Retrieved from https://www.statmodel.com/download/relatinglca.pdf Dang W, Xu Y, Ji J, Wang K, Zhao S, Yu B, Ma Y. Study of the SCL-90 scale and changes in the Chinese norms. Front Psychiatry. 2020;11:524395. 10.3389/fpsyt.2020.524395 . Dean N, Raftery AE. An evaluation of the bootstrap for model validation in mixture models. Comput Stat Data Anal. 2019;131:80–90. 10.1016/j.csda.2018.07.014 . Diop A, Sirois C, Guertin JR, Schnitzer ME, Brophy JM, Blais C, Talbot D. A bootstrap approach for evaluating uncertainty in the number of groups identified by latent class growth models. Int J Biostat. 2024;20(2):467–90. 10.1515/ijb-2023-0116 . Dong J, He Y, Jiang F, Liu Z, Ni Y, Tang Y, Luo J, Zhang Z, Huang Y. Teacher-student relationships and mental disorders of undergraduate and graduate students in online education: A moderated mediation model of mobile phone addiction and hometown setting. Comput Hum Behav Rep. 2024;14:100406. 10.1016/j.chbr.2024.100406 . Du X. Quantitative assessment of college students’ mental health based on AHP-TOPSIS algorithm. Lect Notes Educ Psychol Public Media. 2025;106(1):143–51. 10.54254/2753-7048/2025.cb25595 . Gao H. Research on the construction of college students’ mental health security system. J Healthc Eng. 2022;2022:1–5. 10.1155/2022/4001603 . Han H. Fuzzy clustering algorithm for university students’ psychological fitness and performance detection. Heliyon. 2023;9(8):e18550. 10.1016/j.heliyon.2023.e18550 . Infurna FJ, Grimm KJ. The use of growth mixture modeling for studying resilience to major life stressors in adulthood and old age: Lessons for class size and identification and model selection. J Gerontol B Psychol Sci Soc Sci. 2018;73(1):148–59. 10.1093/geronb/gbx019 . Infurna FJ, Luthar SS. Re-evaluating the notion that resilience is commonplace: A review and distillation of directions for future research, practice, and policy. Clin Psychol Rev. 2018;65:43–56. 10.1016/j.cpr.2018.07.003 . Kalkbrenner MT, Arroyos EC, Mims TD. Recognize and refer? Differences by gender, ethnicity, and help-seeking history. J Coll Couns. 2021;24(2):162–77. 10.1002/jocc.12183 . Kuhn HW. The Hungarian method for the assignment problem. Nav Res Logist Q. 1955;2(1–2):83–97. 10.1002/nav.3800020109 . Kwon JY, Sawatzky R, Baumbusch J, Lauck S, Ratner PA. Growth mixture models: A case example of the longitudinal analysis of patient-reported outcomes data captured by a clinical registry. BMC Med Res Methodol. 2021;21:79. 10.1186/s12874-021-01276-z . Liu X, Li Y, Gao W. Subjective well-being of college students: Developmental trajectories, predictors, and risk for depression. J Psychol Afr. 2024;34(5):477–86. 10.1080/14330237.2024.2398871 . Liu X, Zhang Y, Gao W, Cao X. Developmental trajectories of depression, anxiety, and stress among college students: A piecewise growth mixture model analysis. Humanit Soc Sci Commun. 2023;10:726. 10.1057/s41599-023-02252-2 . Ma C, Yang Q, Li X, Ji W, Qi S. Group heterogeneity in the relationship between physical health level and psychological depression in college students. Sci Rep. 2025;15(1). 10.1038/s41598-025-24978-6 . Muthén B. Latent variable analysis: Growth mixture modeling and related techniques for longitudinal data. In: Kaplan D, editor. The SAGE handbook of quantitative methodology for the social sciences. Sage; 2004. pp. 345–68. Nagin DS, Odgers CL. Group-based trajectory modeling in clinical research. Annu RevClinPsychol. 2010;6:109–38. 10.1146/annurev.clinpsy.121208.131413 . Nogueira MJC, Sequeira CA. Positive and negative correlates of psychological well-being and distress in college students’ mental health: A correlational study. Healthcare. 2024;12(11):1085. 10.3390/healthcare12111085 . Nylund KL, Asparouhov T, Muthén BO. Deciding on the number of classes in latent class analysis and growth mixture modeling: A Monte Carlo simulation study. Struct Equ Model. 2007;14(4):535–69. 10.1080/10705510701575396 . Pedrelli P, Nyer M, Yeung A, Zulauf C, Wilens T. College students: Mental health problems and treatment considerations. Acad Psychiatry. 2014;39(5):503–11. 10.1007/s40596-014-0205-9 . Ram N, Grimm KJ. Growth mixture modeling: A method for identifying differences in longitudinal change among unobserved groups. Int J Behav Dev. 2009;33(6):565–76. 10.1177/0165025409343765 . Seehuus M, Moeller RW, Peisch V. Gender effects on mental health symptoms and treatment in college students. J Am Coll Health. 2019;69(1):95–102. 10.1080/07448481.2019.1656217 . Selvaraj PR, Bhat CS. Predicting the mental health of college students with psychological capital. J Ment Health. 2018;27(3):279–87. 10.1080/09638237.2018.1469738 . Wang J, Fang S. The developmental trajectory of college students’ psychological flexibility: Based on latent growth model. J Contextual Behav Sci. 2024;32:100765. 10.1016/j.jcbs.2024.100765 . Wasil AR, Malhotra T, Nandakumar N, Tuteja N, DeRubeis RJ, Stewart RE, Bhatia A. Improving mental health on college campuses: Perspectives of Indian college students. Behav Ther. 2022;53(2):348–64. 10.1016/j.beth.2021.09.004 . Wei J. College students’ mental health among different racial/ethnic groups. Trans Soc Sci Educ Humanit Res. 2024;13:1–14. 10.62051/2cym9q57 . Wyllie AH, Kerr JFR, Currie AR. Cell death: the significance of apoptosis. In: Bourne GH, Danielli JF, Jeon KW, editors. International review of cytology. London: Academic; 1980. pp. 251–306. Xin M, Yang C, Zhang L, Gao C, Wang S. The impact of perceived life stress and online social support on university students’ mental health during the post-COVID era in Northwestern China: Gender-specific analysis. BMC Public Health. 2024;24(1). 10.1186/s12889-024-17935-x . Xu X. Using big data to analyze the mental health status of college students. J Comput Methods Sci Eng. 2024;24(6):3632–45. 10.1177/14727978241296987 . Zhang H, Liu Y, Gu R. Undergraduate students’ norms for the Chinese version of the Symptom Check-List-90-R (SCL-90-R). World J Psychiatry. 2024;14(8):1224–32. 10.5498/wjp.v14.i8.1224 . Zhang J. A study on mental health assessments of college students based on triangular fuzzy function and entropy weight method. Math Probl Eng. 2021;2021:1–8. 10.1155/2021/6659990 . Zhang JY, Ji XZ, Zhou YQ. The mediating effect of mental health literacy on psychological resilience and psychological distress of medical college students. Perspect Psychiatr Care. 2023;2023(1). 10.1155/2023/3461121 . Additional Declarations No competing interests reported. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-8657826","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":595105713,"identity":"5a2cfd2e-476b-4b6f-87e1-6a450be510c6","order_by":0,"name":"Yajuan Li","email":"","orcid":"","institution":"Hanshan Normal University","correspondingAuthor":false,"prefix":"","firstName":"Yajuan","middleName":"","lastName":"Li","suffix":""},{"id":595105714,"identity":"da79ba5a-d85c-44d3-b9a2-d3e5413ff244","order_by":1,"name":"Gang Xiao","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA7ElEQVRIie3RrwvCQBTA8TcOzjJYvaH+DzcOZpHtX5kMtNgsBoMy0CLm+V9MBPPgwBXBOtCwlVkVRJb8xRTbuSh43/LK+7zyAGSyXwy9pkaKqQxLE90vtkuQdzQuS2iE0vQ82FvL3eSQ5NCsByHKEhHRPcxYbZ25q/3GGE2hzYIQN6iIaAjMKsHcNeOu4gHwVhCqmIgIRpVLlVy5y/xO+iC370RDqqmfxtyixDEeJPxOdE/tMWXGHRJ3jfmUumzOsSkkdBst0vzCbc3vJMe8b9VnkZcJyTOkArSGxQX4PFeUkgPYJfZkMpnsX7sDS15J8weI7sAAAAAASUVORK5CYII=","orcid":"","institution":"Hanshan Normal University","correspondingAuthor":true,"prefix":"","firstName":"Gang","middleName":"","lastName":"Xiao","suffix":""},{"id":595105715,"identity":"c0892853-0e60-41cf-bb04-0a6c9aa35185","order_by":2,"name":"Huanbin Xue","email":"","orcid":"","institution":"Hanshan Normal University","correspondingAuthor":false,"prefix":"","firstName":"Huanbin","middleName":"","lastName":"Xue","suffix":""}],"badges":[],"createdAt":"2026-01-21 09:38:44","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8657826/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8657826/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1186/s40359-026-04581-8","type":"published","date":"2026-04-30T15:57:21+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":103357751,"identity":"228a2076-45ab-404d-9a35-e2a93cbed380","added_by":"auto","created_at":"2026-02-24 19:09:53","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":110509,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eMental Health Trajectories (4-Class LCGM Solution)\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-8657826/v1/3c2200cb08b1d5a26e122e57.png"},{"id":103357735,"identity":"31b968fd-88a2-4107-ab56-28042cc017b3","added_by":"auto","created_at":"2026-02-24 19:09:48","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":62652,"visible":true,"origin":"","legend":"\u003cp\u003eClassification Quality Distributions\u003c/p\u003e","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-8657826/v1/d65ab3a4db63746c63779bd2.png"},{"id":108437593,"identity":"d916808a-868d-4e35-82a9-80c56ab09ca7","added_by":"auto","created_at":"2026-05-04 15:59:51","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":527266,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8657826/v1/24fe9300-9c84-43db-865f-6a36f3d1fe51.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Heterogeneous Mental Health Trajectories in College Students: A Three-Year Longitudinal Study Using Latent Class Growth Modeling","fulltext":[{"header":"1. Background","content":"\u003cp\u003eThe transition to higher education represents a critical developmental period characterized by significant psychological challenges.College students face multiple stressors including academic pressure,social adjustment,identity formation, and career uncertainty (Arnett,2015).Research consistently demonstrates elevated rates of mental health problems in this population. According to the World Mental Health Report released by the World Health Organization (WHO), 35% of full-time college students screened positive for at least one common lifetime disorder (Auerbach et al., \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2018\u003c/span\u003e). Recent studies have documented substantial prevalence of psychological distress among Chinese college students, with depression, anxiety, and stress being the most commonly reported problems (Chen, \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; Xin et al., \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). The mental health challenges faced by college students have become a growing concern for educational institutions and public health systems worldwide (Pedrelli et al., \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e2014\u003c/span\u003e; Wasil et al., \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e2022\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eTraditional approaches to studying college mental health have predominantly employed variable-centered methods, examining mean-level changes or correlations between risk factors and outcomes across entire samples. While informative, such approaches assume population homogeneity and may obscure meaningful subgroup differences in developmental trajectories (Nagin \u0026amp; Odgers, \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e2010\u003c/span\u003e). A growing body of evidence suggests that students follow heterogeneous pathways through their college years, with some showing resilience, others demonstrating recovery, and a subset experiencing persistent or worsening symptoms (Ma et al., \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2025\u003c/span\u003e; Liu et al., \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). Understanding these diverse patterns is essential for developing targeted intervention strategies that address the specific needs of different student subgroups.\u003c/p\u003e \u003cp\u003ePerson-centered analytical approaches, particularly Growth Mixture Modeling (GMM) and Latent Class Growth Modeling (LCGM), offer powerful tools for identifying unobserved subpopulations following distinct developmental trajectories (Muth\u0026eacute;n, \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2004\u003c/span\u003e; Ram \u0026amp; Grimm, \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2009\u003c/span\u003e). These methods can reveal clinically meaningful heterogeneity that would otherwise be masked by aggregate statistics. Recent applications of these approaches in college mental health research have successfully identified three to five distinct trajectory classes (Liu et al., \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Wang \u0026amp; Fang, \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). For example, Liu and colleagues (\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2023\u003c/span\u003e) employed piecewise growth mixture modeling to analyze depression, anxiety, and stress trajectories among Chinese college students, identifying four distinct classes with the majority falling into a \"low and stable\" pattern. Wang and Fang (\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e2024\u003c/span\u003e) used latent growth modeling to examine the developmental trajectory of psychological flexibility among college students, while Zhang et al. (\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e2023\u003c/span\u003e) demonstrated that mental health literacy mediates the relationship between psychological resilience and distress in medical college students.\u003c/p\u003e \u003cp\u003eHowever, methodological challenges persist in trajectory modeling research. Concerns about model identification, classification accuracy, and the stability of extracted classes across different samples and specifications have been raised (Bauer \u0026amp; Curran, \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2003\u003c/span\u003e; Infurna \u0026amp; Luthar, \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2018\u003c/span\u003e). Bootstrap validation has emerged as a valuable approach for assessing classification stability, with recent methodological work demonstrating that bootstrap-based methods can effectively quantify uncertainty in the number of identified groups (Diop et al., \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; Dean \u0026amp; Reiter, 2019). Furthermore, most existing studies have relied on two-step GMM approaches that first estimate individual growth parameters and then cluster individuals, potentially underestimating standard errors and misclassifying borderline cases (Ram \u0026amp; Grimm, \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2009\u003c/span\u003e; Kwon et al., \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2021\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eThe present study addresses these limitations by employing formal Latent Class Growth Modeling with simultaneous parameter estimation via the Expectation-Maximization (EM) algorithm.This approach properly propagates classification uncertainty to parameter estimates and provides correct standard errors. We examine three-year mental health trajectories in a large sample of Chinese college students, with particular attention to: (1) identifying the optimal number and nature of trajectory classes, (2) characterizing a high-risk subgroup requiring intervention, (3) evaluating classification stability through bootstrap validation, and (4) deriving practical implications for campus mental health services.\u003c/p\u003e"},{"header":"2. Methods","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1 Participants and Procedure\u003c/h2\u003e \u003cp\u003e Participants were drawn from the 2022 entering cohort at a comprehensive university in southern China. Mental health screening was conducted at three time points: enrollment in Fall 2022 (T1), Spring 2024 (T2; approximately 18 months post-enrollment), and Spring 2025 (T3; approximately 30 months post-enrollment). All enrolled students were invited to complete the assessment during designated class periods.\u003c/p\u003e \u003cp\u003eOf the 4,501 students who completed the T1 assessment, 3,418 (75.9%) completed T2 and 3,053 (67.8%) completed T3. The analytic sample comprised 2,562 students (56.9% of baseline) with valid data at all three time points. Attrition analysis comparing completers versus non-completers revealed no significant differences in baseline SCL-90 Global Severity Index scores (t\u0026thinsp;=\u0026thinsp;1.23, p = .219), though completers were more likely to be female (74.6% vs. 71.2%, χ\u0026sup2; = 5.89, p = .015).\u003c/p\u003e \u003cp\u003eThe final sample (N\u0026thinsp;=\u0026thinsp;2,562) had a mean age of 18.5 years (SD\u0026thinsp;=\u0026thinsp;0.8) at enrollment. The majority were female (n\u0026thinsp;=\u0026thinsp;1,910, 74.6%), of Han ethnicity (94.2%), and from urban backgrounds (62.8%).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.2 Measures\u003c/h2\u003e \u003cp\u003eSymptom Checklist-90 (SCL-90). The SCL-90 is a 90-item self-report inventory assessing psychological symptom patterns (Derogatis, 1994). Participants rate each symptom on a 5-point Likert scale from 1 (not at all) to 5 (extremely). The Global Severity Index (GSI), calculated as the mean of all 90 items, served as the primary outcome measure. The Chinese version has demonstrated good psychometric properties in college samples (Zhang et al., \u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). In the present study, internal consistency was excellent at all time points (Cronbach's α\u0026thinsp;=\u0026thinsp;.97, .98, .97 for T1, T2, T3, respectively). A GSI score of 2.0 or above was used as the clinical threshold for elevated symptomatology at the individual level, consistent with updated Chinese normative data (Dang et al., \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2020\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eDemographic variables. Gender, age, ethnicity, and hometown (urban/rural) were collected at baseline.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e2.3 Analytic Strategy\u003c/h2\u003e \u003cp\u003eLatent Class Growth Modeling. We employed formal LCGM using the Expectation-Maximization(EM) algorithm to simultaneously estimate:(a) class-specific growth parameters (intercept η\u003csub\u003e0k\u003c/sub\u003e and slope η\u003csub\u003e1k\u003c/sub\u003e), (b) within-class residual variances (σ\u0026sup2;\u003csub\u003ek\u003c/sub\u003e), and (c) individual posterior class membership probabilities.This approach differs from two-step GMM methods by properly propagating classification uncertainty to parameter estimates (Muth\u0026eacute;n, \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2004\u003c/span\u003e; Ram \u0026amp; Grimm, \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2009\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eThe model specification followed a linear growth framework:\u003c/p\u003e \u003cp\u003eY\u003csub\u003eit\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;η\u003csub\u003e0k\u003c/sub\u003e\u0026thinsp;+\u0026thinsp;η\u003csub\u003e1k\u003c/sub\u003e\u0026thinsp;\u0026times;\u0026thinsp;t\u0026thinsp;+\u0026thinsp;ε\u003csub\u003eit\u003c/sub\u003e, where ε\u003csub\u003eit\u003c/sub\u003e\u0026thinsp;~\u0026thinsp;N(0, σ\u0026sup2;\u003csub\u003ek\u003c/sub\u003e)\u003c/p\u003e \u003cp\u003ewhere Y\u003csub\u003eit\u003c/sub\u003e represents the observed GSI score for individual i at time t, η\u003csub\u003e0k\u003c/sub\u003e is the class-specific intercept, η\u003csub\u003e1k\u003c/sub\u003e is the class-specific slope, and σ\u0026sup2;\u003csub\u003ek\u003c/sub\u003e is the class-specific residual variance. Time was coded in months from baseline (0, 18, 30). Unlike standard LCGM that constrains residual variances to be equal across classes, we allowed class-specific residual variances to capture potential heteroscedasticity, which proved particularly important for the high-risk class.\u003c/p\u003e \u003cp\u003eRationale for LCGM over GMM. We chose LCGM (which fixes within-class intercept and slope variances to zero) rather than the more flexible Growth Mixture Model (GMM, which allows random effects within classes) for several reasons. First, with only three measurement occasions, estimating both between-class and within-class random effects would likely result in model identification problems and unstable parameter estimates (Infurna \u0026amp; Grimm, \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2018\u003c/span\u003e). Second, our primary interest was in identifying discrete trajectory classes rather than characterizing continuous individual differences within classes. Third, the class-specific residual variances (σ\u0026sup2;\u003csub\u003ek\u003c/sub\u003e) in our model specification capture substantial within-class heterogeneity, providing an intermediate approach between standard LCGM with equal variances and full GMM with random slopes. As will be shown, the high-risk class exhibited markedly higher residual variance (σ\u0026sup2;=0.314) compared to other classes (0.001\u0026ndash;0.061), suggesting important within-class variability that would need to be interpreted cautiously.\u003c/p\u003e \u003cp\u003eMultiple random initializations (n\u0026thinsp;=\u0026thinsp;10) were employed to avoid local optima, with convergence defined as change in log-likelihood less than 10\u003csup\u003e\u0026minus;\u0026thinsp;5\u003c/sup\u003e. Models with 2 to 6 classes were estimated and compared.\u003c/p\u003e \u003cp\u003eSoftware and Implementation. All analyses were conducted using a custom Python implementation (Python 3.12) of the EM algorithm utilizing NumPy 1.26 and SciPy 1.11 libraries. The implementation incorporates numerical stability techniques including log-sum-exp transformations for posterior probability calculations. Visualization was performed with Matplotlib 3.8 and Seaborn 0.13. The complete analysis code is provided in Supplementary Materials S1 and is available upon request from the corresponding author.\u003c/p\u003e \u003cp\u003eModel Selection. Optimal class enumeration was determined using a composite score integrating multiple criteria with the following weights: BIC (0.25), entropy (0.20), bootstrap stability (0.20), minimum class size (0.10), parsimony (0.10), and clinical relevance (0.15). Clinical relevance was operationalized as identification of a high-risk class with baseline mean GSI approaching the clinical threshold (\u0026ge;\u0026thinsp;1.90), ensuring identification of the most vulnerable subgroup. This threshold is slightly below the individual-level clinical cutoff of 2.0 to account for within-class variability and ensure that students near the clinical threshold are captured in the high-risk group. We acknowledge that these weights represent informed judgments based on the literature and clinical priorities rather than empirically derived optima. Models with 4\u0026ndash;5 classes were prioritized based on theoretical considerations and prior literature (Nagin \u0026amp; Odgers, \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e2010\u003c/span\u003e; Liu et al., \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2023\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eBootstrap Validation. Classification stability was assessed via bootstrap resampling (n\u0026thinsp;=\u0026thinsp;50 samples). While this number is lower than the 500-1,000 samples typically recommended for precise confidence interval estimation (Diop et al., \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; Dean \u0026amp; Reiter, 2019), it was chosen as a balance between computational constraints and obtaining a reasonable estimate of classification stability. For each bootstrap sample, the LCGM was re-estimated with 3 random starts and class labels were matched to the reference solution using the Hungarian algorithm (Kuhn, \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e1955\u003c/span\u003e). Individual-level stability was calculated as the proportion of bootstrap samples in which each participant was assigned to their modal class. The Adjusted Rand Index (ARI) quantified overall agreement between bootstrap and reference classifications.\u003c/p\u003e \u003cp\u003eClassification Quality. Classification accuracy was evaluated using entropy (target\u0026thinsp;\u0026ge;\u0026thinsp;0.80) and average posterior probability (AvePP; target\u0026thinsp;\u0026ge;\u0026thinsp;0.70 for each class). These indices follow recommendations from Celeux and Soromenho (\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e1996\u003c/span\u003e) and Clark and Muth\u0026eacute;n (\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2009\u003c/span\u003e). We also examined the distribution of maximum posterior probabilities to identify \"borderline cases\" (participants with maximum posterior probability\u0026thinsp;\u0026lt;\u0026thinsp;0.70) who may have uncertain class membership.\u003c/p\u003e \u003c/div\u003e"},{"header":"3. Results","content":"\u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003e3.1 Descriptive Statistics\u003c/h2\u003e \u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e presents descriptive statistics for SCL-90 GSI scores across the three assessment points. Mean symptom levels showed a declining trend from T1 (M\u0026thinsp;=\u0026thinsp;1.47, SD\u0026thinsp;=\u0026thinsp;0.47) to T3 (M\u0026thinsp;=\u0026thinsp;1.30, SD\u0026thinsp;=\u0026thinsp;0.40). This overall improvement represented a small-to-medium effect size. Using the average of standard deviations as the denominator (Cohen's d\u0026thinsp;=\u0026thinsp;mean difference / average SD\u0026thinsp;=\u0026thinsp;0.17 / 0.435\u0026thinsp;=\u0026thinsp;0.39), the magnitude of change was comparable to that observed in other longitudinal studies of college mental health (Liu et al., \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). The proportion of students exceeding the clinical threshold (GSI\u0026thinsp;\u0026ge;\u0026thinsp;2.0) decreased from 14.9% at baseline to 7.7% at T3, indicating that the rate of clinically significant distress was approximately halved over the three-year period.\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\u003eDescriptive Statistics for SCL-90 Global Severity Index Across Time Points\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"7\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTime Point\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eN\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eMean\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eSD\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e95% CI\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eRange\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003e% Clinical (\u0026ge;\u0026thinsp;2.0)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eT1 (Enrollment)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2,562\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1.47\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.47\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e[1.46, 1.49]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e1.00\u0026ndash;3.80\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e14.9%\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eT2 (18 months)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2,562\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1.35\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.43\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e[1.34, 1.37]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e1.00\u0026ndash;4.50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e8.4%\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eT3 (30 months)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2,562\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1.30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.40\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e[1.29, 1.32]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e1.00\u0026ndash;4.42\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e7.7%\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"7\"\u003eNote. Clinical threshold (GSI\u0026thinsp;\u0026ge;\u0026thinsp;2.0) based on updated Chinese normative data (Dang et al., \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). CI\u0026thinsp;=\u0026thinsp;confidence interval.\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003e3.2 Model Comparison and Selection\u003c/h2\u003e \u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e presents fit indices for LCGM solutions ranging from 2 to 6 classes. The four-class solution emerged as optimal based on the composite score (0.919), demonstrating acceptable entropy (0.779), excellent bootstrap stability (0.940), and successful identification of a high-risk subgroup.\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\u003eFit Indices for Latent Class Growth Models (2\u0026ndash;6 Classes)\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=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" 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=\"char\" char=\".\" class=\"colspec\" colname=\"c10\" colnum=\"10\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eClasses\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eBIC\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eLog-Likelihood\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eEntropy\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eMin. Class %\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eMin. AvePP\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eStability\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003eARI\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c9\"\u003e \u003cp\u003eHigh-Risk\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c10\"\u003e \u003cp\u003eComposite\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e3320.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e\u0026minus;1632.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.859\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e49.0%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.958\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.985\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.941\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003eNo\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e0.554\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1918.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e\u0026minus;916.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.823\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e25.1%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.905\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.975\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.927\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003eNo\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e0.735\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003e4\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003e1353.4\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003e\u0026minus;617.8\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e0.779\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e13.2%\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e0.844\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e\u003cb\u003e0.940\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e\u003cb\u003e0.840\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u003cb\u003eYes\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e\u003cb\u003e0.919\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1173.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e\u0026minus;512.1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.721\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e8.6%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.792\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.839\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.633\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e0.894\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1137.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e\u0026minus;478.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.712\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e6.7%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.674\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.926\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.803\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e0.865\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"10\"\u003eNote. BIC\u0026thinsp;=\u0026thinsp;Bayesian Information Criterion; AvePP\u0026thinsp;=\u0026thinsp;average posterior probability; ARI\u0026thinsp;=\u0026thinsp;Adjusted Rand Index; Stability\u0026thinsp;=\u0026thinsp;bootstrap classification stability. The selected four-class solution is highlighted. High-Risk\u0026thinsp;=\u0026thinsp;identification of class with baseline mean approaching clinical threshold (\u0026ge;\u0026thinsp;1.90). This threshold is used for model selection purposes and differs from the individual-level clinical cutoff of GSI\u0026thinsp;\u0026ge;\u0026thinsp;2.0.\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eThe four-class solution was preferred over the five-class model despite the latter's lower BIC for several reasons: (1) substantially higher bootstrap stability (0.940 vs. 0.839), (2) higher ARI (0.840 vs. 0.633), (3) entropy above the acceptable threshold of 0.70, and (4) adequate minimum class size (13.2% vs. 8.6%). Notably, the five-class model showed a marked decline in both stability and ARI, suggesting that the additional class may represent an artifact of sample-specific variation rather than a reliable subpopulation. This non-monotonic pattern\u0026mdash;where the 6-class model recovered somewhat in stability (0.926) but with further reduced entropy and minimum class size\u0026mdash;underscores the importance of evaluating multiple fit indices rather than relying on any single criterion.\u003c/p\u003e \u003cp\u003eSensitivity Analysis for Model Selection. To evaluate the robustness of the four-class solution to alternative weight specifications in the composite score, we conducted sensitivity analyses varying each weight by \u0026plusmn;\u0026thinsp;50%. The four-class solution remained optimal under all tested weight combinations, with composite scores ranging from 0.88 to 0.94. The selection was particularly robust to changes in the parsimony and clinical relevance weights, but more sensitive to entropy weighting. When entropy weight was increased to 0.30, the three-class solution became marginally competitive (composite\u0026thinsp;=\u0026thinsp;0.91 vs. 0.92 for four-class), though the four-class solution still identified the high-risk subgroup that was absent in the three-class model. These results support the robustness of our model selection decision.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec9\" class=\"Section2\"\u003e \u003ch2\u003e3.3 Trajectory Class Characteristics\u003c/h2\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e displays the four identified trajectory classes, and Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e presents their characteristics. The classes were labeled based on their baseline levels and developmental patterns.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. Shows four trajectory lines from T1 to T3, with horizontal reference lines at GSI\u0026thinsp;=\u0026thinsp;2.0 (clinical threshold) and GSI\u0026thinsp;=\u0026thinsp;1.5 (moderate-risk threshold). The High-Risk-Improving trajectory (purple) starts near 2.0 and shows the steepest decline. Low-Optimal (red) remains near 1.0 throughout.\u003c/p\u003e \u003cp\u003eMental health trajectories across three years of college (N\u0026thinsp;=\u0026thinsp;2,562). The four-class LCGM solution shows distinct patterns: Low-Optimal (red, 13.2%), Low-Stable (gray, 29.8%), Moderate-Improving (brown, 32.9%), and High-Risk-Improving (purple, 24.0%). Dashed lines indicate clinical threshold at GSI\u0026thinsp;=\u0026thinsp;2.0 and moderate-risk threshold at GSI\u0026thinsp;=\u0026thinsp;1.5.\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\u003eCharacteristics of the Four Trajectory Classes\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=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c10\" colnum=\"10\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTrajectory Class\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eN (%)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eT1 Mean\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eT2 Mean\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eT3 Mean\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eChange\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eSlope/Month\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003eT1 Clinical %\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c9\"\u003e \u003cp\u003eT3 Clinical %\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c10\"\u003e \u003cp\u003eStability\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLow-Optimal\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e338 (13.2%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1.04\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1.03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e1.01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e\u0026minus;0.03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e\u0026minus;0.0010\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.0%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0.0%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e0.993\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLow-Stable\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e764 (29.8%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1.19\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1.13\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e1.09\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e\u0026minus;0.10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e\u0026minus;0.0035\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.0%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0.0%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e0.959\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eModerate-Improving\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e844 (32.9%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1.47\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1.36\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e1.28\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e\u0026minus;0.19\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e\u0026minus;0.0063\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e3.7%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0.0%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e0.928\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eHigh-Risk-Improving\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003e616 (24.0%)\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003e1.98\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e1.80\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e1.68\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e\u0026minus;0.30\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e\u003cb\u003e\u0026minus;0.0100\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e\u003cb\u003e56.8%\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e\u003cb\u003e31.8%\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e\u003cb\u003e0.904\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"10\"\u003eNote. Change\u0026thinsp;=\u0026thinsp;T3 minus T1. Slope expressed as GSI change per month. Clinical threshold defined as GSI\u0026thinsp;\u0026ge;\u0026thinsp;2.0. The High-Risk-Improving class (highlighted) represents the high-risk subgroup. Stability\u0026thinsp;=\u0026thinsp;bootstrap classification stability for each class. Class sizes (N) are based on maximum posterior probability assignment; EM-estimated mixing proportions are reported in Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e.\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eGender distribution did not differ significantly across the four trajectory classes (χ\u0026sup2; = 4.87, df\u0026thinsp;=\u0026thinsp;3, p =\u0026thinsp;.182), with female students comprising 73.4% to 76.1% of each class.\u003c/p\u003e \u003cp\u003e \u003cb\u003eClass 1: Low-Optimal (n\u0026thinsp;=\u0026thinsp;338, 13.2%).\u003c/b\u003e This class exhibited the lowest symptom levels across all time points, with scores near the minimum possible (M\u003csub\u003eT1\u003c/sub\u003e = 1.04). The trajectory was essentially flat (slope\u0026thinsp;=\u0026thinsp;\u0026minus;\u0026thinsp;0.0010/month), indicating stable optimal mental health. Classification stability was highest in this class (0.993).\u003c/p\u003e \u003cp\u003e \u003cb\u003eClass 2: Low-Stable (n\u0026thinsp;=\u0026thinsp;764, 29.8%).\u003c/b\u003e Students in this class showed low-to-normal symptom levels with a slight declining trend (M\u003csub\u003eT1\u003c/sub\u003e = 1.19 to M\u003csub\u003eT3\u003c/sub\u003e = 1.09). No students in this class exceeded the clinical threshold at any time point. Stability was excellent (0.959).\u003c/p\u003e \u003cp\u003e \u003cb\u003eClass 3: Moderate-Improving (n\u0026thinsp;=\u0026thinsp;844, 32.9%).\u003c/b\u003e The largest class demonstrated moderate baseline symptoms (M\u003csub\u003eT1\u003c/sub\u003e = 1.47) with consistent improvement over time (slope\u0026thinsp;=\u0026thinsp;\u0026minus;\u0026thinsp;0.0063/month). While 3.7% exceeded the clinical threshold at T1, none remained above threshold by T3. This pattern suggests successful adaptation to college life.\u003c/p\u003e \u003cp\u003e \u003cb\u003eClass 4: High-Risk-Improving (n\u0026thinsp;=\u0026thinsp;616, 24.0%).\u003c/b\u003e This high-risk class exhibited the highest baseline symptoms (M\u003csub\u003eT1\u003c/sub\u003e = 1.98, near the clinical threshold) and, notably, the steepest improvement trajectory (slope\u0026thinsp;=\u0026thinsp;\u0026minus;\u0026thinsp;0.0100/month). Over half (56.8%) exceeded the clinical threshold at enrollment. Despite substantial improvement (total change\u0026thinsp;=\u0026thinsp;\u0026minus;\u0026thinsp;0.30), 31.8% (approximately 196 students) remained above the clinical threshold at T3. This class showed the highest within-class heterogeneity, as detailed below.\u003c/p\u003e \u003cp\u003eEffect Sizes. The magnitude of change within the high-risk class represented a medium effect. The residual variance in our heteroscedastic LCGM represents the within-class variability around the class-specific trajectory; thus \u0026radic;σ\u0026sup2; provides an estimate of the within-class standard deviation. Using this approach (SD = \u0026radic;0.314\u0026thinsp;=\u0026thinsp;0.56), Cohen's d\u0026thinsp;=\u0026thinsp;0.30 / 0.56\u0026thinsp;=\u0026thinsp;0.54. Between-class differences at baseline were substantial: a one-way ANOVA on T1 GSI scores across the four classes yielded η\u0026sup2; = 0.62, indicating that trajectory class membership explained 62% of variance in baseline symptoms. This large effect size supports the clinical meaningfulness of the identified trajectory classes and is consistent with the group heterogeneity observed in other studies of college student mental health (Ma et al., \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2025\u003c/span\u003e).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec10\" class=\"Section2\"\u003e \u003ch2\u003e3.4 Growth Parameter Estimates\u003c/h2\u003e \u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e presents the formal growth parameter estimates from the EM algorithm, including class-specific intercepts, slopes, residual variances, and mixing proportions.\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\u003eGrowth Parameter Estimates for the Four-Class LCGM Solution\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eParameter\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eLow-Optimal\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eLow-Stable\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eModerate-Improving\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eHigh-Risk-Improving\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eIntercept (η\u003csub\u003e0\u003c/sub\u003e)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1.043\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1.194\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1.471\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e1.983\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSlope (η\u003csub\u003e1\u003c/sub\u003e)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e\u0026minus;0.0010\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e\u0026minus;0.0035\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e\u0026minus;0.0063\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e\u0026minus;0.0100\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eResidual Variance (σ\u0026sup2;)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.011\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.061\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.314\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eClass Proportion (π)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.126\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.289\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.328\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.257\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"5\"\u003eNote. Slopes represent GSI change per month. All parameters estimated simultaneously via EM algorithm with 10 random starts. Residual variances are class-specific (heteroscedastic model). Class proportions (π) represent EM-estimated mixing probabilities based on the probabilistic (soft) classification, which may differ slightly from the hard classification percentages in Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e (e.g., 25.7% vs. 24.0% for the high-risk class) due to the accumulation of classification uncertainty across participants with posterior probabilities between 0.5 and 1.0.\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eA striking finding was the large residual variance in the High-Risk-Improving class (σ\u0026sup2; = 0.314), which was 5 to 314 times larger than in the other classes. This substantial within-class heterogeneity warrants careful interpretation. In our LCGM framework where within-class intercept and slope variances are fixed to zero, the residual variance captures all within-class variability around the class-specific growth curve. The exceptionally high residual variance in the high-risk class suggests that this group may contain distinct subpopulations with different underlying mechanisms or response patterns\u0026mdash;some showing rapid recovery, others showing modest improvement, and a subset showing persistent difficulties. This finding points to the need for future research with additional measurement occasions or GMM approaches that can formally model within-class random effects. In contrast, the Low-Optimal class showed minimal residual variance (σ\u0026sup2;= 0.001), indicating a highly homogeneous group.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec11\" class=\"Section2\"\u003e \u003ch2\u003e3.5 Classification Quality\u003c/h2\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e displays the distributions of classification probabilities and bootstrap stability scores. The majority of participants (approximately 75%) had maximum posterior probabilities exceeding 0.70, indicating confident classification. Bootstrap stability scores were concentrated near 1.0, with over 92% of participants showing stability above 0.80.\u003c/p\u003e \u003cp\u003eApproximately 10\u0026ndash;15% of participants had maximum posterior probabilities below 0.70, representing \"borderline cases\" with uncertain class membership. These individuals were primarily located at the boundaries between adjacent classes (e.g., between Low-Stable and Moderate-Improving, or between Moderate-Improving and High-Risk-Improving). The entropy value of 0.779, while slightly below the ideal threshold of 0.80, indicates acceptable overall classification precision given the continuous nature of the underlying construct.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. Distributions of classification quality indices. Left: Maximum posterior probability for each participant's most likely class assignment. Right: Bootstrap classification stability (proportion of 50 bootstrap samples with consistent assignment). Vertical dashed lines indicate threshold values (red\u0026thinsp;=\u0026thinsp;0.70 for posterior probability; red\u0026thinsp;=\u0026thinsp;0.50 and green\u0026thinsp;=\u0026thinsp;0.70 for stability).\u003c/p\u003e \u003c/div\u003e"},{"header":"4. Discussion","content":"\u003cp\u003eThis study employed formal Latent Class Growth Modeling to identify distinct mental health trajectories among Chinese college students over three years. Four trajectory classes emerged, representing qualitatively different patterns of psychological adaptation to college life. Approximately one quarter of students (24.0%) followed a high-risk trajectory characterized by elevated baseline distress and, despite showing the most rapid improvement, a substantial proportion (31.8%) remained above clinical threshold at the end of the study period.\u003c/p\u003e \u003cdiv id=\"Sec13\" class=\"Section2\"\u003e \u003ch2\u003e4.1 Trajectory Heterogeneity\u003c/h2\u003e \u003cp\u003eThe identification of four distinct trajectories confirms that college students are not a homogeneous population with respect to mental health development. This finding aligns with recent research using person-centered approaches in college populations. For example, Liu and colleagues (\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2023\u003c/span\u003e) identified four classes of depression trajectories among Chinese college students using piecewise growth mixture modeling, with a \"low and stable\" class comprising approximately 79% of the sample. Wang and Fang (\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e2024\u003c/span\u003e) demonstrated that college students' psychological flexibility follows distinct developmental patterns, while Zhang et al. (\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e2023\u003c/span\u003e) showed that mental health literacy plays a mediating role in the relationship between psychological resilience and distress among medical college students.\u003c/p\u003e \u003cp\u003eThe largest group in our study (Moderate-Improving, 32.9%) showed the pattern often assumed in traditional analyses: moderate initial symptoms that gradually improve as students adapt to college. However, this pattern characterized only one-third of the sample. The Low-Optimal (13.2%) and Low-Stable (29.8%) groups, comprising 43% of the sample, exhibited consistently low symptom levels throughout college. These students likely possess robust psychological resources or face fewer stressors, and may not require targeted mental health services. Importantly, combining these two groups in a simpler three-class solution would have masked meaningful differences in their baseline levels and trajectories.\u003c/p\u003e \u003cp\u003eMost clinically significant is the High-Risk-Improving class (24.0%), which began college with symptoms near the clinical threshold (M\u0026thinsp;=\u0026thinsp;1.98). These students showed the steepest improvement slope (\u0026minus;\u0026thinsp;0.0100/month), suggesting that many benefited from natural adaptation processes or existing support systems. However, the finding that 31.8% remained above clinical threshold at T3 indicates that a substantial subset requires more intensive intervention than they are currently receiving. This prevalence is consistent with recent findings documenting the heterogeneity in college student mental health (Ma et al., \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2025\u003c/span\u003e; Seehuus et al., \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2019\u003c/span\u003e).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec14\" class=\"Section2\"\u003e \u003ch2\u003e4.2 The High-Risk Subgroup and Within-Class Heterogeneity\u003c/h2\u003e \u003cp\u003eThe 24.0% prevalence of the high-risk trajectory is higher than some previous estimates but consistent with recent meta-analytic findings (Auerbach et al., \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2018\u003c/span\u003e). The exceptionally large residual variance in this class (σ\u0026sup2; = 0.314) warrants particular attention and has important methodological and clinical implications.\u003c/p\u003e \u003cp\u003eFrom a methodological perspective, while our a priori rationale for LCGM over GMM was sound given the measurement design (three time points insufficient for random effects estimation), the unexpectedly large residual variance in the high-risk class (σ\u0026sup2; = 0.314 vs. 0.001\u0026ndash;0.061 in other classes) suggests that this group may have benefited from a more flexible model specification had additional measurement occasions been available. This heterogeneity raises questions about whether a Growth Mixture Model allowing within-class random effects might better characterize this subgroup. However, with only three measurement occasions, estimating such models would likely result in identification problems. The high residual variance in our LCGM can be interpreted as capturing the combined effect of: (a) true individual differences in trajectories within the class, (b) measurement error, and (c) potential model misspecification. Future research with more intensive longitudinal designs (e.g., 5\u0026thinsp;+\u0026thinsp;waves) could employ GMM to formally distinguish these sources of variance.\u003c/p\u003e \u003cp\u003eFrom a clinical perspective, this heterogeneity suggests that \"high-risk\" students are not a uniform group but may include: (a) students with transient stress reactions who recover fully, (b) students with moderate chronic symptoms that improve partially, and (c) students with persistent severe symptoms requiring clinical intervention. The 31.8% remaining above threshold at T3 likely represents this latter subgroup. Future research using more intensive longitudinal designs or qualitative methods could illuminate these subpopulations and identify differential predictors of recovery versus persistence (Selvaraj \u0026amp; Bhat, \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; Nogueira \u0026amp; Sequeira, \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2024\u003c/span\u003e).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec15\" class=\"Section2\"\u003e \u003ch2\u003e4.3 Methodological Contributions\u003c/h2\u003e \u003cp\u003eThis study makes several methodological contributions to the trajectory modeling literature. First, the use of formal LCGM with simultaneous EM estimation addresses concerns raised about two-step GMM approaches (Ram \u0026amp; Grimm, \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2009\u003c/span\u003e; Kwon et al., \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). By estimating growth parameters and class membership probabilities jointly, our approach properly propagates classification uncertainty and provides appropriate standard errors.\u003c/p\u003e \u003cp\u003eSecond, the comprehensive model selection strategy integrating multiple criteria (BIC, entropy, stability, clinical relevance) moves beyond reliance on any single fit index. While we acknowledge that the specific weights used (e.g., clinical relevance\u0026thinsp;=\u0026thinsp;0.15) reflect our priorities and could be adjusted by other researchers, making these weights explicit improves transparency and replicability. Notably, we did not have access to the Lo-Mendell-Rubin likelihood ratio test (LMR-LRT) or Bootstrap Likelihood Ratio Test (BLRT) in our Python implementation, which are commonly used in Mplus-based analyses. Future implementations could incorporate these tests for more comprehensive model comparison (Kwon et al., \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Nylund et al., \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2007\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eThird, bootstrap validation with Hungarian algorithm label matching provides a rigorous test of classification stability. Although our use of 50 bootstrap samples is lower than methodological recommendations of 500-1,000 samples (Diop et al., \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2024\u003c/span\u003e), the excellent stability observed (0.940) and the strongly right-skewed distribution of individual stability scores (with \u0026gt;\u0026thinsp;92% above 0.80) give confidence that the identified classes are reproducible. Future studies with greater computational resources could employ larger bootstrap samples to obtain more precise stability estimates and confidence intervals.\u003c/p\u003e \u003cp\u003eFourth, our finding that the 5-class model showed anomalous declines in both stability (0.839) and ARI (0.633) while the 6-class model partially recovered (stability\u0026thinsp;=\u0026thinsp;0.926) highlights the complexity of model selection in mixture modeling. This non-monotonic pattern underscores the importance of evaluating classification stability alongside traditional fit indices, as overfitting can manifest in unstable solutions that fail to replicate across bootstrap samples.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec16\" class=\"Section2\"\u003e \u003ch2\u003e4.4 Clinical and Practical Implications\u003c/h2\u003e \u003cp\u003eThese findings support the implementation of tiered early warning systems in college mental health services (Gao, \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Kalkbrenner et al., \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). Based on the observed trajectory class boundaries\u0026mdash;with the high-risk class averaging GSI\u0026thinsp;=\u0026thinsp;1.98 at baseline and the moderate-improving class averaging 1.47\u0026mdash;we propose a three-tier framework with thresholds that require independent validation before clinical implementation:\u003c/p\u003e \u003cp\u003e \u003cb\u003eProposed Three-Tier Early Warning System\u003c/b\u003e \u003c/p\u003e \u003cp\u003e \u003cstrong\u003eTier 1 (High Priority)\u003c/strong\u003e \u003cp\u003eStudents with baseline GSI\u0026thinsp;\u0026ge;\u0026thinsp;2.0 (~\u0026thinsp;24% of entering students)\u003c/p\u003e \u003c/p\u003e \u003cp\u003e\u0026rarr; Proactive outreach within first month; individual counseling assessment; peer support programs\u003c/p\u003e \u003cp\u003e \u003cstrong\u003eTier 2 (Moderate Priority)\u003c/strong\u003e \u003cp\u003eStudents with baseline GSI 1.4\u0026ndash;2.0 (~\u0026thinsp;33% of students)\u003c/p\u003e \u003c/p\u003e \u003cp\u003e\u0026rarr; Invitation to stress management workshops; periodic check-ins; psychoeducational materials\u003c/p\u003e \u003cp\u003e \u003cstrong\u003eTier 3 (Universal)\u003c/strong\u003e \u003cp\u003eStudents with baseline GSI\u0026thinsp;\u0026lt;\u0026thinsp;1.4 (~\u0026thinsp;43% of students)\u003c/p\u003e \u003c/p\u003e \u003cp\u003e\u0026rarr; Standard orientation programming; awareness campaigns; available but not mandated services\u003c/p\u003e \u003cp\u003eWe note that the proposed thresholds (1.4 and 2.0) are derived from the observed distribution of trajectory class means. Formal ROC curve analysis with follow-up outcomes (e.g., service utilization, academic difficulties, clinical diagnoses) would provide empirical support for optimal cutpoints. Researchers and practitioners should validate these thresholds in their own populations before implementation (Du, \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2025\u003c/span\u003e; Xu, \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e2024\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eCritically, the finding that nearly one-third of high-risk students remain above clinical threshold after three years suggests that current university mental health resources may be insufficient for this population. Enhanced services might include increased counseling capacity, evidence-based group interventions targeting specific symptoms (e.g., anxiety, interpersonal sensitivity), and systematic follow-up protocols for students identified as high-risk at enrollment (Chen et al., \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2020\u003c/span\u003e; Wasil et al., \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e2022\u003c/span\u003e).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec17\" class=\"Section2\"\u003e \u003ch2\u003e4.5 Limitations and Future Directions\u003c/h2\u003e \u003cp\u003eSeveral limitations should be noted. First, the sample was drawn from a single Chinese university, limiting generalizability to other cultural contexts or institutional types. Cross-cultural replication is needed to determine whether similar trajectory patterns emerge in Western or more diverse samples. Recent research has documented both similarities and differences in college mental health patterns across cultural contexts (Auerbach et al., \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; Wei, \u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; Cheng et al., \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2016\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eSecond, reliance on self-report measures introduces potential biases including social desirability and recall effects. Future studies might incorporate clinical interviews, informant reports, or physiological markers to provide multi-method validation (Zhang, \u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Han, \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2023\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eThird, with only three measurement occasions, we could only model linear trajectories. Important non-linear patterns\u0026mdash;such as initial deterioration followed by recovery, or early improvement followed by plateau\u0026mdash;cannot be captured with this design. Future studies should incorporate more frequent assessments, particularly during the critical first semester of college (Liu et al., \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2023\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eFourth, the entropy value (0.779) fell slightly below the ideal threshold of 0.80, indicating some classification uncertainty, particularly for participants at the boundaries between adjacent classes. However, the excellent bootstrap stability (0.940) and ARI (0.840) suggest that this limitation does not substantially compromise the validity of the identified classes. Researchers interpreting individual-level classifications should consider posterior probabilities rather than treating class assignments as deterministic.\u003c/p\u003e \u003cp\u003eFifth, this study focused on describing trajectories without examining predictors or outcomes. Future research should identify risk and protective factors that differentiate trajectory classes (e.g., family support, coping styles, prior mental health history) and examine downstream consequences such as academic performance, social functioning, and mental health service utilization (Dong et al., \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; Xin et al., \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). The large within-class heterogeneity observed in the high-risk class suggests that identifying predictors of recovery versus persistence within this group would be particularly valuable for intervention targeting.\u003c/p\u003e \u003cp\u003eSixth, given the predominantly female sample (74.6%), future research should specifically investigate potential gender differences in mental health trajectories. Although gender distribution did not differ significantly across trajectory classes in our sample, prior research has documented gender effects on mental health symptoms and help-seeking behaviors among college students (Seehuus et al., \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Kalkbrenner et al., \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2021\u003c/span\u003e).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec18\" class=\"Section2\"\u003e \u003ch2\u003e4.6 Conclusions\u003c/h2\u003e \u003cp\u003eUsing formal Latent Class Growth Modeling with simultaneous parameter estimation implemented in Python, this study identified four distinct mental health trajectories among Chinese college students. Approximately one quarter followed a high-risk pattern characterized by elevated baseline symptoms and, despite significant improvement, persistent clinical concerns for a substantial subset. The excellent classification stability achieved through bootstrap validation supports the robustness of these findings, although the high within-class heterogeneity in the high-risk group suggests that this class may contain meaningful subpopulations warranting further investigation. Results highlight the importance of person-centered approaches for understanding mental health development and inform the design of tiered early intervention programs in college settings.\u003c/p\u003e \u003c/div\u003e"},{"header":"Declarations","content":"\u003cp\u003e \u003cstrong\u003eEthics approval and consent to participate:\u003c/strong\u003e \u003cp\u003e All procedures involving human participants were performed in accordance with the ethical standards of the Ethics Committee of Hanshan Normal University and with the 1964 Helsinki Declaration and its later amendments. This study was approved by the aforementioned committee (Approval No. 2026010804). Informed consent was obtained from all individual participants included in the study.\u003c/p\u003e \u003c/p\u003e \u003cp\u003e \u003cstrong\u003eConsent for publication:\u003c/strong\u003e \u003cp\u003eNot applicable.\u003c/p\u003e \u003c/p\u003e\u003cp\u003e \u003ch2\u003eCompeting interests:\u003c/h2\u003e \u003cp\u003eThe authors declare no competing interests.\u003c/p\u003e \u003c/p\u003e\u003cp\u003e \u003ch2\u003eAuthor\u0026rsquo; Contributions\u003c/h2\u003e \u003cp\u003eYajuan Li contributed to data collection and interpretation, supervised the project, and revised the manuscript. Gang Xiao conceptualized the study, developed the Python implementation, conducted analyses, and drafted the manuscript.Huanbin Xue conducted analyses, and drafted the manuscript. All authors approved the final version.\u003c/p\u003e \u003c/p\u003e \u003cp\u003e \u003cstrong\u003eAcknowledgments\u003c/strong\u003e \u003cp\u003eWe thank the students who participated in this study and the university counseling center staff who facilitated data collection.\u003c/p\u003e \u003c/p\u003e\u003ch2\u003eFunding:\u003c/h2\u003e \u003cp\u003eThis research was supported by the the National Natural Science Foundation(NSF) of China ( Grant12372009), supported by the NSF of Guangdong (Grant 2022A1515011971), Education Science Planning Project of Guangdong Province (Grant No.2023GXJK385), Hanshan Normal University Institutional Projects (Grant Nos.QD2024111 and E24035), the Collaborative Innovation Research Center for East Guangdong Educational Region at Hanshan Normal University, and the Natural Science Foundation of Hanshan Normal University (Grant No. PNB221103).\u003c/p\u003e\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eYajuan Li contributed to data collection and interpretation, supervised the project, and revised the manuscript. Gang Xiao conceptualized the study, developed the Python implementation, conducted analyses, and drafted the manuscript.Huanbin Xue conducted analyses, and drafted the manuscript. All authors approved the final version.\u003c/p\u003e\u003ch2\u003eAcknowledgement\u003c/h2\u003e\u003cp\u003eWe thank the students who participated in this study and the university counseling center staff who facilitated data collection.\u003c/p\u003e\u003ch2\u003eData Availability\u003c/h2\u003e\u003cp\u003eDe-identified data are available from the corresponding author upon reasonable request, subject to institutional data sharing agreements. The Python analysis code is provided in Supplementary Materials S1 and will be deposited in a public repository upon publication.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eArnett JJ. Emerging adulthood: The winding road from the late teens through the twenties. 2nd ed. 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Perspect Psychiatr Care. 2023;2023(1). \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1155/2023/3461121\u003c/span\u003e\u003cspan address=\"10.1155/2023/3461121\" 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":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"bmc-psychology","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"psyo","sideBox":"Learn more about [BMC Psychology](http://bmcpsychology.biomedcentral.com/)","snPcode":"","submissionUrl":"","title":"BMC Psychology","twitterHandle":"BMC_series","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"BMC Series","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"mental health trajectories, college students, latent class growth modeling, SCL-90, longitudinal study, early warning system, EM algorithm","lastPublishedDoi":"10.21203/rs.3.rs-8657826/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8657826/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003ch2\u003eBackground\u003c/h2\u003e \u003cp\u003eCollege students face significant mental health challenges during their academic journey, yet the heterogeneity in their psychological adaptation patterns remains poorly understood. Traditional variable-centered approaches fail to capture the diverse trajectories that students may follow. Recent studies indicate that 20\u0026ndash;30% of Chinese college students experience clinically significant psychological distress, highlighting the need for person-centered analytical approaches.\u003c/p\u003e\u003ch2\u003eMethods\u003c/h2\u003e \u003cp\u003eThis longitudinal study employed formal Latent Class Growth Modeling (LCGM) using the Expectation-Maximization algorithm implemented in Python to identify distinct mental health trajectories among 2,562 Chinese college students assessed at enrollment (T1), sophomore year (T2, 18 months), and junior year (T3, 30 months). The Symptom Checklist-90 (SCL-90) Global Severity Index served as the primary outcome. Model selection was based on a composite score integrating BIC, entropy, bootstrap stability, and clinical relevance.\u003c/p\u003e\u003ch2\u003eResults\u003c/h2\u003e \u003cp\u003eA four-class solution demonstrated optimal fit (composite score\u0026thinsp;=\u0026thinsp;0.919, entropy\u0026thinsp;=\u0026thinsp;0.779, bootstrap stability\u0026thinsp;=\u0026thinsp;0.940). Four trajectories emerged: Low-Optimal (13.2%; M\u003csub\u003eT1\u003c/sub\u003e = 1.04), Low-Stable (29.8%; M\u003csub\u003eT1\u003c/sub\u003e=1.19), Moderate-Improving (32.9%; M\u003csub\u003eT1\u003c/sub\u003e=1.47), and High-Risk-Improving (24.0%; M\u003csub\u003eT1\u003c/sub\u003e=1.98). Between-class differences were substantial (η\u0026sup2; = 0.62). The high-risk class showed the steepest decline (slope\u0026thinsp;=\u0026thinsp;\u0026minus;\u0026thinsp;0.0100/month)but 31.8% remained above clinical threshold at T3.Growth parameters revealed substantial within-class heterogeneity in the high-risk group (σ\u0026sup2; = 0.314).\u003c/p\u003e\u003ch2\u003eConclusions\u003c/h2\u003e \u003cp\u003eApproximately one quarter of college students follow a high-risk mental health trajectory requiring targeted intervention.The formal LCGM approach with simultaneous parameter estimation provides robust classification with excellent stability. These findings support implementing tiered early warning systems based on baseline screening.\u003c/p\u003e","manuscriptTitle":"Heterogeneous Mental Health Trajectories in College Students: A Three-Year Longitudinal Study Using Latent Class Growth Modeling","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-02-24 19:09:10","doi":"10.21203/rs.3.rs-8657826/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2026-03-03T04:18:42+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-03-02T19:36:58+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"173933647832973492507441130896960199013","date":"2026-03-02T12:53:05+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"306542276942170095264397107140920701973","date":"2026-03-02T06:53:29+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"145380460794475934680915051561873447366","date":"2026-03-01T18:15:23+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"72012290059434371685238007861312956502","date":"2026-03-01T13:48:19+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"31655903675847819141926792007547694731","date":"2026-03-01T07:54:08+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"312046709842118162457895159720722437438","date":"2026-03-01T07:26:46+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-02-28T18:32:32+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"235898750502093478843390068358352005117","date":"2026-02-20T16:56:56+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2026-02-19T12:15:15+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2026-02-19T12:12:30+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2026-02-09T04:26:55+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2026-02-07T03:50:46+00:00","index":"","fulltext":""},{"type":"submitted","content":"BMC Psychology","date":"2026-02-07T03:44:58+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"bmc-psychology","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"psyo","sideBox":"Learn more about [BMC Psychology](http://bmcpsychology.biomedcentral.com/)","snPcode":"","submissionUrl":"","title":"BMC Psychology","twitterHandle":"BMC_series","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"BMC Series","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"21fe88a9-50aa-43b6-8ed7-848980d3aad3","owner":[],"postedDate":"February 24th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2026-05-04T15:59:25+00:00","versionOfRecord":{"articleIdentity":"rs-8657826","link":"https://doi.org/10.1186/s40359-026-04581-8","journal":{"identity":"bmc-psychology","isVorOnly":false,"title":"BMC Psychology"},"publishedOn":"2026-04-30 15:57:21","publishedOnDateReadable":"April 30th, 2026"},"versionCreatedAt":"2026-02-24 19:09:10","video":"","vorDoi":"10.1186/s40359-026-04581-8","vorDoiUrl":"https://doi.org/10.1186/s40359-026-04581-8","workflowStages":[]},"version":"v1","identity":"rs-8657826","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8657826","identity":"rs-8657826","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}