Bridging the Digital Divide: Machine Learning Analysis of Internet Access Effects on Subjective Well-Being

Bridging the Digital Divide: Machine Learning Analysis of Internet Access Effects on Subjective Well-Being | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Bridging the Digital Divide: Machine Learning Analysis of Internet Access Effects on Subjective Well-Being Jiaxu Zhang, Chao Li, Bo Shi, Alexander Ryota Keeley, Shunsuke Managi This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8160157/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract In this rapidly evolving digital age, the impact of internet access on human well-being has become a key issue of social equity and development. As the global digital divide widens, little is known about how internet access affects individual subjective well-being (SWB). This study uses the Gallup World Poll (GWP) dataset, covering approximately 1 million observations from 168 countries between 2016 and 2022. Using machine learning techniques with propensity score matching models, we explore how digital connectivity influences SWB across dimensions. Our study finds that internet access can increase SWB by 9.2% and help bridge the digital divide. This relationship varies across time, countries, and demographic characteristics. The positive impact peaked during the COVID-19 pandemic and gradually declined afterward. Across different levels of national development, the positive effect of internet access on SWB is more pronounced and stable in developed countries compared to developing countries. Demographically, Internet access enhances the subjective well-being of young and middle-aged groups. Additionally, internet access helps reduce the negative impact of poor health and low income on SWB. Governments should bridge the digital divide through infrastructure and subsidies for vulnerable groups, ensuring equal internet access to enhance social well-being. Health sciences/Health care Physical sciences/Mathematics and computing Subjective well-being Digital divide Machine learning Propensity score matching Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Introduction In the fast-changing digital age of the 21st century, the Internet has become a key component of modern life. It has completely changed how people communicate, work, learn, and access information(Castells, 2011 ). As digital technology spreads through every part of society, it’s important to understand how Internet access affects people’s well-being. This is a major topic for research and has big effects on policymaking, social development, and individual quality of life. One important idea in this research is Subjective Well-Being (SWB). SWB is a way to measure how people feel about their lives, including how satisfied they are and their emotional experiences (Diener, 1984 ; Diener et al., 1999 ). It shows not only how happy someone feels about their life overall but also their mental and emotional health. This makes SWB a good way to measure well-being and quality of life (Kahneman & Deaton, 2010a ; Oswald & Wu, 2010a ). SWB doesn’t just affect individuals. It has a bigger impact on health, productivity, and how well people work together in society (Helliwell et al., 2013 ; Lyubomirsky et al., 2005 ). Higher SWB often means better health, stronger relationships, and a more connected community. The digital revolution is moving fast, and its impact on well-being has become a big topic for researchers, policymakers, and global organizations like the ITU ( 2021 ), OECD ( 2019a ), and UN (2023a). There are several reasons for this focus. First, the number of Internet users has grown a lot. In 2005, there were 1 billion users. By 2021, that number had risen to 4.9 billion, covering 63% of the world’s population (ITU, 2021 ). The Internet is now a daily part of life for most people. Second, the digital economy is expanding quickly. It is reshaping how economies work, creating new jobs and business models, and changing how people work, earn money, and live (World Economic Forum, 2020 ). Third, social media and instant messaging have changed how people build and maintain relationships. This shift can affect social connections and personal well-being (Burke & Kraut, 2016 ). Fourth, the Internet offers vast amounts of information and learning opportunities. These resources can help people gain knowledge, improve skills, and feel more accomplished (Eszter & Yuli, 2013). Fifth, even though Internet access is growing, large gaps remain. These gaps can create or worsen social inequalities (Van Dijk, 2019 ). Sixth, digital health services like telemedicine, health apps, and online mental health support play a role in improving health management and well-being (Torous et al., 2019 ). Seventh, the Internet also brings challenges. Problems like cyberbullying, privacy breaches, information overload, and addiction can harm mental health (Lin et al., 2020 ). These factors show how the Internet has changed society. It has brought many benefits but also created new challenges, affecting well-being in many ways. Many research delves into the link between the Internet and well-being, showing that its impact depends on usage patterns and individual traits rather than being determined by a single factor (Reinecke et al., 2017a ; Sabatini & Saracino, 2017). This underscores the necessity of considering multiple factors, especially those that vary among different populations. Przybylski & Weinstein ( 2017a ) identified a "Goldilocks effect" in their study on adolescents' digital screen use: moderate screen time correlated with higher well-being. In comparison, both excessive and minimal use were linked to lower well-being. This finding resonates with the "rich-get-richer" hypothesis proposed by Kraut et al. ( 2002 ), highlighting the non-linear nature of the Internet's impact on well-being. Furthermore, Huang ( 2010 ) supports this view, indicating a complex, non-linear relationship between Internet use and psychological well-being. For the elderly, Internet use can enhance social capital, reduce loneliness, and improve life satisfaction (Heo et al., 2015 ; Cotten et al., 2012a ), thereby promoting social inclusion and addressing the challenges of aging. However, digital skills and the digital divide limit the realization of these benefits. Van Deursen and van Dijk ( 2010 ) emphasized the importance of digital skills. Büchi et al. ( 2015 ) found that individuals with lower socioeconomic status (SES) face difficulties in accessing and monetizing the Internet. Scheerder et al.'s ( 2017 ) review further revealed the multifaceted nature of digital inequality, including differences in motivation, access, skills, and usage patterns, which has given rise to what is known as the "secondary digital divide". Király et al. ( 2020 ) highlighted digital technology's dual role in maintaining social connections and mental health, warning of overuse risks. Balanced use is crucial. Some studies have also examined the relationship between the Internet and well-being from the perspective of countries and major events, such as the COVID-19 pandemic. Graham and Nikolova ( 2013 ) found that Internet access boosts life ratings globally using GWP data, but this varies by country and income level. Ganju et al. ( 2016 ) explored ICT development and national well-being, emphasizing national-level factors. These studies show the importance of national and cultural contexts in understanding the Internet's impact. During COVID-19, digital tools reduced loneliness and improved resilience, but overuse worsened anxiety and depression (Marciano et al., 2022 ). Karakose et al. ( 2022 ) studied the relationship between internet usage by school administrators and teachers and their well-being during the pandemic. They found that during the pandemic, the decline in the quality of life of school administrators and teachers, caused by increased feelings of loneliness, led to internet addiction, which in turn reduced their well-being. Lin et al. ( 2023 ) analyzed the relationship between adolescents' internet usage time and subjective well-being during the COVID-19 pandemic through a survey. They found that prolonged internet use during the pandemic led to a decrease in subjective well-being by promoting problematic internet use and lowering self-esteem. Existing research has valuable insights but key shortcomings. Most studies focus on specific areas, lacking global comparison. Nonlinear relationships and interactions, crucial for understanding Internet access impact, are often overlooked. Our research bridges a gap by examining internet access and health globally. We use innovative methods, key among them a large GWP dataset from 168 countries, offering a unique perspective. Advanced machine learning, like eXtreme Gradient Boosting (XGBoost) and SHAP (SHapley Additive exPlanations), uncovers complex relationships missed by traditional methods. Our longitudinal study (2016–2022) tracks changes and assesses global events' impact, like COVID-19. By integrating age, income, education, and health, we create a holistic framework. This multifaceted approach combines insights from various disciplines, providing a stronger analysis than single-discipline studies. Our results benefit academia and inform digital inclusion policies. Materials and Methodology Materials Survey Information The GWP, conducted by Gallup, Inc., is a comprehensive global survey at the individual level that provides a rich and unique data resource for studying human well-being and social attitudes. This dataset spans 18 years, from 2005 to 2022, encompassing 17 survey waves across 168 countries and territories, with a total of 2.594 million individual observations. The scale and breadth of the GWP make it the largest global dataset focused on human well-being, widely utilized in academic research and policymaking (Deaton, 2018 ; Diener et al., 2010 ; Helliwell et al., 2024 ; Jones, 2017 ). In each survey wave, the GWP samples at least 1,000 individuals per participating country, employing rigorous random sampling methods to ensure data representativeness and reliability. The survey content covers multiple aspects, including life satisfaction, emotional experiences, health status, employment situations, and educational levels, providing researchers with comprehensive information at both individual and societal levels. This multidimensional data collection enables researchers to conduct in-depth analyses of various factors affecting human well-being and explore the complex relationships among them. Detailed sampling methods and data collection procedures for the GWP are reported on Gallup's website. During the data processing phase, several critical steps are conducted to improve the usability of the dataset. Firstly, regarding internet connectivity survey data, waves 1–10 and waves 11–17 used different questioning approaches. In waves 1–10, the survey question was "Does your home have access to the internet?", while in waves 11–17, the question was "Do you have access to the internet in any way, whether on a mobile phone, a computer, or some other device?". Clearly, these two questions differ significantly in meaning, with waves 11–17 having a broader scope, focusing on whether individuals can access the internet through any means and devices, not limited to the home environment. Therefore, these two cannot be directly combined, so we chose to use data from waves 11–17, which better reflects the actual internet connectivity situation. After this step, 1035,079 observations were retained. In the remaining waves, for respondents who did not answer income-related questions, we imputed missing income values using the average income of respondents from the same country and wave. The average income was calculated by averaging other available values from the GWP survey for the corresponding country and wave. If income questions were not asked for a particular country in a specific wave, data for that country were removed. This step resulted in 1018,406 observations being retained. Furthermore, as our dependent variable is well-being, we required respondents to have answered the well-being question. This step retained 1002,937 observations. Previous research has shown that disability significantly affects human well-being (Fredrickson et al., 2013 ; Kobau et al., 2010 ); therefore, we removed observations without available answers for this variable. This left us with 994,328 observations. Given that our study focuses on the relationship between digitalization and well-being, internet usage is an essential variable, as internet connectivity is the fundamental infrastructure for digitalization. The ability to connect to the internet directly impacts the digitalization process and leads to the so-called "digital divide." Additionally, age, gender, and employment status are indispensable variables. After dropping observations with no-answer items for these variables, our final dataset retained 963,870 observations. Subjective Well-Being Measurement As a metric for capturing human well-being, SWB has gained substantial validation in the literature (Diener, 1984 ; Diener et al., 2018 ; Oswald & Wu, 2010). Among various approaches to quantifying SWB, overall life evaluation stands out as a particularly valuable technique (Diener et al., 2018 ; Helliwell & Aknin, 2018 ; Kahneman & Deaton, 2010), allowing researchers to derive well-being assessments from how individuals perceive the overall quality of their lives. The GWP utilizes the Cantril ladder—an 11-point scale developed by psychologist Hadley Cantril in the 1960s (Hadley Cantril, 1965 )—to capture this dimension of human well-being. When responding to this instrument, participants visualize a vertical scale anchored at two extremes: the lowest point (0) symbolizes the most unfavorable life circumstances imaginable, while the highest point (10) denotes an ideal life scenario. Participants then position themselves on this scale based on their perceived current life conditions, yielding a numerical score between 0 and 10. This self-anchoring design enables meaningful comparisons across diverse cultural contexts, as respondents apply their own subjective criteria when making evaluations. Given its accessibility and established track record in prior investigations (Blanchflower, 2021 ; Jebb et al., 2018 ), we employ this indicator as our dependent variable. Independent Variables For this research, we utilized a dataset with 66 independent variables, which are "Age", "Anger", "Approval of Leadership Performance", "Assaulted", "Children Under15", "Confidence in Election Honesty", "Confidence in Financial System", "Confidence in Judicial System", "Confidence in Local Police", "Confidence in Military", "Confidence in National Government", "Corruption within Business", "Corruption within Government", "Country", "Donated", "Economic Changing Direction", "Economic Rating", "Education", "Employment", "Enjoyment", "Enough Food", "Enough Shelter", "Feeling Income", "Freedom of Choosing Life", "Freedom of Media", "Gender", "Good Place for Ethnic Minority", "Good Place for Gay or Lesbian", "Good Place for Immigrants", "Having Relatives to Rely on", "Health Disability", "Help Stranger", "Household Income", "Income Level", "Interesting Things", "Internet Access available", "Living Standard Changing Direction", "Local Job Outlook", "Marital Status", "Native-born", "Opportunity for Children Learning", "Physical Pain", "Recommended Live Place", "Religious importance", "Respected", "Sadness", "Safety of Alone Night Walking", "Satisfied with Affordable House", "Satisfied with Air Quality", "Satisfied with City", "Satisfied with Education", "Satisfied with Environmental Efforts", "Satisfied with Healthcare", "Satisfied with Opportunity to Make Friends", "Satisfied with Poverty Alleviation", "Satisfied with Public Transportation", "Satisfied with Road", "Satisfied with Water Quality", "Smile", "Stolen", "Stress", "Voiced Opinion to Official", "Volunteer", "Wave", "Well Rested", and "Worry". Methodology The overall methodological workflow of the study is shown in Fig. 1 . Starting from the raw Gallup data, we perform preprocessing and feature engineering, then use an XGBoost classifier to estimate the propensity scores for internet connection and conduct PSM matching. Afterward, we run SMD balance tests on the matched samples and build stratified XGBoost regression models to predict subjective well-being. Finally, we use SHAP to interpret the contribution of variables to subjective well-being and conduct comparative analyses. The Impact of Internet Access on Well-being As digital technology keeps growing, more people are paying attention to how it affects well-being (OECD, 2019; United Nations, 2023). Research shows that digitalization, like internet access, usually has a positive effect on well-being (Castellacci & Tveito, 2018; Przybylski & Weinstein, 2017). The size of the effect can differ between groups. Still, it seems to match what we expect and see in daily life. However, we still do not have clear global data to fully understand or explain this connection. Due to limitations in data volume and technological capabilities, linear regression always served as a compromise yet effective method for analyzing this relationship. The linear regression technology is not particularly adept at fitting non-linear relationships. In contrast, machine learning models are designed to optimize predictive accuracy by minimizing prediction errors (Chen & Guestrin, 2016 ). Furthermore, machine learning models do not make assumptions about the shape of relationships, which enhances their capacity to fit non-linear relationships (Bentéjac et al., 2021 ; Chen & Guestrin, 2016 ). This study employs a Propensity Score Matching (PSM) model enhanced by machine learning techniques to replace traditional PSM models. This method deals with selection bias and confounding factors, making good use of the advantages of machine learning models. As a result, the reliability and accuracy of analysis are significantly improved. In studying the complex relationship between digitalization and well-being, this kind of methodological thinking is very important. Since the relationship might not be linear, we need analysis methods that can catch more detailed patterns, not just simple linear ones. Machine learning offers a promising way to find these complex connections, helping us better understand how digitalization affects well-being in different situations and groups of people. XGBoost model and its fine-tuning This study investigates the empirical association between digitalization and well-being through a machine learning framework. Given that machine learning algorithms lack the interpretability of conventional linear approaches, we incorporate explainability techniques to uncover their underlying mechanisms (Christoph Molnar, 2020 ; Lundberg et al., 2020 ). Specifically, we employ the XGBoost regressor as an alternative to linear regression and comparable methods prevalent in earlier literature, enabling us to characterize the digitalization-well-being nexus. As the outcome variable constitutes an 11-point Cantril Ladder measure of subjective well-being, we frame this as a regression problem. The SHAP framework (Lundberg et al., 2020 ) serves as our primary tool for model interpretation. XGBoost presents multiple methodological advantages for this analysis. As an algorithm grounded in decision tree architecture (Chen & Guestrin, 2016 ), it excels at modeling intricate non-linear patterns within feature-rich tabular datasets (Bentéjac et al., 2021 ). Decision trees accommodate diverse variable types—binary, continuous, and categorical—without difficulty. Moreover, this approach is fully non-parametric, imposing no distributional assumptions on the underlying data (Chen & Guestrin, 2016 ). A well-known limitation of single decision trees is their susceptibility to overfitting when permitted excessive depth. This shortcoming is mitigated through ensemble strategies, including gradient boosting and random forests, which aggregate multiple decision trees as base learners to achieve superior predictive accuracy. While conventional gradient boosting operates sequentially and resists parallelization (Chen & Guestrin, 2016 ), XGBoost represents an enhanced implementation featuring parallel processing capabilities and GPU support. Consequently, XGBoost constitutes our principal analytical tool. The XGBoost regressor training procedure for the complete dataset follows this formulation: $$\:{XGB}_{td}=\text{G}({\varvec{I}\varvec{t}\varvec{r}}_{td},\:{\varvec{j}\varvec{t}\varvec{r}}_{td},\:{\varvec{H}\varvec{P}}_{td})$$ 1 In this expression, \(\:{XGB}_{td}\) ​ denotes the trained XGBoost model utilizing the full dataset encompassing all predictors and observations; \(\:{\varvec{I}\varvec{t}\varvec{r}}_{td}\) ​ indicates the predictor matrix from the training partition; \(\:{\varvec{j}\varvec{t}\varvec{r}}_{td}\) signifies the response variable within the training partition; \(\:{\varvec{H}\varvec{P}}_{td}\) tspecifies the hyperparameter configuration for optimal model performance; and \(\:\text{G}\) symbolizes the learning algorithm. We allocate data between training and testing subsets at a 9:1 ratio—specifically, 90% for model development and the remaining 10% for validation purposes The hyperparameter configuration \(\:{\varvec{H}\varvec{P}}_{td}\) encompasses: tree count ("n_estimators"), individual tree depth limit ("max_depth"), step size shrinkage ("learning_rate"), loss threshold for node splitting ("gamma"), minimum child node weight ("min_child_weight"), training instance sampling proportion ("subsample"), weight update magnitude constraint ("max_delta_step"), L1 weight penalty ("reg_alpha"), and L2 weight penalty ("reg_lambda"). These parameter identifiers in quotation marks correspond directly to the XGBoost Python API, ensuring reproducibility. Optimal hyperparameters are identified via 10-fold cross-validation, with test set R² serving as the optimization criterion. The model’s predictions on the test set are given by: $$\:\widehat{{\varvec{j}\varvec{t}\varvec{e}}_{td}}={XGB}_{td}\left({\varvec{I}\varvec{t}\varvec{e}}_{td}\right)$$ 2 $$\:{R}_{test\:td}^{2}=1-\frac{{({\varvec{j}\varvec{t}\varvec{e}}_{td}\:-\:\widehat{{\varvec{j}\varvec{t}\varvec{e}}_{\varvec{t}\varvec{d}}})}^{2}}{{({\varvec{j}\varvec{t}\varvec{e}}_{td}\:-\:\stackrel{-}{{\varvec{j}\varvec{t}\varvec{e}}_{td}})}^{2}}$$ 3 Here, \(\:\widehat{{\varvec{j}\varvec{t}\varvec{e}}_{td}}\) denotes the predictions generated by the well-trained XGBoost model \(\:{XGB}_{td}\) on the test dataset \(\:{\varvec{I}\varvec{t}\varvec{e}}_{td}\) , while \(\:\stackrel{-}{{\varvec{j}\varvec{t}\varvec{e}}_{td}}\) represents the actual mean of the independent variable. Additionally, \(\:{R}_{test\:td}^{2}\) is the R 2 metric computed on the test dataset using the model trained on the training set extracted from the entire dataset. Combining Equations ( 1 ), ( 2 ), and (3), it is evident that \(\:{R}_{test\:td}^{2}\) is significantly related to the model's hyperparameters. Hyperparameter optimization employs a Bayesian approach (Turner et al., 2021 ), which proceeds through four stages: initialization using preliminary hyperparameter configurations, surrogate model construction, iterative hyperparameter proposal with performance estimation, and surrogate refinement. Our implementation executes 50 optimization cycles. The surrogate function maps hyperparameter inputs to estimated test R² values. Hyperparameter search boundaries are specified as: "n_estimators" spanning 300–4000; "learning_rate" within 0.005–0.1; "max_depth" between 5–16; "subsample" ranging 0.5–0.8; "min_child_weight" from 0.1–10; "max_delta_step" covering 0.01–10; "gamma" across 0.001–5; "reg_alpha" within 0.001–5; and "reg_lambda" spanning 0.1–10. Comparative analysis between 50-iteration Bayesian optimization and exhaustive grid search (exceeding 2,000 configurations) demonstrated superior performance from the Bayesian approach. Although extended grid search might yield incremental improvements, the associated computational burden renders this impractical. Thus, Bayesian optimization is adopted for hyperparameter tuning across all XGBoost models in this research. Propensity Score Matching (PSM) and its testing In our investigation of how digitalization (internet access) affects people's well-being, PSM (Rosenbaum & Rubin, 1983 ) emerges as a crucial methodology, enabling us to discern this impact more accurately. PSM, in essence, facilitates a fair comparative experiment. Consider the scenario where we directly compare the well-being of individuals with and without internet access; we might conclude that internet access enhances well-being. However, this approach is problematic because those with internet access may inherently possess superior living conditions, such as higher income or education levels, factors that could independently contribute to greater well-being. PSM addresses this issue. The method begins by identifying all significant factors influencing an individual's likelihood of internet access, including age, income, educational attainment, and other relevant variables. Subsequently, based on these factors, it calculates the probability of each individual obtaining internet access, termed the "propensity score". As demonstrated in Eq. 4 , The propensity score e(X) is the probability that an individual will receive the treatment given the covariate X . where: T is a dichotomous treatment variable (e.g., 1 means accepting the treatment, 0 means not accepting the treatment) and X is a vector of covariates. $$\:\varvec{e}\left(\varvec{X}\right)=\varvec{P}(\varvec{T}=1\mid\:\varvec{X})$$ 4 Subsequently, we match each individual with internet access to one or several individuals without internet access but with very similar conditions (i.e., comparable propensity scores) as comparative subjects. This methodology allows us to ensure, to the greatest extent possible, that the two groups being compared are similar in all aspects except for internet access, thereby minimizing confounding effects from other factors. In our study, we employ the XGBoost Classifier as the propensity score model due to its capacity to handle complex non-linear relationships, sensitivity to feature interactions, and excellent performance with high-dimensional data. We use BayesSearch for hyperparameter tuning to optimize model performance, focusing on parameters such as n_estimators, learning_rate, and max_depth. We aim to maximize the ROC-AUC score during the optimization process, employing 10-fold cross-validation and setting 50 iterations to search for the optimal parameter combination. The model results show that the training accuracy is 88.58% and the testing accuracy is 84.69%; the ROC AUC for the training set is 95.10%, and the ROC AUC for the testing set is 91.84%. These results indicate that the model has good generalization ability and does not suffer from severe overfitting. Following the construction of the propensity score model, we calculate propensity scores for each observation, representing the probability of each individual obtaining internet access. To balance matching quality and post-matching sample size, we set the caliper to 0.2, implying a matching tolerance of 0.2 standard deviation units, and restrict each control unit to be matched only once to prevent overuse of certain control samples, which could affect subsequent model training. To enhance processing efficiency for large datasets, we implement the BallTree data structure for efficient nearest neighbor search and adopt a batch processing approach, handling 10,000 samples per batch. Post-PSM matching, the sample size is 321,910. However, the application of PSM alone is insufficient; we must ensure the effectiveness of this matching. This is where the Standardized Mean Difference (SMD)(Jacob Cohen, 1988 ) method proves valuable. SMD serves as a verification tool, helping us validate whether PSM has indeed made the two groups more similar across various aspects. Its operational principle is straightforward: for each factor under consideration (e.g., age, income), SMD calculates the average difference between the groups with and without internet access, then standardizes this difference. As shown in Eq. 5 , µ_t represents the mean of the treatment group (with internet access), µ_c is the mean of the control group (without internet access), σ²_t denotes the variance of the treatment group, and σ²_c is the variance of the control group. This formula can be interpreted as the mean difference between the two groups divided by the average of their standard deviations. $$\:\varvec{S}\varvec{M}\varvec{D}\:=\:(\varvec{\mu\:}\_\varvec{t}-\:\varvec{\mu\:}\_\varvec{c})\:/\:\sqrt{\left(\right(\varvec{\sigma\:}²\_\varvec{t}\:+\:\varvec{\sigma\:}²\_\varvec{c})\:/\:2)}$$ 5 Generally, an SMD value less than 0.1 typically indicates good balance. By comparing the SMD values before and after matching (The absolute mean value before matching was 0.13, and the absolute mean value after matching was 0.03), we confirm that PSM effectively enhanced the similarity between the two groups, significantly reducing the imbalance in covariates. The post-matching SMD value, well below 0.1, indicates a good balance (See Table 1 for details.). Table 1 : Comparison of SMD for Variables Before and After Matching (except "Country") Table 1 Comparison of SMD for Variables Before and After Matching Variable SMD Before SMD After Wave 0.35 0.09 Household Income 0.60 0.12 Cantril Ladder 0.54 0.17 Health Disability -0.42 -0.10 Having Relatives to Rely on 0.39 0.09 Living Standard Changing Direction 0.26 0.07 Enough Food -0.54 -0.12 Enough Shelter -0.36 -0.08 Well Rested 0.10 0.03 Respected 0.21 0.05 Smile 0.17 0.05 Interesting Things 0.26 0.07 Enjoyment 0.26 0.06 Physical Pain -0.35 -0.09 Worry -0.19 -0.05 Sadness -0.27 -0.07 Stress -0.03 -0.01 Anger -0.12 -0.02 Satisfied with City 0.14 0.03 Recommended Live Place 0.23 0.06 Economic Rating 0.31 0.07 Economic Changing Direction 0.12 0.03 Local Job Outlook 0.06 0.03 Satisfied with Public Transportation 0.06 0.02 Satisfied with Road 0.15 0.03 Satisfied with Education 0.05 0.01 Satisfied with Air Quality -0.06 -0.02 Satisfied with Water Quality 0.17 0.05 Satisfied with Healthcare 0.14 0.04 Satisfied with Affordable House -0.01 0.01 Satisfied with Opportunity to Make Friends 0.09 0.02 Good Place for Ethnic Minority 0.08 0.03 Good Place for Gay or Lesbian 0.47 0.10 Good Place for Immigrants 0.21 0.05 Donated 0.27 0.07 Volunteer 0.06 0.02 Help Stranger 0.16 0.05 Voiced Opinion to Official 0.07 0.03 Confidence in Local Police 0.02 0.01 Safety of Alone Night Walking 0.17 0.03 Stolen -0.09 -0.01 Assaulted -0.09 -0.01 Religious importance -0.58 -0.11 Opportunity for Children Learning 0.06 0.02 Satisfied with Poverty Alleviation -0.10 -0.01 Satisfied with Environmental Efforts -0.14 -0.02 Freedom of Choosing Life 0.12 0.03 Confidence in Military -0.01 0.00 Confidence in Judicial System -0.09 -0.02 Confidence in National Government -0.22 -0.04 Confidence in Financial System -0.01 0.00 Confidence in Election Honesty -0.02 0.00 Freedom of Media 0.07 0.02 Corruption within Business -0.06 0.00 Corruption within Government -0.02 0.01 Approval of Leadership Performance -0.13 -0.02 Gender_female -0.14 -0.03 Age -0.27 -0.07 Education 1.17 0.09 Marital Status -0.14 -0.03 Employment -0.48 -0.10 Children Under15 -0.28 -0.04 Feeling Income -0.67 -0.15 Native-born -0.13 -0.03 Income Level 0.38 0.09 Such a marked improvement in covariate balance strengthens the validity of our subsequent analyses, as it minimizes the potential for confounding effects and enhances the comparability between the treatment and control groups. This approach to matching and balance assessment helps enhance the credibility of our study’s findings regarding the impact of internet access on well-being. Stratified XGBoost Analysis Following the completion of PSM and SMD, this study further employed a stratified modeling approach. Two independent XGBoost models were constructed for groups with and without internet access, respectively. This methodology allows for an in-depth exploration of how internet access moderates various factors influencing SWB. Through this stratified analysis, we were able to identify and compare key predictors of well-being across these two subpopulations. The models are presented as follows: $$\:\left\{\begin{array}{c}\begin{array}{c}{XGB}_{a}=G\left({\varvec{I}\varvec{t}\varvec{r}}_{\varvec{a}},\:{\varvec{j}\varvec{t}\varvec{e}}_{\varvec{a}},\:{\varvec{H}\varvec{P}}_{a}\right)\\\:{XGB}_{u}=G\left({\varvec{I}\varvec{t}\varvec{r}}_{\varvec{u}},\:{\varvec{j}\varvec{t}\varvec{e}}_{\varvec{u}},\:{\varvec{H}\varvec{P}}_{u}\right)\end{array}\end{array}\right.$$ 6 where \(\:{XGB}_{a}\) and \(\:{XGB}_{u}\) denote the well-train XGBoost regression models based on the internet access available population and internet access unavailable population, respectively, \(\:{\varvec{I}\varvec{t}\varvec{r}}_{\varvec{a}}\) and \(\:{\varvec{I}\varvec{t}\varvec{r}}_{\varvec{u}}\) represent the independent variables of the training dataset split from the access available population and internet access unavailable population datasets, respectively, \(\:{\varvec{j}\varvec{t}\varvec{e}}_{\varvec{a}}\) and \(\:{\varvec{j}\varvec{t}\varvec{e}}_{\varvec{u}}\:\) represent the dependent variables of those two datasets, and \(\:{\varvec{H}\varvec{P}}_{a}\) and \(\:{\varvec{H}\varvec{P}}_{u}\) denote three distinct groups of hyperparameters used to train high-accuracy XGBoost models for each sub-dataset. We also employ cross-validation to identify the optimal hyperparameter sets following the same procedure outlined in Equations ( 1 ), ( 2 ), and (3) . Additionally, it must be noted that the independent variable “internet access available” is not included in the sub-dataset, when training the models and predicting. The models with and without internet access achieved accuracies of 28.34% and 26.89%, respectively, with MAE values of 1.44 and 1.59. Given the individual variability and measurement fluctuations inherent in subjective well-being, this level of accuracy is acceptable. Moreover, the optimized XGBoost model reduced prediction error by an average of 51.5% compared with the mean baseline, demonstrating that the model successfully captured the predictive patterns influencing subjective well-being. This approach's advantage lies in its ability to determine whether internet access affects well-being and elucidate the mechanisms of its influence. By comparing variables' relative importance and effect sizes across the two models, we can reveal how internet access moderates the relationships between various socioeconomic and behavioral factors and SWB. This stratified modeling approach provides a more nuanced analytical framework, enabling us to capture heterogeneous effects that might be overlooked in an aggregate analysis. This contributes to a more comprehensive understanding of the digital divide's impact on well-being and provides an empirical foundation for formulating targeted policy interventions. Contributions of Independent Variables to Well-being The non-parametric nature of tree-based ensemble algorithms, including XGBoost, poses substantial challenges for result interpretation (Christoph Molnar, 2020 ). To address this limitation, the SHAP method has emerged as an innovative and robust framework for quantifying how each predictor individually influences the outcome variable within machine learning contexts (Lundberg et al., 2020 ). Rooted in cooperative game theory and the concept of Shapley values, this technique guarantees an equitable and balanced attribution of predictor contributions to model outputs (Christoph Molnar, 2020 ; Lundberg et al., 2020 ). Operationally, Shapley values are derived by measuring prediction shifts in a fully trained model when a target predictor is introduced across all feasible combinations of the other predictors, subsequently computing the mean of these incremental effects. The predictor-level contribution for each observation can be formalized as: $$\:{\varvec{S}\varvec{H}\varvec{A}\varvec{P}\varvec{t}\varvec{e}}_{td}=\theta\:({\varvec{X}\varvec{G}\varvec{B}}_{td},\:{\varvec{I}\varvec{t}\varvec{e}}_{td})$$ 7 In this formulation, \(\:{\varvec{X}\varvec{G}\varvec{B}}_{td}\) signifies the XGBoost regression or classification model developed from training data extracted from the complete dataset, \(\:\varvec{S}\varvec{H}\varvec{A}\varvec{P}\) refers to the canonical SHAP computational procedure, and \(\:{\varvec{S}\varvec{H}\varvec{A}\varvec{P}\varvec{t}\varvec{e}}_{td}\) captures the attribution scores for every predictor-observation pair within the test subset. From a theoretical standpoint, applying the trained XGBoost model in conjunction with the SHAP algorithm to interpret all observations remains feasible even under overfitting conditions. This robustness stems from SHAP's exhaustive enumeration of all predictor subsets containing the variable under examination. Within this comprehensive collection of subsets, only a single configuration matches the complete input feature set. Should the model have memorized training observations during fitting, its predictive accuracy on those instances would substantially exceed that on novel observations. To circumvent this concern, our analysis restricts attention to test set observations. An alternative strategy involves implementing a 10-fold explanation protocol across the entire dataset, analogous to 10-fold cross-validation: partitioning observations into ten segments, fitting XGBoost on nine segments, generating SHAP explanations for the held-out segment, and cycling through until all segment combinations are exhausted. Nevertheless, SHAP computation demands considerable resources. Each test subset comprises roughly 90,000 records (the dual model variant contains 11,000 observations). Under reasonable computational parameters, a minimum of 50 GPU hours is required to complete the analysis (stratified XGBoost analyses each consume approximately 5 GPU hours). Results Overall Analysis This study examines how internet access affects people's well-being. It used the Cantril ladder score (0–10) to measure well-being. To make sure the groups were comparable, the study used a method called PSM. The results show a clear link between internet access and higher well-being. On average, people with internet access had a Cantril ladder score of 5.38. In contrast, those without access scored 4.92. This gives a difference of 0.46 points. The difference is highly significant, with a t-value of 49.69 and a p-value of less than 0.0001. This means it is very unlikely that the difference is due to chance. A kernel density estimation (KDE) plot (Fig. 2 ) helps explain these findings. It shows how well-being scores are distributed in both groups. Both groups have a similar shape in their distributions, with a peak around 5 points. This may reflect a common "moderate well-being" level. However, people with internet access had a slightly higher distribution above 5 points, matching their higher average score. The internet access group also had more people scoring between 6 and 8 points. This suggests that internet access might improve moderate to high well-being levels. On the other hand, the non-internet access group had a higher density of scores between 0 and 3 points. This suggests that internet access might help reduce very low well-being scores. Temporal and Regional Analysis From 2016 to 2022, internet access had a changing impact on well-being (Fig. 3 ). The positive effects rose and fell over this time. In 2016, the effect was strongest. People with internet access scored 0.58 points higher on the Cantril ladder compared to those without access. By 2018, this dropped to 0.38 points. Then, it rose again, peaking at 0.47 points in 2020. After 2020, the effect declined, reaching 0.37 points in 2022. This pattern reveals some important points. First, internet access improved well-being throughout the seven years, but the strength of the effect changed. Second, the changes in effect size may reflect shifts in the world. For example, the 2018 drop might link to data scandals like those involving Facebook, rising trade tensions between the US and China, and global economic worries. The 2020 increase likely happened because the internet became more important for social connections, remote work, and information during COVID-19. Third, the decline from 2020 to 2022 is worth noting. It could mean the digital divide narrowed, pandemic restrictions eased, and offline activities resumed, lowering internet reliance. It might also show growing concerns about too much internet use, such as addiction or information overload. Looking at developed and developing countries gives more insight (Fig. 4 ). Both groups followed similar patterns, but developed countries saw stronger overall effects from internet access. This difference could come from better digital infrastructure, higher digital skills, and more uses for the internet in developed nations. The big 2020 peak shows the internet was key for social and personal well-being during the global crisis, especially in developed countries. This reflects their faster shift to remote work, online learning, and digital socializing. However, both groups saw a drop in the effect from 2020 to 2022. The decline was sharper in developing countries. This may reflect challenges like weaker digital systems, uneven economic recovery, or struggles to keep using digital tools after the pandemic. For developed countries, the slower decline might suggest they reached a balance where the internet is fully part of daily life, its extra benefits have leveled off. Furthermore, through an in-depth analysis of two periods - before and after COVID-19 (2016–2019 and 2020–2022)—shows how internet access affected well-being differently across countries (Figs. 5 and 6 ). Most countries had positive effects in both periods, but the strength of these effects varied. Many countries, especially in the Americas, Europe, and East Asia, saw a rise in the effect during the second period. This lines up with the COVID-19 outbreak, supporting the idea that the internet played a key role during the crisis. High internet use and smaller digital divides in these regions likely helped. However, not every country followed this upward trend. Some, like India, Finland, and Australia, saw declines in the effect during 2020–2022. These differences may reflect how each country handled the crisis and used digital tools. This shows that the internet’s impact on well-being during the pandemic was complex and varied. Analysis of influencing factors Analysis of factors affecting Internet access Based on our analysis of the SHAP values for various variables, we can gain a comprehensive understanding of the key factors influencing the prediction of internet connectivity. Age, income, education level, and health status all affect the model’s predictions to varying degrees, as shown in Fig. 7 . Age shows a significant negative correlation with predicted internet connectivity: the younger cohort aged 0–40 is more likely to be predicted as having internet connectivity, with predominantly positive SHAP values; the middle-aged group of 40–60 years begins to show a negative influence; and the elderly group above 60 years exhibits markedly negative SHAP values that decrease with increasing age. This reflects the disparities in technological adaptability and usage habits across different age groups. Household Income displays a strong positive correlation with predicted internet connectivity. Low-income groups have negative SHAP values, indicating a reduced likelihood of predicted internet connectivity, while high-income groups show significantly positive SHAP values with a broad range of influence, underscoring the crucial role of economic factors in internet access. Notably, the impact of income exhibits a saturation effect at higher levels, suggesting that beyond a certain income threshold, further increases have a diminishing effect on internet connectivity predictions. Educational attainment similarly exhibits a strong positive influence. Low education levels (primary school and below) are associated with negative SHAP values, middle education levels (secondary school) show relatively neutral effects, and higher education levels demonstrate markedly positive SHAP values. This trend presents non-linear characteristics, with the transition from low to middle education levels having a more pronounced impact on prediction outcomes, emphasizing the significance of basic education in bridging the digital divide. Although exerting a comparatively minor influence, health status reveals noteworthy patterns. Individuals without health issues have slightly positive SHAP values, while those with health problems affecting daily activities show negative SHAP values. This suggests that health impediments may indirectly affect internet access by influencing an individual's economic status, social interactions, or ability to use devices. Difference analysis of variable contribution in Stratified XGBoost models Based on our comparative analysis of SHAP values for various variables in both models, we can comprehensively understand the key factors influencing well-being with and without internet connectivity. By comparing the importance and degree of difference among variables, we have once again selected age, income, education, and health status as critical variables for analysis, as shown in Fig. 8 . In the age dimension, the impact of the internet on well-being exhibits a pronounced U-shaped curve. For individuals under 20 and over 50, the SHAP value distributions are generally consistent regardless of internet access, indicating that internet connectivity has little influence on their happiness. However, there are significant differences among individuals aged 20–50. In this age group, although the SHAP values are negative in both scenarios, those with internet access show significantly higher SHAP values compared to those without. This may reflect the effects of learning, work-related stress, and family responsibilities on young and middle-aged individuals—issues that the internet cannot fundamentally resolve but can help alleviate to some extent. In the dimension of household income, internet access has a notably different impact across income groups. For low-income individuals (annual income below 5,000), SHAP values improve with internet access, shifting from entirely negative (-1.0 to 0) to partially positive (-0.5 to 0.25). This suggests that the internet may provide more economic opportunities and better access to information, thereby improving life satisfaction for low-income groups to some extent. For middle-income groups (annual income between 5,000 and 10,000), the SHAP value trends are largely similar regardless of internet access, showing an upward trajectory, which indicates that increasing income itself improves life satisfaction and that internet access has limited additional impact. The same holds true for high-income groups (annual income over 10,000), where SHAP values remain stable between 0 and 0.75 with or without internet access. This suggests that high-income individuals already have sufficient resources and channels to fulfill their information, social, and entertainment needs, making the presence of internet access less influential on their quality of life. Regarding education level, the impact of internet access also varies across different educational backgrounds. For individuals with low education levels (primary school), SHAP values increase from mostly negative (-0.25 to 0) to partially positive (-0.2 to 0.1) with internet access, indicating that the internet may help bridge educational gaps through online learning and skill development. For those with medium education levels (middle to high school), the distribution of SHAP values becomes broader with internet access (-0.05 to 0.15 compared to 0 to 0.15 without), which may reflect new challenges introduced by the internet, such as youth internet addiction. Interestingly, for highly educated individuals, SHAP values decrease from 0.02–0.3 without internet to 0–0.2 with internet access. This shift warrants further research and may be related to unique pressures faced by highly educated individuals in the digital age. In terms of health status, internet access appears to play a moderating role in the relationship between physical health and well-being. For individuals without health problems, internet access slightly reduces the positive impact on well-being (SHAP values decline from 0–0.15 to -0.05–0.12), which may be linked to sub-health conditions caused by excessive use of electronic devices. However, among individuals with health issues, although most SHAP values remain in the negative range, those with internet access show a noticeably higher proportion of positive values. Their SHAP values expand from a range of -0.3 to 0.05 (no internet) to -0.3 to 0.15 (with internet). This finding highlights the potential of the internet in supporting telemedicine consultations, access to health information, and chronic disease management. Discussion Our research shows that internet access has a clear and positive effect on well-being. People with internet access score higher on well-being (5.32) compared to those without it (4.96). This highlights how internet connectivity can improve well-being. It supports earlier studies that show the internet helps people by providing access to information, connecting socially, and offering economic opportunities (World Bank, 2016 ; Castellacci & Tveito, 2018c ). The kernel density plot (Fig. 2 ) gives us a closer look at well-being scores. It shows that people with internet access tend to have moderate to high levels of well-being. This might be because the internet helps with personal growth, social activities, and access to useful resources (Lissitsa & Chachashvili-Bolotin, 2016 ). On the other hand, the slightly higher density of low scores (0–3) in the group without internet access suggests that lack of connectivity may be associated with a higher risk of extremely low well-being, highlighting the potential of internet access as a protective factor against severe declines in life satisfaction. Our time series analysis from 2016 to 2022 shows that the relationship between Internet access and well-being is evolving under the influence of global events and social changes, with significant differences observed across different types of countries. We saw a peak in 2020, which aligns with the COVID-19 pandemic. During this time, the positive effects of internet access increased, supporting findings that digital technologies were crucial for staying connected, working remotely, and getting information during lockdowns (Beaunoyer et al., 2020 ; Nguyen et al., 2020 ). However, from 2020 to 2022, the effect started to decrease. This trend needs careful analysis. It might mean people are getting used to the internet in daily life, leading to less noticeable benefits. Or it could suggest a growing awareness of downsides like information overload or digital fatigue (Reinecke et al., 2017b ). Internet access has had a stronger positive effect in developed countries than in developing ones. This shows the link between digital infrastructure, economic development, and well-being. Developed countries likely benefit from better digital systems, higher digital literacy, and more varied internet use (Pick & Sarkar, 2015 ). In contrast, developing countries faced a sharper decline in the internet's positive effects after 2020. This highlights their challenges in maintaining digital progress post-pandemic and the need for targeted policies and investments to close the digital gap(Broadband Commission, 2020 ). We also examined other factors affecting internet access and its impact on well-being. There is a negative correlation between age and internet use, with younger people being more likely to have internet access, indicating generational differences in technology adoption (Friemel, 2014 ). Interestingly, the impact of internet access on well-being forms a U-shaped curve across different age groups, where internet connectivity can somewhat alleviate the negative impact on well-being for younger and middle-aged groups. For young and middle-aged people, this might be related to the internet providing more career development and social opportunities (García Galera et al., 2013 ). Income is strongly correlated with internet access, showing that economic barriers are a significant factor in accessing the internet (Cai, 2008 ). However, internet access can alleviate some of the negative effects faced by low-income groups, which is consistent with research on the internet's ability to promote economic opportunities and reduce inequalities (World Bank, 2016 ). Education plays a key role in internet access and its impact on well-being. Digital literacy is crucial for maximizing online benefits(van Deursen & van Dijk, 2010 ). However, there’s an unexpected drop in the positive impact of internet access for highly educated groups, which needs further study. It could reflect unique challenges these groups face in the digital age. Lastly, internet access significantly moderates the relationship between physical health and well-being. This aligns with research on the benefits of online health services and telemedicine. For people with health issues, the internet makes it easier to access health information and services, improving their outcomes(Litchfield et al., 2021 ). Our study's approach and findings greatly enhance understanding of the link between digitalization and well-being, showing clear benefits over earlier research. First, we used the XGBoost regression model instead of traditional linear regression. This model captures complex, non-linear relationships and interactions between variables. This is crucial when studying complex social topics like how internet access affects well-being. For instance, (Castellacci & Tveito, 2018c )noted that many studies use linear models to explore this link, which might miss non-linear effects. Our XGBoost model, with its tree structure and ensemble learning, captures these complex patterns, providing a more accurate analysis. Second, we applied the PSM method to address selection bias, improving on many past studies. (Lissitsa & Chachashvili-Bolotin, 2016 ) conducted a large-scale study on internet use and life satisfaction in Israel from 2003 to 2013. However, they mainly used multivariate regression without fully controlling for the endogeneity between internet access and other socioeconomic factors. Our PSM approach reduces the influence of these confounding factors by creating comparable treatment and control groups. Our SMD results validate this; the average absolute SMD dropped from 0.12 to 0.02 after matching, well below the standard threshold of 0.1. This enhances the reliability of our research findings. Third, we used SHAP to interpret our model's results, adding depth to traditional regression coefficient interpretation. Compared to Jebb et al., 2018 , our approach not only pinpoints key factors affecting well-being but also measures the contribution of each factor in various contexts. This method offers a more detailed analysis, showing different effects of internet access on well-being across income groups or age brackets. Lastly, our research uses a large dataset from the GWP dataset, covering 17 survey waves from 2005 to 2022 across 168 countries and regions, with 2.594 million observations. After careful cleaning and processing, our final sample includes around 1 million observations. While this reduced our sample size, the data's scale and scope still surpass many previous studies. For instance, (Çikrıkci, 2016 ) studied the impact of internet use on well-being in more detail but had a shorter time span and smaller sample size compared to ours. We reduced our sample to ensure high data quality, removing incomplete records and ensuring consistency across time and regions. This processed dataset enhances the representativeness and generalizability of our findings and allows detailed cross-country and time trend analyses. This large, multi-country dataset helps us thoroughly examine the impact of internet access on well-being, considering various socioeconomic factors. Overall, our research provides more comprehensive, accurate, and reliable insights into the impact of internet access on well-being by combining advanced machine learning techniques, rigorous methods, and large-scale cross-national data. These methodological innovations enable us to move beyond simple correlation analysis, revealing more complex and nuanced relationship patterns, and providing more valuable reference for policymakers and researchers. Our study has many strengths, but there are still some important limitations. These point to good directions for future research. First, we used advanced methods like PSM to reduce selection bias. However, since our data is cross-sectional, it is hard to draw clear cause-and-effect conclusions. Future studies could use designs like experiments or follow people over time. These approaches could show how internet access impacts well-being in the long run. Second, we mostly looked at whether people had internet access or not. We didn’t focus much on the quality of access, like speed and reliability, or how people use the internet. Future research could gather more details about this. For example, they could study how often people go online, what they do, and if the speed of their connection matters. This could give a clearer picture of how the internet affects well-bing. Third, we used SHAP methods to explain the results of our XGBoost model. But machine learning models are still difficult to fully understand due to their “black box” nature. Future research could try other methods that are easier to explain. Combining these with interviews or surveys could also help. This would make it easier for researchers and policymakers to understand the results. By solving these issues, future studies can help us learn more about the link between the internet and well-being. They can also provide better evidence for creating policies to improve people’s lives in the digital age. Conclusion This study uses the GWP global dataset from 2016 to 2022 to explore how internet access affects well-being. We found clear evidence that internet access has a positive impact on people’s well-being. However, the effects are different for various groups of people. The results show that having internet access improves well-being, especially during the COVID-19 pandemic. After the pandemic, the positive effects gradually became weaker through 2022.The impact of internet access also depends on the region. In developed countries, the benefits are stronger and more stable. In developing countries, the effects are less consistent. Using XGBoost and SHAP analysis, we also found some interesting patterns. For example, internet access can alleviate the negative impact on well-being experienced by young and middle-aged groups. When we looked at income, we found that internet access is most helpful for people in low-income groups. For education, those with less schooling benefit more from having internet access. Internet access also helps people with health problems feel better by reducing the negative effects of those issues. These findings have crucial implications for policymaking, suggesting the need for targeted digital inclusion strategies considering age-specific needs, continued enhancement of digital infrastructure, especially in developing countries, development of comprehensive digital health services, and tailored digital literacy education programs. Declarations Funding This research was supported by JSPS KAKENHI (Grant Nos. JP20H00648 and JP21K17927) and JST Mirai Program (Grant No. JPMJMI22I4). Author Contribution J.Z. wrote the main manuscript text and designed the model; C.L. provided technical support; B.S. assisted with data processing; A.R.K. polished the manuscript text; S.M. provided the raw data and contributed to revising the manuscript text. All authors reviewed the manuscript. 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A Large-Scale Test of the Goldilocks Hypothesis: Quantifying the Relations Between Digital-Screen Use and the Mental Well-Being of Adolescents. Psychol. Sci. 28 (2), 204–215. https://doi.org/10.1177/0956797616678438 (2017a). Przybylski, A. K. & Weinstein, N. A Large-Scale Test of the Goldilocks Hypothesis: Quantifying the Relations Between Digital-Screen Use and the Mental Well-Being of Adolescents. Psychol. Sci. 28 (2), 204–215. https://doi.org/10.1177/0956797616678438 (2017b). Reinecke, L. et al. Digital Stress over the Life Span: The Effects of Communication Load and Internet Multitasking on Perceived Stress and Psychological Health Impairments in a German Probability Sample. Media Psychol. 20 (1), 90–115. https://doi.org/10.1080/15213269.2015.1121832 (2017a). Reinecke, L. et al. Digital Stress over the Life Span: The Effects of Communication Load and Internet Multitasking on Perceived Stress and Psychological Health Impairments in a German Probability Sample. Media Psychol. 20 (1), 90–115. https://doi.org/10.1080/15213269.2015.1121832 (2017b). Rosenbaum, P. R. & Rubin, D. B. The central role of the propensity score in observational studies for causal effects. Biometrika 70 (1), 41–55. https://doi.org/10.1093/biomet/70.1.41 (1983). Sabatini, F. & Sarracino, F. Online Networks and Subjective Well-Being. Kyklos 70 (3), 456–480. https://doi.org/10.1111/kykl.12145 (2017). Scheerder, A., van Deursen, A. & van Dijk, J. Determinants of Internet skills, uses and outcomes. A systematic review of the second- and third-level digital divide. Telematics Inform. 34 (8), 1607–1624. https://doi.org/10.1016/J.TELE.2017.07.007 (2017). Torous, J. et al. Towards a consensus around standards for smartphone apps and digital mental health. World Psychiatry . 18 (1), 97–98. https://doi.org/https://doi.org/10.1002/wps.20592 (2019). Turner, R. et al. Bayesian Optimization is Superior to Random Search for Machine Learning Hyperparameter Tuning: Analysis of the Black-Box Optimization Challenge 2020 . (2021). United Nations. The Sustainable Development Goals Report 2023 . (2023a). United Nations. The Sustainable Development Goals Report-Special edition . (2023b). van Deursen, A. & van Dijk, J. Internet skills and the digital divide. New. Media Soc. 13 (6), 893–911. https://doi.org/10.1177/1461444810386774 (2010). Van Dijk, J. A. G. M. The Digital Divide . (2019). World Bank. World Development Report 2016: Digital Dividends . (2016). World Economic Forum. The Future of Jobs Report 2020 . (2020). Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. 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Cantril Ladder Score\u003c/p\u003e","description":"","filename":"floatimage2.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-8160157/v1/9336ceddad0418e990f67240.jpeg"},{"id":108181119,"identity":"1445e220-19c2-4f52-a2e4-189939a0b8fd","added_by":"auto","created_at":"2026-04-30 08:57:36","extension":"jpeg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":85556,"visible":true,"origin":"","legend":"\u003cp\u003eThe Impact of Internet Access on Cantril Ladder Score\u003c/p\u003e","description":"","filename":"floatimage3.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-8160157/v1/e475dce35c605a9dc7750d83.jpeg"},{"id":108006421,"identity":"bac6484d-1ce8-48a7-83d0-588898bb13af","added_by":"auto","created_at":"2026-04-28 12:55:27","extension":"jpeg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":136274,"visible":true,"origin":"","legend":"\u003cp\u003eInternet Effect on Cantril Ladder Score\u003c/p\u003e","description":"","filename":"floatimage4.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-8160157/v1/6240940d5e7e5a4f8b726862.jpeg"},{"id":107900486,"identity":"9188fdc7-85c6-4b4f-9a02-1aa5983e8b56","added_by":"auto","created_at":"2026-04-27 11:35:19","extension":"jpeg","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":225989,"visible":true,"origin":"","legend":"\u003cp\u003eInternet Effect on Cantril Ladder Score by Country (2016-2019 Average)\u003c/p\u003e","description":"","filename":"floatimage5.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-8160157/v1/f457fea67f777a8ba0d97290.jpeg"},{"id":108006328,"identity":"eac78ab3-b75b-4cea-9125-80a25cc1909f","added_by":"auto","created_at":"2026-04-28 12:55:09","extension":"jpeg","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":226749,"visible":true,"origin":"","legend":"\u003cp\u003eInternet Effect on Cantril Ladder Score by Country (2020-2022 Average)\u003c/p\u003e","description":"","filename":"floatimage6.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-8160157/v1/5f77af579dcc30e6e39786c4.jpeg"},{"id":107900487,"identity":"d71998ef-6a99-4110-8d9b-dd178c01b961","added_by":"auto","created_at":"2026-04-27 11:35:19","extension":"jpeg","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":204249,"visible":true,"origin":"","legend":"\u003cp\u003eFactors influencing internet access\u003c/p\u003e","description":"","filename":"floatimage7.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-8160157/v1/fe81de0ad02daa196748cb81.jpeg"},{"id":107900489,"identity":"40d46f32-f36a-45ea-be0f-31469ffa88a5","added_by":"auto","created_at":"2026-04-27 11:35:19","extension":"jpeg","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":359205,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of variables with and without internet access.\u003c/p\u003e","description":"","filename":"floatimage8.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-8160157/v1/11342bb1b39a06efcec120f5.jpeg"},{"id":108183483,"identity":"9b6ba02a-218e-4396-b0f7-c56c4a5a486c","added_by":"auto","created_at":"2026-04-30 09:01:33","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1998271,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8160157/v1/bfecebd1-1834-49d7-a093-d6e398e69474.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Bridging the Digital Divide: Machine Learning Analysis of Internet Access Effects on Subjective Well-Being","fulltext":[{"header":"Introduction","content":"\u003cp\u003eIn the fast-changing digital age of the 21st century, the Internet has become a key component of modern life. It has completely changed how people communicate, work, learn, and access information(Castells, \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2011\u003c/span\u003e). As digital technology spreads through every part of society, it\u0026rsquo;s important to understand how Internet access affects people\u0026rsquo;s well-being. This is a major topic for research and has big effects on policymaking, social development, and individual quality of life. One important idea in this research is Subjective Well-Being (SWB). SWB is a way to measure how people feel about their lives, including how satisfied they are and their emotional experiences (Diener, \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e1984\u003c/span\u003e; Diener et al., \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e1999\u003c/span\u003e). It shows not only how happy someone feels about their life overall but also their mental and emotional health. This makes SWB a good way to measure well-being and quality of life (Kahneman \u0026amp; Deaton, \u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e2010a\u003c/span\u003e; Oswald \u0026amp; Wu, \u003cspan citationid=\"CR54\" class=\"CitationRef\"\u003e2010a\u003c/span\u003e). SWB doesn\u0026rsquo;t just affect individuals. It has a bigger impact on health, productivity, and how well people work together in society (Helliwell et al., \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e2013\u003c/span\u003e; Lyubomirsky et al., \u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e2005\u003c/span\u003e). Higher SWB often means better health, stronger relationships, and a more connected community.\u003c/p\u003e \u003cp\u003eThe digital revolution is moving fast, and its impact on well-being has become a big topic for researchers, policymakers, and global organizations like the ITU (\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e2021\u003c/span\u003e), OECD (\u003cspan citationid=\"CR52\" class=\"CitationRef\"\u003e2019a\u003c/span\u003e), and UN (2023a). There are several reasons for this focus. First, the number of Internet users has grown a lot. In 2005, there were 1\u0026nbsp;billion users. By 2021, that number had risen to 4.9\u0026nbsp;billion, covering 63% of the world\u0026rsquo;s population (ITU, \u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). The Internet is now a daily part of life for most people. Second, the digital economy is expanding quickly. It is reshaping how economies work, creating new jobs and business models, and changing how people work, earn money, and live (World Economic Forum, \u003cspan citationid=\"CR71\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). Third, social media and instant messaging have changed how people build and maintain relationships. This shift can affect social connections and personal well-being (Burke \u0026amp; Kraut, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2016\u003c/span\u003e). Fourth, the Internet offers vast amounts of information and learning opportunities. These resources can help people gain knowledge, improve skills, and feel more accomplished (Eszter \u0026amp; Yuli, 2013). Fifth, even though Internet access is growing, large gaps remain. These gaps can create or worsen social inequalities (Van Dijk, \u003cspan citationid=\"CR69\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). Sixth, digital health services like telemedicine, health apps, and online mental health support play a role in improving health management and well-being (Torous et al., \u003cspan citationid=\"CR64\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). Seventh, the Internet also brings challenges. Problems like cyberbullying, privacy breaches, information overload, and addiction can harm mental health (Lin et al., \u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). These factors show how the Internet has changed society. It has brought many benefits but also created new challenges, affecting well-being in many ways.\u003c/p\u003e \u003cp\u003eMany research delves into the link between the Internet and well-being, showing that its impact depends on usage patterns and individual traits rather than being determined by a single factor (Reinecke et al., \u003cspan citationid=\"CR59\" class=\"CitationRef\"\u003e2017a\u003c/span\u003e; Sabatini \u0026amp; Saracino, 2017). This underscores the necessity of considering multiple factors, especially those that vary among different populations. Przybylski \u0026amp; Weinstein (\u003cspan citationid=\"CR57\" class=\"CitationRef\"\u003e2017a\u003c/span\u003e) identified a \"Goldilocks effect\" in their study on adolescents' digital screen use: moderate screen time correlated with higher well-being. In comparison, both excessive and minimal use were linked to lower well-being. This finding resonates with the \"rich-get-richer\" hypothesis proposed by Kraut et al. (\u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e2002\u003c/span\u003e), highlighting the non-linear nature of the Internet's impact on well-being. Furthermore, Huang (\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e2010\u003c/span\u003e) supports this view, indicating a complex, non-linear relationship between Internet use and psychological well-being. For the elderly, Internet use can enhance social capital, reduce loneliness, and improve life satisfaction (Heo et al., \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e2015\u003c/span\u003e; Cotten et al., \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2012a\u003c/span\u003e), thereby promoting social inclusion and addressing the challenges of aging. However, digital skills and the digital divide limit the realization of these benefits. Van Deursen and van Dijk (\u003cspan citationid=\"CR68\" class=\"CitationRef\"\u003e2010\u003c/span\u003e) emphasized the importance of digital skills. B\u0026uuml;chi et al. (\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2015\u003c/span\u003e) found that individuals with lower socioeconomic status (SES) face difficulties in accessing and monetizing the Internet. Scheerder et al.'s (\u003cspan citationid=\"CR63\" class=\"CitationRef\"\u003e2017\u003c/span\u003e) review further revealed the multifaceted nature of digital inequality, including differences in motivation, access, skills, and usage patterns, which has given rise to what is known as the \"secondary digital divide\". Kir\u0026aacute;ly et al. (\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e2020\u003c/span\u003e) highlighted digital technology's dual role in maintaining social connections and mental health, warning of overuse risks. Balanced use is crucial.\u003c/p\u003e \u003cp\u003eSome studies have also examined the relationship between the Internet and well-being from the perspective of countries and major events, such as the COVID-19 pandemic. Graham and Nikolova (\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2013\u003c/span\u003e) found that Internet access boosts life ratings globally using GWP data, but this varies by country and income level. Ganju et al. (\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e2016\u003c/span\u003e) explored ICT development and national well-being, emphasizing national-level factors. These studies show the importance of national and cultural contexts in understanding the Internet's impact. During COVID-19, digital tools reduced loneliness and improved resilience, but overuse worsened anxiety and depression (Marciano et al., \u003cspan citationid=\"CR50\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). Karakose et al. (\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e2022\u003c/span\u003e) studied the relationship between internet usage by school administrators and teachers and their well-being during the pandemic. They found that during the pandemic, the decline in the quality of life of school administrators and teachers, caused by increased feelings of loneliness, led to internet addiction, which in turn reduced their well-being. Lin et al. (\u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e2023\u003c/span\u003e) analyzed the relationship between adolescents' internet usage time and subjective well-being during the COVID-19 pandemic through a survey. They found that prolonged internet use during the pandemic led to a decrease in subjective well-being by promoting problematic internet use and lowering self-esteem.\u003c/p\u003e \u003cp\u003eExisting research has valuable insights but key shortcomings. Most studies focus on specific areas, lacking global comparison. Nonlinear relationships and interactions, crucial for understanding Internet access impact, are often overlooked. Our research bridges a gap by examining internet access and health globally. We use innovative methods, key among them a large GWP dataset from 168 countries, offering a unique perspective. Advanced machine learning, like eXtreme Gradient Boosting (XGBoost) and SHAP (SHapley Additive exPlanations), uncovers complex relationships missed by traditional methods. Our longitudinal study (2016\u0026ndash;2022) tracks changes and assesses global events' impact, like COVID-19. By integrating age, income, education, and health, we create a holistic framework. This multifaceted approach combines insights from various disciplines, providing a stronger analysis than single-discipline studies. Our results benefit academia and inform digital inclusion policies.\u003c/p\u003e"},{"header":"Materials and Methodology","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003eMaterials\u003c/h2\u003e \u003cdiv id=\"Sec4\" class=\"Section3\"\u003e \u003ch2\u003eSurvey Information\u003c/h2\u003e \u003cp\u003eThe GWP, conducted by Gallup, Inc., is a comprehensive global survey at the individual level that provides a rich and unique data resource for studying human well-being and social attitudes. This dataset spans 18 years, from 2005 to 2022, encompassing 17 survey waves across 168 countries and territories, with a total of 2.594\u0026nbsp;million individual observations. The scale and breadth of the GWP make it the largest global dataset focused on human well-being, widely utilized in academic research and policymaking (Deaton, \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; Diener et al., \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2010\u003c/span\u003e; Helliwell et al., \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; Jones, \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e2017\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eIn each survey wave, the GWP samples at least 1,000 individuals per participating country, employing rigorous random sampling methods to ensure data representativeness and reliability. The survey content covers multiple aspects, including life satisfaction, emotional experiences, health status, employment situations, and educational levels, providing researchers with comprehensive information at both individual and societal levels. This multidimensional data collection enables researchers to conduct in-depth analyses of various factors affecting human well-being and explore the complex relationships among them. Detailed sampling methods and data collection procedures for the GWP are reported on Gallup's website.\u003c/p\u003e \u003cp\u003eDuring the data processing phase, several critical steps are conducted to improve the usability of the dataset. Firstly, regarding internet connectivity survey data, waves 1\u0026ndash;10 and waves 11\u0026ndash;17 used different questioning approaches. In waves 1\u0026ndash;10, the survey question was \"Does your home have access to the internet?\", while in waves 11\u0026ndash;17, the question was \"Do you have access to the internet in any way, whether on a mobile phone, a computer, or some other device?\". Clearly, these two questions differ significantly in meaning, with waves 11\u0026ndash;17 having a broader scope, focusing on whether individuals can access the internet through any means and devices, not limited to the home environment. Therefore, these two cannot be directly combined, so we chose to use data from waves 11\u0026ndash;17, which better reflects the actual internet connectivity situation. After this step, 1035,079 observations were retained. In the remaining waves, for respondents who did not answer income-related questions, we imputed missing income values using the average income of respondents from the same country and wave. The average income was calculated by averaging other available values from the GWP survey for the corresponding country and wave. If income questions were not asked for a particular country in a specific wave, data for that country were removed. This step resulted in 1018,406 observations being retained. Furthermore, as our dependent variable is well-being, we required respondents to have answered the well-being question. This step retained 1002,937 observations. Previous research has shown that disability significantly affects human well-being (Fredrickson et al., \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2013\u003c/span\u003e; Kobau et al., \u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e2010\u003c/span\u003e); therefore, we removed observations without available answers for this variable. This left us with 994,328 observations. Given that our study focuses on the relationship between digitalization and well-being, internet usage is an essential variable, as internet connectivity is the fundamental infrastructure for digitalization. The ability to connect to the internet directly impacts the digitalization process and leads to the so-called \"digital divide.\" Additionally, age, gender, and employment status are indispensable variables. After dropping observations with no-answer items for these variables, our final dataset retained 963,870 observations.\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e\n\u003ch3\u003eSubjective Well-Being Measurement\u003c/h3\u003e\n\u003cp\u003eAs a metric for capturing human well-being, SWB has gained substantial validation in the literature (Diener, \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e1984\u003c/span\u003e; Diener et al., \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; Oswald \u0026amp; Wu, 2010). Among various approaches to quantifying SWB, overall life evaluation stands out as a particularly valuable technique (Diener et al., \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; Helliwell \u0026amp; Aknin, \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; Kahneman \u0026amp; Deaton, 2010), allowing researchers to derive well-being assessments from how individuals perceive the overall quality of their lives. The GWP utilizes the Cantril ladder\u0026mdash;an 11-point scale developed by psychologist Hadley Cantril in the 1960s (Hadley Cantril, \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e1965\u003c/span\u003e)\u0026mdash;to capture this dimension of human well-being. When responding to this instrument, participants visualize a vertical scale anchored at two extremes: the lowest point (0) symbolizes the most unfavorable life circumstances imaginable, while the highest point (10) denotes an ideal life scenario. Participants then position themselves on this scale based on their perceived current life conditions, yielding a numerical score between 0 and 10. This self-anchoring design enables meaningful comparisons across diverse cultural contexts, as respondents apply their own subjective criteria when making evaluations. Given its accessibility and established track record in prior investigations (Blanchflower, \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Jebb et al., \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e2018\u003c/span\u003e), we employ this indicator as our dependent variable.\u003c/p\u003e\n\u003ch3\u003eIndependent Variables\u003c/h3\u003e\n\u003cp\u003eFor this research, we utilized a dataset with 66 independent variables, which are \"Age\", \"Anger\", \"Approval of Leadership Performance\", \"Assaulted\", \"Children Under15\", \"Confidence in Election Honesty\", \"Confidence in Financial System\", \"Confidence in Judicial System\", \"Confidence in Local Police\", \"Confidence in Military\", \"Confidence in National Government\", \"Corruption within Business\", \"Corruption within Government\", \"Country\", \"Donated\", \"Economic Changing Direction\", \"Economic Rating\", \"Education\", \"Employment\", \"Enjoyment\", \"Enough Food\", \"Enough Shelter\", \"Feeling Income\", \"Freedom of Choosing Life\", \"Freedom of Media\", \"Gender\", \"Good Place for Ethnic Minority\", \"Good Place for Gay or Lesbian\", \"Good Place for Immigrants\", \"Having Relatives to Rely on\", \"Health Disability\", \"Help Stranger\", \"Household Income\", \"Income Level\", \"Interesting Things\", \"Internet Access available\", \"Living Standard Changing Direction\", \"Local Job Outlook\", \"Marital Status\", \"Native-born\", \"Opportunity for Children Learning\", \"Physical Pain\", \"Recommended Live Place\", \"Religious importance\", \"Respected\", \"Sadness\", \"Safety of Alone Night Walking\", \"Satisfied with Affordable House\", \"Satisfied with Air Quality\", \"Satisfied with City\", \"Satisfied with Education\", \"Satisfied with Environmental Efforts\", \"Satisfied with Healthcare\", \"Satisfied with Opportunity to Make Friends\", \"Satisfied with Poverty Alleviation\", \"Satisfied with Public Transportation\", \"Satisfied with Road\", \"Satisfied with Water Quality\", \"Smile\", \"Stolen\", \"Stress\", \"Voiced Opinion to Official\", \"Volunteer\", \"Wave\", \"Well Rested\", and \"Worry\".\u003c/p\u003e\n\u003ch3\u003eMethodology\u003c/h3\u003e\n\u003cp\u003eThe overall methodological workflow of the study is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. Starting from the raw Gallup data, we perform preprocessing and feature engineering, then use an XGBoost classifier to estimate the propensity scores for internet connection and conduct PSM matching. Afterward, we run SMD balance tests on the matched samples and build stratified XGBoost regression models to predict subjective well-being. Finally, we use SHAP to interpret the contribution of variables to subjective well-being and conduct comparative analyses.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003eThe Impact of Internet Access on Well-being\u003c/h2\u003e \u003cp\u003eAs digital technology keeps growing, more people are paying attention to how it affects well-being (OECD, 2019; United Nations, 2023). Research shows that digitalization, like internet access, usually has a positive effect on well-being (Castellacci \u0026amp; Tveito, 2018; Przybylski \u0026amp; Weinstein, 2017). The size of the effect can differ between groups. Still, it seems to match what we expect and see in daily life. However, we still do not have clear global data to fully understand or explain this connection.\u003c/p\u003e \u003cp\u003eDue to limitations in data volume and technological capabilities, linear regression always served as a compromise yet effective method for analyzing this relationship. The linear regression technology is not particularly adept at fitting non-linear relationships. In contrast, machine learning models are designed to optimize predictive accuracy by minimizing prediction errors (Chen \u0026amp; Guestrin, \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2016\u003c/span\u003e). Furthermore, machine learning models do not make assumptions about the shape of relationships, which enhances their capacity to fit non-linear relationships (Bent\u0026eacute;jac et al., \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Chen \u0026amp; Guestrin, \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2016\u003c/span\u003e). This study employs a Propensity Score Matching (PSM) model enhanced by machine learning techniques to replace traditional PSM models. This method deals with selection bias and confounding factors, making good use of the advantages of machine learning models. As a result, the reliability and accuracy of analysis are significantly improved.\u003c/p\u003e \u003cp\u003eIn studying the complex relationship between digitalization and well-being, this kind of methodological thinking is very important. Since the relationship might not be linear, we need analysis methods that can catch more detailed patterns, not just simple linear ones. Machine learning offers a promising way to find these complex connections, helping us better understand how digitalization affects well-being in different situations and groups of people.\u003c/p\u003e \u003c/div\u003e\n\u003ch3\u003eXGBoost model and its fine-tuning\u003c/h3\u003e\n\u003cp\u003eThis study investigates the empirical association between digitalization and well-being through a machine learning framework. Given that machine learning algorithms lack the interpretability of conventional linear approaches, we incorporate explainability techniques to uncover their underlying mechanisms (Christoph Molnar, \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2020\u003c/span\u003e; Lundberg et al., \u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). Specifically, we employ the XGBoost regressor as an alternative to linear regression and comparable methods prevalent in earlier literature, enabling us to characterize the digitalization-well-being nexus. As the outcome variable constitutes an 11-point Cantril Ladder measure of subjective well-being, we frame this as a regression problem. The SHAP framework (Lundberg et al., \u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e2020\u003c/span\u003e) serves as our primary tool for model interpretation.\u003c/p\u003e \u003cp\u003eXGBoost presents multiple methodological advantages for this analysis. As an algorithm grounded in decision tree architecture (Chen \u0026amp; Guestrin, \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2016\u003c/span\u003e), it excels at modeling intricate non-linear patterns within feature-rich tabular datasets (Bent\u0026eacute;jac et al., \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). Decision trees accommodate diverse variable types\u0026mdash;binary, continuous, and categorical\u0026mdash;without difficulty. Moreover, this approach is fully non-parametric, imposing no distributional assumptions on the underlying data (Chen \u0026amp; Guestrin, \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2016\u003c/span\u003e). A well-known limitation of single decision trees is their susceptibility to overfitting when permitted excessive depth. This shortcoming is mitigated through ensemble strategies, including gradient boosting and random forests, which aggregate multiple decision trees as base learners to achieve superior predictive accuracy. While conventional gradient boosting operates sequentially and resists parallelization (Chen \u0026amp; Guestrin, \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2016\u003c/span\u003e), XGBoost represents an enhanced implementation featuring parallel processing capabilities and GPU support. Consequently, XGBoost constitutes our principal analytical tool.\u003c/p\u003e \u003cp\u003eThe XGBoost regressor training procedure for the complete dataset follows this formulation:\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\:{XGB}_{td}=\\text{G}({\\varvec{I}\\varvec{t}\\varvec{r}}_{td},\\:{\\varvec{j}\\varvec{t}\\varvec{r}}_{td},\\:{\\varvec{H}\\varvec{P}}_{td})$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eIn this expression, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{XGB}_{td}\\)\u003c/span\u003e\u003c/span\u003e​ denotes the trained XGBoost model utilizing the full dataset encompassing all predictors and observations; \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\varvec{I}\\varvec{t}\\varvec{r}}_{td}\\)\u003c/span\u003e\u003c/span\u003e​ indicates the predictor matrix from the training partition; \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\varvec{j}\\varvec{t}\\varvec{r}}_{td}\\)\u003c/span\u003e\u003c/span\u003e signifies the response variable within the training partition; \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\varvec{H}\\varvec{P}}_{td}\\)\u003c/span\u003e\u003c/span\u003etspecifies the hyperparameter configuration for optimal model performance; and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{G}\\)\u003c/span\u003e\u003c/span\u003e symbolizes the learning algorithm. We allocate data between training and testing subsets at a 9:1 ratio\u0026mdash;specifically, 90% for model development and the remaining 10% for validation purposes\u003c/p\u003e \u003cp\u003eThe hyperparameter configuration \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\varvec{H}\\varvec{P}}_{td}\\)\u003c/span\u003e\u003c/span\u003e encompasses: tree count (\"n_estimators\"), individual tree depth limit (\"max_depth\"), step size shrinkage (\"learning_rate\"), loss threshold for node splitting (\"gamma\"), minimum child node weight (\"min_child_weight\"), training instance sampling proportion (\"subsample\"), weight update magnitude constraint (\"max_delta_step\"), L1 weight penalty (\"reg_alpha\"), and L2 weight penalty (\"reg_lambda\"). These parameter identifiers in quotation marks correspond directly to the XGBoost Python API, ensuring reproducibility. Optimal hyperparameters are identified via 10-fold cross-validation, with test set R\u0026sup2; serving as the optimization criterion. The model\u0026rsquo;s predictions on the test set are given by:\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$$\\:\\widehat{{\\varvec{j}\\varvec{t}\\varvec{e}}_{td}}={XGB}_{td}\\left({\\varvec{I}\\varvec{t}\\varvec{e}}_{td}\\right)$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ3\" name=\"EquationSource\"\u003e\n$$\\:{R}_{test\\:td}^{2}=1-\\frac{{({\\varvec{j}\\varvec{t}\\varvec{e}}_{td}\\:-\\:\\widehat{{\\varvec{j}\\varvec{t}\\varvec{e}}_{\\varvec{t}\\varvec{d}}})}^{2}}{{({\\varvec{j}\\varvec{t}\\varvec{e}}_{td}\\:-\\:\\stackrel{-}{{\\varvec{j}\\varvec{t}\\varvec{e}}_{td}})}^{2}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e3\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eHere, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\widehat{{\\varvec{j}\\varvec{t}\\varvec{e}}_{td}}\\)\u003c/span\u003e\u003c/span\u003e denotes the predictions generated by the well-trained XGBoost model \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{XGB}_{td}\\)\u003c/span\u003e\u003c/span\u003e on the test dataset \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\varvec{I}\\varvec{t}\\varvec{e}}_{td}\\)\u003c/span\u003e\u003c/span\u003e, while \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\stackrel{-}{{\\varvec{j}\\varvec{t}\\varvec{e}}_{td}}\\)\u003c/span\u003e\u003c/span\u003e represents the actual mean of the independent variable. Additionally, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{test\\:td}^{2}\\)\u003c/span\u003e\u003c/span\u003e is the \u003cem\u003eR\u003c/em\u003e\u003csup\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sup\u003e metric computed on the test dataset using the model trained on the training set extracted from the entire dataset. Combining Equations (\u003cspan refid=\"Equ1\" class=\"InternalRef\"\u003e1\u003c/span\u003e), (\u003cspan refid=\"Equ2\" class=\"InternalRef\"\u003e2\u003c/span\u003e), and (3), it is evident that \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{test\\:td}^{2}\\)\u003c/span\u003e\u003c/span\u003e is significantly related to the model's hyperparameters.\u003c/p\u003e \u003cp\u003eHyperparameter optimization employs a Bayesian approach (Turner et al., \u003cspan citationid=\"CR65\" class=\"CitationRef\"\u003e2021\u003c/span\u003e), which proceeds through four stages: initialization using preliminary hyperparameter configurations, surrogate model construction, iterative hyperparameter proposal with performance estimation, and surrogate refinement. Our implementation executes 50 optimization cycles. The surrogate function maps hyperparameter inputs to estimated test R\u0026sup2; values. Hyperparameter search boundaries are specified as: \"n_estimators\" spanning 300\u0026ndash;4000; \"learning_rate\" within 0.005\u0026ndash;0.1; \"max_depth\" between 5\u0026ndash;16; \"subsample\" ranging 0.5\u0026ndash;0.8; \"min_child_weight\" from 0.1\u0026ndash;10; \"max_delta_step\" covering 0.01\u0026ndash;10; \"gamma\" across 0.001\u0026ndash;5; \"reg_alpha\" within 0.001\u0026ndash;5; and \"reg_lambda\" spanning 0.1\u0026ndash;10. Comparative analysis between 50-iteration Bayesian optimization and exhaustive grid search (exceeding 2,000 configurations) demonstrated superior performance from the Bayesian approach. Although extended grid search might yield incremental improvements, the associated computational burden renders this impractical. Thus, Bayesian optimization is adopted for hyperparameter tuning across all XGBoost models in this research.\u003c/p\u003e\n\u003ch3\u003ePropensity Score Matching (PSM) and its testing\u003c/h3\u003e\n\u003cp\u003eIn our investigation of how digitalization (internet access) affects people's well-being, PSM (Rosenbaum \u0026amp; Rubin, \u003cspan citationid=\"CR61\" class=\"CitationRef\"\u003e1983\u003c/span\u003e) emerges as a crucial methodology, enabling us to discern this impact more accurately. PSM, in essence, facilitates a fair comparative experiment. Consider the scenario where we directly compare the well-being of individuals with and without internet access; we might conclude that internet access enhances well-being. However, this approach is problematic because those with internet access may inherently possess superior living conditions, such as higher income or education levels, factors that could independently contribute to greater well-being. PSM addresses this issue.\u003c/p\u003e \u003cp\u003eThe method begins by identifying all significant factors influencing an individual's likelihood of internet access, including age, income, educational attainment, and other relevant variables. Subsequently, based on these factors, it calculates the probability of each individual obtaining internet access, termed the \"propensity score\".\u003c/p\u003e \u003cp\u003eAs demonstrated in Eq.\u0026nbsp;\u003cspan refid=\"Equ4\" class=\"InternalRef\"\u003e4\u003c/span\u003e, The propensity score \u003cem\u003ee(X)\u003c/em\u003e is the probability that an individual will receive the treatment given the covariate \u003cem\u003eX\u003c/em\u003e. where: T is a dichotomous treatment variable (e.g., 1 means accepting the treatment, 0 means not accepting the treatment) and \u003cem\u003eX\u003c/em\u003e is a vector of covariates.\u003cdiv id=\"Equ4\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ4\" name=\"EquationSource\"\u003e\n$$\\:\\varvec{e}\\left(\\varvec{X}\\right)=\\varvec{P}(\\varvec{T}=1\\mid\\:\\varvec{X})$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e4\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eSubsequently, we match each individual with internet access to one or several individuals without internet access but with very similar conditions (i.e., comparable propensity scores) as comparative subjects. This methodology allows us to ensure, to the greatest extent possible, that the two groups being compared are similar in all aspects except for internet access, thereby minimizing confounding effects from other factors.\u003c/p\u003e \u003cp\u003eIn our study, we employ the XGBoost Classifier as the propensity score model due to its capacity to handle complex non-linear relationships, sensitivity to feature interactions, and excellent performance with high-dimensional data. We use BayesSearch for hyperparameter tuning to optimize model performance, focusing on parameters such as n_estimators, learning_rate, and max_depth. We aim to maximize the ROC-AUC score during the optimization process, employing 10-fold cross-validation and setting 50 iterations to search for the optimal parameter combination. The model results show that the training accuracy is 88.58% and the testing accuracy is 84.69%; the ROC AUC for the training set is 95.10%, and the ROC AUC for the testing set is 91.84%. These results indicate that the model has good generalization ability and does not suffer from severe overfitting.\u003c/p\u003e \u003cp\u003eFollowing the construction of the propensity score model, we calculate propensity scores for each observation, representing the probability of each individual obtaining internet access. To balance matching quality and post-matching sample size, we set the caliper to 0.2, implying a matching tolerance of 0.2 standard deviation units, and restrict each control unit to be matched only once to prevent overuse of certain control samples, which could affect subsequent model training. To enhance processing efficiency for large datasets, we implement the BallTree data structure for efficient nearest neighbor search and adopt a batch processing approach, handling 10,000 samples per batch. Post-PSM matching, the sample size is 321,910.\u003c/p\u003e \u003cp\u003eHowever, the application of PSM alone is insufficient; we must ensure the effectiveness of this matching. This is where the Standardized Mean Difference (SMD)(Jacob Cohen, \u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e1988\u003c/span\u003e) method proves valuable. SMD serves as a verification tool, helping us validate whether PSM has indeed made the two groups more similar across various aspects. Its operational principle is straightforward: for each factor under consideration (e.g., age, income), SMD calculates the average difference between the groups with and without internet access, then standardizes this difference.\u003c/p\u003e \u003cp\u003eAs shown in Eq.\u0026nbsp;\u003cspan refid=\"Equ5\" class=\"InternalRef\"\u003e5\u003c/span\u003e, \u003cb\u003e\u0026micro;_t\u003c/b\u003e represents the mean of the treatment group (with internet access), \u003cb\u003e\u0026micro;_c\u003c/b\u003e is the mean of the control group (without internet access), \u003cb\u003eσ\u0026sup2;_t\u003c/b\u003e denotes the variance of the treatment group, and \u003cb\u003eσ\u0026sup2;_c\u003c/b\u003e is the variance of the control group. This formula can be interpreted as the mean difference between the two groups divided by the average of their standard deviations.\u003cdiv id=\"Equ5\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ5\" name=\"EquationSource\"\u003e\n$$\\:\\varvec{S}\\varvec{M}\\varvec{D}\\:=\\:(\\varvec{\\mu\\:}\\_\\varvec{t}-\\:\\varvec{\\mu\\:}\\_\\varvec{c})\\:/\\:\\sqrt{\\left(\\right(\\varvec{\\sigma\\:}\u0026sup2;\\_\\varvec{t}\\:+\\:\\varvec{\\sigma\\:}\u0026sup2;\\_\\varvec{c})\\:/\\:2)}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e5\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eGenerally, an SMD value less than 0.1 typically indicates good balance. By comparing the SMD values before and after matching (The absolute mean value before matching was 0.13, and the absolute mean value after matching was 0.03), we confirm that PSM effectively enhanced the similarity between the two groups, significantly reducing the imbalance in covariates. The post-matching SMD value, well below 0.1, indicates a good balance (See Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e for details.). Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e: Comparison of SMD for Variables Before and After Matching (except \"Country\")\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\u003eComparison of SMD for Variables Before and After Matching\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"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 \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eVariable\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSMD Before\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eSMD After\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eWave\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.35\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.09\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eHousehold Income\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.60\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.12\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCantril Ladder\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.54\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.17\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eHealth Disability\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-0.42\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-0.10\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eHaving Relatives to Rely on\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.39\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.09\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLiving Standard Changing Direction\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.26\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.07\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eEnough Food\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-0.54\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-0.12\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eEnough Shelter\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-0.36\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-0.08\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eWell Rested\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.03\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRespected\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.21\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.05\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSmile\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.17\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.05\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eInteresting Things\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.26\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.07\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eEnjoyment\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.26\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.06\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePhysical Pain\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-0.35\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-0.09\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eWorry\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-0.19\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-0.05\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSadness\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-0.27\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-0.07\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eStress\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-0.03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-0.01\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAnger\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-0.12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-0.02\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSatisfied with City\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.14\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.03\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRecommended Live Place\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.23\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.06\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eEconomic Rating\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.31\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.07\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eEconomic Changing Direction\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.03\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLocal Job Outlook\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.06\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.03\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSatisfied with Public Transportation\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.06\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.02\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSatisfied with Road\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.03\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSatisfied with Education\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.05\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.01\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSatisfied with Air Quality\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-0.06\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-0.02\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSatisfied with Water Quality\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.17\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.05\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSatisfied with Healthcare\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.14\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.04\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSatisfied with Affordable House\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-0.01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.01\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSatisfied with Opportunity to Make Friends\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.09\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.02\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGood Place for Ethnic Minority\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.08\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.03\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGood Place for Gay or Lesbian\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.47\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.10\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGood Place for Immigrants\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.21\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.05\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDonated\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.27\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.07\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eVolunteer\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.06\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.02\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eHelp Stranger\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.16\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.05\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eVoiced Opinion to Official\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.07\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.03\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eConfidence in Local Police\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.01\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSafety of Alone Night Walking\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.17\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.03\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eStolen\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-0.09\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-0.01\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAssaulted\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-0.09\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-0.01\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eReligious importance\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-0.58\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-0.11\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eOpportunity for Children Learning\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.06\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.02\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSatisfied with Poverty Alleviation\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-0.10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-0.01\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSatisfied with Environmental Efforts\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-0.14\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-0.02\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFreedom of Choosing Life\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.03\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eConfidence in Military\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-0.01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.00\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eConfidence in Judicial System\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-0.09\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-0.02\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eConfidence in National Government\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-0.22\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-0.04\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eConfidence in Financial System\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-0.01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.00\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eConfidence in Election Honesty\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-0.02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.00\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFreedom of Media\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.07\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.02\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCorruption within Business\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-0.06\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.00\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCorruption within Government\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-0.02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.01\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eApproval of Leadership Performance\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-0.13\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-0.02\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGender_female\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-0.14\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-0.03\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAge\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-0.27\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-0.07\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eEducation\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1.17\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.09\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMarital Status\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-0.14\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-0.03\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eEmployment\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-0.48\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-0.10\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eChildren Under15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-0.28\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-0.04\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFeeling Income\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-0.67\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-0.15\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eNative-born\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-0.13\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-0.03\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eIncome Level\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.38\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.09\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eSuch a marked improvement in covariate balance strengthens the validity of our subsequent analyses, as it minimizes the potential for confounding effects and enhances the comparability between the treatment and control groups. This approach to matching and balance assessment helps enhance the credibility of our study\u0026rsquo;s findings regarding the impact of internet access on well-being.\u003c/p\u003e \u003cdiv id=\"Sec11\" class=\"Section2\"\u003e \u003ch2\u003eStratified XGBoost Analysis\u003c/h2\u003e \u003cp\u003eFollowing the completion of PSM and SMD, this study further employed a stratified modeling approach. Two independent XGBoost models were constructed for groups with and without internet access, respectively. This methodology allows for an in-depth exploration of how internet access moderates various factors influencing SWB. Through this stratified analysis, we were able to identify and compare key predictors of well-being across these two subpopulations. The models are presented as follows:\u003cdiv id=\"Equ6\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ6\" name=\"EquationSource\"\u003e\n$$\\:\\left\\{\\begin{array}{c}\\begin{array}{c}{XGB}_{a}=G\\left({\\varvec{I}\\varvec{t}\\varvec{r}}_{\\varvec{a}},\\:{\\varvec{j}\\varvec{t}\\varvec{e}}_{\\varvec{a}},\\:{\\varvec{H}\\varvec{P}}_{a}\\right)\\\\\\:{XGB}_{u}=G\\left({\\varvec{I}\\varvec{t}\\varvec{r}}_{\\varvec{u}},\\:{\\varvec{j}\\varvec{t}\\varvec{e}}_{\\varvec{u}},\\:{\\varvec{H}\\varvec{P}}_{u}\\right)\\end{array}\\end{array}\\right.$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e6\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{XGB}_{a}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{XGB}_{u}\\)\u003c/span\u003e\u003c/span\u003e denote the well-train XGBoost regression models based on the internet access available population and internet access unavailable population, respectively, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\varvec{I}\\varvec{t}\\varvec{r}}_{\\varvec{a}}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\varvec{I}\\varvec{t}\\varvec{r}}_{\\varvec{u}}\\)\u003c/span\u003e\u003c/span\u003e represent the independent variables of the training dataset split from the access available population and internet access unavailable population datasets, respectively, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\varvec{j}\\varvec{t}\\varvec{e}}_{\\varvec{a}}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\varvec{j}\\varvec{t}\\varvec{e}}_{\\varvec{u}}\\:\\)\u003c/span\u003e\u003c/span\u003erepresent the dependent variables of those two datasets, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\varvec{H}\\varvec{P}}_{a}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\varvec{H}\\varvec{P}}_{u}\\)\u003c/span\u003e\u003c/span\u003e denote three distinct groups of hyperparameters used to train high-accuracy XGBoost models for each sub-dataset. We also employ cross-validation to identify the optimal hyperparameter sets following the same procedure outlined in Equations (\u003cspan refid=\"Equ1\" class=\"InternalRef\"\u003e1\u003c/span\u003e), (\u003cspan refid=\"Equ2\" class=\"InternalRef\"\u003e2\u003c/span\u003e), \u003cb\u003eand (3)\u003c/b\u003e. Additionally, it must be noted that the independent variable \u0026ldquo;internet access available\u0026rdquo; is not included in the sub-dataset, when training the models and predicting. The models with and without internet access achieved accuracies of 28.34% and 26.89%, respectively, with MAE values of 1.44 and 1.59. Given the individual variability and measurement fluctuations inherent in subjective well-being, this level of accuracy is acceptable. Moreover, the optimized XGBoost model reduced prediction error by an average of 51.5% compared with the mean baseline, demonstrating that the model successfully captured the predictive patterns influencing subjective well-being.\u003c/p\u003e \u003cp\u003eThis approach's advantage lies in its ability to determine whether internet access affects well-being and elucidate the mechanisms of its influence. By comparing variables' relative importance and effect sizes across the two models, we can reveal how internet access moderates the relationships between various socioeconomic and behavioral factors and SWB.\u003c/p\u003e \u003cp\u003eThis stratified modeling approach provides a more nuanced analytical framework, enabling us to capture heterogeneous effects that might be overlooked in an aggregate analysis. This contributes to a more comprehensive understanding of the digital divide's impact on well-being and provides an empirical foundation for formulating targeted policy interventions.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec12\" class=\"Section2\"\u003e \u003ch2\u003eContributions of Independent Variables to Well-being\u003c/h2\u003e \u003cp\u003eThe non-parametric nature of tree-based ensemble algorithms, including XGBoost, poses substantial challenges for result interpretation (Christoph Molnar, \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). To address this limitation, the SHAP method has emerged as an innovative and robust framework for quantifying how each predictor individually influences the outcome variable within machine learning contexts (Lundberg et al., \u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). Rooted in cooperative game theory and the concept of Shapley values, this technique guarantees an equitable and balanced attribution of predictor contributions to model outputs (Christoph Molnar, \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2020\u003c/span\u003e; Lundberg et al., \u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). Operationally, Shapley values are derived by measuring prediction shifts in a fully trained model when a target predictor is introduced across all feasible combinations of the other predictors, subsequently computing the mean of these incremental effects. The predictor-level contribution for each observation can be formalized as:\u003cdiv id=\"Equ7\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ7\" name=\"EquationSource\"\u003e\n$$\\:{\\varvec{S}\\varvec{H}\\varvec{A}\\varvec{P}\\varvec{t}\\varvec{e}}_{td}=\\theta\\:({\\varvec{X}\\varvec{G}\\varvec{B}}_{td},\\:{\\varvec{I}\\varvec{t}\\varvec{e}}_{td})$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e7\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eIn this formulation, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\varvec{X}\\varvec{G}\\varvec{B}}_{td}\\)\u003c/span\u003e\u003c/span\u003e signifies the XGBoost regression or classification model developed from training data extracted from the complete dataset, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\varvec{S}\\varvec{H}\\varvec{A}\\varvec{P}\\)\u003c/span\u003e\u003c/span\u003e refers to the canonical SHAP computational procedure, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\varvec{S}\\varvec{H}\\varvec{A}\\varvec{P}\\varvec{t}\\varvec{e}}_{td}\\)\u003c/span\u003e\u003c/span\u003e captures the attribution scores for every predictor-observation pair within the test subset. From a theoretical standpoint, applying the trained XGBoost model in conjunction with the SHAP algorithm to interpret all observations remains feasible even under overfitting conditions. This robustness stems from SHAP's exhaustive enumeration of all predictor subsets containing the variable under examination. Within this comprehensive collection of subsets, only a single configuration matches the complete input feature set. Should the model have memorized training observations during fitting, its predictive accuracy on those instances would substantially exceed that on novel observations. To circumvent this concern, our analysis restricts attention to test set observations. An alternative strategy involves implementing a 10-fold explanation protocol across the entire dataset, analogous to 10-fold cross-validation: partitioning observations into ten segments, fitting XGBoost on nine segments, generating SHAP explanations for the held-out segment, and cycling through until all segment combinations are exhausted. Nevertheless, SHAP computation demands considerable resources. Each test subset comprises roughly 90,000 records (the dual model variant contains 11,000 observations). Under reasonable computational parameters, a minimum of 50 GPU hours is required to complete the analysis (stratified XGBoost analyses each consume approximately 5 GPU hours).\u003c/p\u003e \u003c/div\u003e"},{"header":"Results","content":"\u003cdiv id=\"Sec14\" class=\"Section2\"\u003e \u003ch2\u003eOverall Analysis\u003c/h2\u003e \u003cp\u003eThis study examines how internet access affects people's well-being. It used the Cantril ladder score (0\u0026ndash;10) to measure well-being. To make sure the groups were comparable, the study used a method called PSM. The results show a clear link between internet access and higher well-being. On average, people with internet access had a Cantril ladder score of 5.38. In contrast, those without access scored 4.92. This gives a difference of 0.46 points. The difference is highly significant, with a t-value of 49.69 and a p-value of less than 0.0001. This means it is very unlikely that the difference is due to chance.\u003c/p\u003e \u003cp\u003eA kernel density estimation (KDE) plot (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e) helps explain these findings. It shows how well-being scores are distributed in both groups. Both groups have a similar shape in their distributions, with a peak around 5 points. This may reflect a common \"moderate well-being\" level. However, people with internet access had a slightly higher distribution above 5 points, matching their higher average score. The internet access group also had more people scoring between 6 and 8 points. This suggests that internet access might improve moderate to high well-being levels. On the other hand, the non-internet access group had a higher density of scores between 0 and 3 points. This suggests that internet access might help reduce very low well-being scores.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec15\" class=\"Section2\"\u003e \u003ch2\u003eTemporal and Regional Analysis\u003c/h2\u003e \u003cp\u003eFrom 2016 to 2022, internet access had a changing impact on well-being (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e). The positive effects rose and fell over this time. In 2016, the effect was strongest. People with internet access scored 0.58 points higher on the Cantril ladder compared to those without access. By 2018, this dropped to 0.38 points. Then, it rose again, peaking at 0.47 points in 2020. After 2020, the effect declined, reaching 0.37 points in 2022.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThis pattern reveals some important points. First, internet access improved well-being throughout the seven years, but the strength of the effect changed. Second, the changes in effect size may reflect shifts in the world. For example, the 2018 drop might link to data scandals like those involving Facebook, rising trade tensions between the US and China, and global economic worries. The 2020 increase likely happened because the internet became more important for social connections, remote work, and information during COVID-19. Third, the decline from 2020 to 2022 is worth noting. It could mean the digital divide narrowed, pandemic restrictions eased, and offline activities resumed, lowering internet reliance. It might also show growing concerns about too much internet use, such as addiction or information overload.\u003c/p\u003e \u003cp\u003eLooking at developed and developing countries gives more insight (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e). Both groups followed similar patterns, but developed countries saw stronger overall effects from internet access. This difference could come from better digital infrastructure, higher digital skills, and more uses for the internet in developed nations. The big 2020 peak shows the internet was key for social and personal well-being during the global crisis, especially in developed countries. This reflects their faster shift to remote work, online learning, and digital socializing. However, both groups saw a drop in the effect from 2020 to 2022. The decline was sharper in developing countries. This may reflect challenges like weaker digital systems, uneven economic recovery, or struggles to keep using digital tools after the pandemic. For developed countries, the slower decline might suggest they reached a balance where the internet is fully part of daily life, its extra benefits have leveled off.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFurthermore, through an in-depth analysis of two periods - before and after COVID-19 (2016\u0026ndash;2019 and 2020\u0026ndash;2022)\u0026mdash;shows how internet access affected well-being differently across countries (Figs.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e and \u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e). Most countries had positive effects in both periods, but the strength of these effects varied. Many countries, especially in the Americas, Europe, and East Asia, saw a rise in the effect during the second period. This lines up with the COVID-19 outbreak, supporting the idea that the internet played a key role during the crisis. High internet use and smaller digital divides in these regions likely helped. However, not every country followed this upward trend. Some, like India, Finland, and Australia, saw declines in the effect during 2020\u0026ndash;2022. These differences may reflect how each country handled the crisis and used digital tools. This shows that the internet\u0026rsquo;s impact on well-being during the pandemic was complex and varied.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec16\" class=\"Section2\"\u003e \u003ch2\u003eAnalysis of influencing factors\u003c/h2\u003e \u003cdiv id=\"Sec17\" class=\"Section3\"\u003e \u003ch2\u003eAnalysis of factors affecting Internet access\u003c/h2\u003e \u003cp\u003eBased on our analysis of the SHAP values for various variables, we can gain a comprehensive understanding of the key factors influencing the prediction of internet connectivity. Age, income, education level, and health status all affect the model\u0026rsquo;s predictions to varying degrees, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eAge shows a significant negative correlation with predicted internet connectivity: the younger cohort aged 0\u0026ndash;40 is more likely to be predicted as having internet connectivity, with predominantly positive SHAP values; the middle-aged group of 40\u0026ndash;60 years begins to show a negative influence; and the elderly group above 60 years exhibits markedly negative SHAP values that decrease with increasing age. This reflects the disparities in technological adaptability and usage habits across different age groups.\u003c/p\u003e \u003cp\u003eHousehold Income displays a strong positive correlation with predicted internet connectivity. Low-income groups have negative SHAP values, indicating a reduced likelihood of predicted internet connectivity, while high-income groups show significantly positive SHAP values with a broad range of influence, underscoring the crucial role of economic factors in internet access. Notably, the impact of income exhibits a saturation effect at higher levels, suggesting that beyond a certain income threshold, further increases have a diminishing effect on internet connectivity predictions.\u003c/p\u003e \u003cp\u003eEducational attainment similarly exhibits a strong positive influence. Low education levels (primary school and below) are associated with negative SHAP values, middle education levels (secondary school) show relatively neutral effects, and higher education levels demonstrate markedly positive SHAP values. This trend presents non-linear characteristics, with the transition from low to middle education levels having a more pronounced impact on prediction outcomes, emphasizing the significance of basic education in bridging the digital divide.\u003c/p\u003e \u003cp\u003eAlthough exerting a comparatively minor influence, health status reveals noteworthy patterns. Individuals without health issues have slightly positive SHAP values, while those with health problems affecting daily activities show negative SHAP values. This suggests that health impediments may indirectly affect internet access by influencing an individual's economic status, social interactions, or ability to use devices.\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv id=\"Sec18\" class=\"Section2\"\u003e \u003ch2\u003eDifference analysis of variable contribution in Stratified XGBoost models\u003c/h2\u003e \u003cp\u003eBased on our comparative analysis of SHAP values for various variables in both models, we can comprehensively understand the key factors influencing well-being with and without internet connectivity. By comparing the importance and degree of difference among variables, we have once again selected age, income, education, and health status as critical variables for analysis, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eIn the age dimension, the impact of the internet on well-being exhibits a pronounced U-shaped curve. For individuals under 20 and over 50, the SHAP value distributions are generally consistent regardless of internet access, indicating that internet connectivity has little influence on their happiness. However, there are significant differences among individuals aged 20\u0026ndash;50. In this age group, although the SHAP values are negative in both scenarios, those with internet access show significantly higher SHAP values compared to those without. This may reflect the effects of learning, work-related stress, and family responsibilities on young and middle-aged individuals\u0026mdash;issues that the internet cannot fundamentally resolve but can help alleviate to some extent.\u003c/p\u003e \u003cp\u003eIn the dimension of household income, internet access has a notably different impact across income groups. For low-income individuals (annual income below 5,000), SHAP values improve with internet access, shifting from entirely negative (-1.0 to 0) to partially positive (-0.5 to 0.25). This suggests that the internet may provide more economic opportunities and better access to information, thereby improving life satisfaction for low-income groups to some extent. For middle-income groups (annual income between 5,000 and 10,000), the SHAP value trends are largely similar regardless of internet access, showing an upward trajectory, which indicates that increasing income itself improves life satisfaction and that internet access has limited additional impact. The same holds true for high-income groups (annual income over 10,000), where SHAP values remain stable between 0 and 0.75 with or without internet access. This suggests that high-income individuals already have sufficient resources and channels to fulfill their information, social, and entertainment needs, making the presence of internet access less influential on their quality of life.\u003c/p\u003e \u003cp\u003eRegarding education level, the impact of internet access also varies across different educational backgrounds. For individuals with low education levels (primary school), SHAP values increase from mostly negative (-0.25 to 0) to partially positive (-0.2 to 0.1) with internet access, indicating that the internet may help bridge educational gaps through online learning and skill development. For those with medium education levels (middle to high school), the distribution of SHAP values becomes broader with internet access (-0.05 to 0.15 compared to 0 to 0.15 without), which may reflect new challenges introduced by the internet, such as youth internet addiction. Interestingly, for highly educated individuals, SHAP values decrease from 0.02\u0026ndash;0.3 without internet to 0\u0026ndash;0.2 with internet access. This shift warrants further research and may be related to unique pressures faced by highly educated individuals in the digital age.\u003c/p\u003e \u003cp\u003eIn terms of health status, internet access appears to play a moderating role in the relationship between physical health and well-being. For individuals without health problems, internet access slightly reduces the positive impact on well-being (SHAP values decline from 0\u0026ndash;0.15 to -0.05\u0026ndash;0.12), which may be linked to sub-health conditions caused by excessive use of electronic devices. However, among individuals with health issues, although most SHAP values remain in the negative range, those with internet access show a noticeably higher proportion of positive values. Their SHAP values expand from a range of -0.3 to 0.05 (no internet) to -0.3 to 0.15 (with internet). This finding highlights the potential of the internet in supporting telemedicine consultations, access to health information, and chronic disease management.\u003c/p\u003e \u003c/div\u003e"},{"header":"Discussion","content":"\u003cp\u003eOur research shows that internet access has a clear and positive effect on well-being. People with internet access score higher on well-being (5.32) compared to those without it (4.96). This highlights how internet connectivity can improve well-being. It supports earlier studies that show the internet helps people by providing access to information, connecting socially, and offering economic opportunities (World Bank, \u003cspan citationid=\"CR70\" class=\"CitationRef\"\u003e2016\u003c/span\u003e; Castellacci \u0026amp; Tveito, \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2018c\u003c/span\u003e). The kernel density plot (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e) gives us a closer look at well-being scores. It shows that people with internet access tend to have moderate to high levels of well-being. This might be because the internet helps with personal growth, social activities, and access to useful resources (Lissitsa \u0026amp; Chachashvili-Bolotin, \u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e2016\u003c/span\u003e). On the other hand, the slightly higher density of low scores (0\u0026ndash;3) in the group without internet access suggests that lack of connectivity may be associated with a higher risk of extremely low well-being, highlighting the potential of internet access as a protective factor against severe declines in life satisfaction.\u003c/p\u003e \u003cp\u003eOur time series analysis from 2016 to 2022 shows that the relationship between Internet access and well-being is evolving under the influence of global events and social changes, with significant differences observed across different types of countries. We saw a peak in 2020, which aligns with the COVID-19 pandemic. During this time, the positive effects of internet access increased, supporting findings that digital technologies were crucial for staying connected, working remotely, and getting information during lockdowns (Beaunoyer et al., \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e2020\u003c/span\u003e; Nguyen et al., \u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). However, from 2020 to 2022, the effect started to decrease. This trend needs careful analysis. It might mean people are getting used to the internet in daily life, leading to less noticeable benefits. Or it could suggest a growing awareness of downsides like information overload or digital fatigue (Reinecke et al., \u003cspan citationid=\"CR60\" class=\"CitationRef\"\u003e2017b\u003c/span\u003e). Internet access has had a stronger positive effect in developed countries than in developing ones. This shows the link between digital infrastructure, economic development, and well-being. Developed countries likely benefit from better digital systems, higher digital literacy, and more varied internet use (Pick \u0026amp; Sarkar, \u003cspan citationid=\"CR56\" class=\"CitationRef\"\u003e2015\u003c/span\u003e). In contrast, developing countries faced a sharper decline in the internet's positive effects after 2020. This highlights their challenges in maintaining digital progress post-pandemic and the need for targeted policies and investments to close the digital gap(Broadband Commission, \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2020\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eWe also examined other factors affecting internet access and its impact on well-being. There is a negative correlation between age and internet use, with younger people being more likely to have internet access, indicating generational differences in technology adoption (Friemel, \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2014\u003c/span\u003e). Interestingly, the impact of internet access on well-being forms a U-shaped curve across different age groups, where internet connectivity can somewhat alleviate the negative impact on well-being for younger and middle-aged groups. For young and middle-aged people, this might be related to the internet providing more career development and social opportunities (Garc\u0026iacute;a Galera et al., \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2013\u003c/span\u003e). Income is strongly correlated with internet access, showing that economic barriers are a significant factor in accessing the internet (Cai, \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2008\u003c/span\u003e). However, internet access can alleviate some of the negative effects faced by low-income groups, which is consistent with research on the internet's ability to promote economic opportunities and reduce inequalities (World Bank, \u003cspan citationid=\"CR70\" class=\"CitationRef\"\u003e2016\u003c/span\u003e). Education plays a key role in internet access and its impact on well-being. Digital literacy is crucial for maximizing online benefits(van Deursen \u0026amp; van Dijk, \u003cspan citationid=\"CR68\" class=\"CitationRef\"\u003e2010\u003c/span\u003e). However, there\u0026rsquo;s an unexpected drop in the positive impact of internet access for highly educated groups, which needs further study. It could reflect unique challenges these groups face in the digital age. Lastly, internet access significantly moderates the relationship between physical health and well-being. This aligns with research on the benefits of online health services and telemedicine. For people with health issues, the internet makes it easier to access health information and services, improving their outcomes(Litchfield et al., \u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e2021\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eOur study's approach and findings greatly enhance understanding of the link between digitalization and well-being, showing clear benefits over earlier research. First, we used the XGBoost regression model instead of traditional linear regression. This model captures complex, non-linear relationships and interactions between variables. This is crucial when studying complex social topics like how internet access affects well-being. For instance, (Castellacci \u0026amp; Tveito, \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2018c\u003c/span\u003e)noted that many studies use linear models to explore this link, which might miss non-linear effects. Our XGBoost model, with its tree structure and ensemble learning, captures these complex patterns, providing a more accurate analysis. Second, we applied the PSM method to address selection bias, improving on many past studies. (Lissitsa \u0026amp; Chachashvili-Bolotin, \u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e2016\u003c/span\u003e) conducted a large-scale study on internet use and life satisfaction in Israel from 2003 to 2013. However, they mainly used multivariate regression without fully controlling for the endogeneity between internet access and other socioeconomic factors. Our PSM approach reduces the influence of these confounding factors by creating comparable treatment and control groups. Our SMD results validate this; the average absolute SMD dropped from 0.12 to 0.02 after matching, well below the standard threshold of 0.1. This enhances the reliability of our research findings. Third, we used SHAP to interpret our model's results, adding depth to traditional regression coefficient interpretation. Compared to Jebb et al., \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e2018\u003c/span\u003e, our approach not only pinpoints key factors affecting well-being but also measures the contribution of each factor in various contexts. This method offers a more detailed analysis, showing different effects of internet access on well-being across income groups or age brackets. Lastly, our research uses a large dataset from the GWP dataset, covering 17 survey waves from 2005 to 2022 across 168 countries and regions, with 2.594\u0026nbsp;million observations. After careful cleaning and processing, our final sample includes around 1\u0026nbsp;million observations. While this reduced our sample size, the data's scale and scope still surpass many previous studies. For instance, (\u0026Ccedil;ikrıkci, \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2016\u003c/span\u003e) studied the impact of internet use on well-being in more detail but had a shorter time span and smaller sample size compared to ours. We reduced our sample to ensure high data quality, removing incomplete records and ensuring consistency across time and regions. This processed dataset enhances the representativeness and generalizability of our findings and allows detailed cross-country and time trend analyses. This large, multi-country dataset helps us thoroughly examine the impact of internet access on well-being, considering various socioeconomic factors. Overall, our research provides more comprehensive, accurate, and reliable insights into the impact of internet access on well-being by combining advanced machine learning techniques, rigorous methods, and large-scale cross-national data. These methodological innovations enable us to move beyond simple correlation analysis, revealing more complex and nuanced relationship patterns, and providing more valuable reference for policymakers and researchers.\u003c/p\u003e \u003cp\u003eOur study has many strengths, but there are still some important limitations. These point to good directions for future research. First, we used advanced methods like PSM to reduce selection bias. However, since our data is cross-sectional, it is hard to draw clear cause-and-effect conclusions. Future studies could use designs like experiments or follow people over time. These approaches could show how internet access impacts well-being in the long run. Second, we mostly looked at whether people had internet access or not. We didn\u0026rsquo;t focus much on the quality of access, like speed and reliability, or how people use the internet. Future research could gather more details about this. For example, they could study how often people go online, what they do, and if the speed of their connection matters. This could give a clearer picture of how the internet affects well-bing. Third, we used SHAP methods to explain the results of our XGBoost model. But machine learning models are still difficult to fully understand due to their \u0026ldquo;black box\u0026rdquo; nature. Future research could try other methods that are easier to explain. Combining these with interviews or surveys could also help. This would make it easier for researchers and policymakers to understand the results. By solving these issues, future studies can help us learn more about the link between the internet and well-being. They can also provide better evidence for creating policies to improve people\u0026rsquo;s lives in the digital age.\u003c/p\u003e"},{"header":"Conclusion","content":"\u003cp\u003eThis study uses the GWP global dataset from 2016 to 2022 to explore how internet access affects well-being. We found clear evidence that internet access has a positive impact on people\u0026rsquo;s well-being. However, the effects are different for various groups of people. The results show that having internet access improves well-being, especially during the COVID-19 pandemic. After the pandemic, the positive effects gradually became weaker through 2022.The impact of internet access also depends on the region. In developed countries, the benefits are stronger and more stable. In developing countries, the effects are less consistent. Using XGBoost and SHAP analysis, we also found some interesting patterns. For example, internet access can alleviate the negative impact on well-being experienced by young and middle-aged groups. When we looked at income, we found that internet access is most helpful for people in low-income groups. For education, those with less schooling benefit more from having internet access. Internet access also helps people with health problems feel better by reducing the negative effects of those issues. These findings have crucial implications for policymaking, suggesting the need for targeted digital inclusion strategies considering age-specific needs, continued enhancement of digital infrastructure, especially in developing countries, development of comprehensive digital health services, and tailored digital literacy education programs.\u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eFunding\u003c/h2\u003e \u003cp\u003eThis research was supported by JSPS KAKENHI (Grant Nos. JP20H00648 and JP21K17927) and JST Mirai Program (Grant No. JPMJMI22I4).\u003c/p\u003e\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eJ.Z. wrote the main manuscript text and designed the model; C.L. provided technical support; B.S. assisted with data processing; A.R.K. polished the manuscript text; S.M. provided the raw data and contributed to revising the manuscript text. All authors reviewed the manuscript.\u003c/p\u003e\u003ch2\u003eData Availability\u003c/h2\u003e\u003cp\u003eWe used the Gallup World Poll dataset, and the data can be accessed at the following link: https://www.gallup.com/178667/gallup-world-poll-work.aspx\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eBeaunoyer, E., Dup\u0026eacute;r\u0026eacute;, S. \u0026amp; Guitton, M. J. COVID-19 and digital inequalities: Reciprocal impacts and mitigation strategies. \u003cem\u003eComput. Hum. 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(2020).\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Subjective well-being, Digital divide, Machine learning, Propensity score matching","lastPublishedDoi":"10.21203/rs.3.rs-8160157/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8160157/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eIn this rapidly evolving digital age, the impact of internet access on human well-being has become a key issue of social equity and development. As the global digital divide widens, little is known about how internet access affects individual subjective well-being (SWB). This study uses the Gallup World Poll (GWP) dataset, covering approximately 1\u0026nbsp;million observations from 168 countries between 2016 and 2022. Using machine learning techniques with propensity score matching models, we explore how digital connectivity influences SWB across dimensions. Our study finds that internet access can increase SWB by 9.2% and help bridge the digital divide. This relationship varies across time, countries, and demographic characteristics. The positive impact peaked during the COVID-19 pandemic and gradually declined afterward. Across different levels of national development, the positive effect of internet access on SWB is more pronounced and stable in developed countries compared to developing countries. Demographically, Internet access enhances the subjective well-being of young and middle-aged groups. Additionally, internet access helps reduce the negative impact of poor health and low income on SWB. Governments should bridge the digital divide through infrastructure and subsidies for vulnerable groups, ensuring equal internet access to enhance social well-being.\u003c/p\u003e","manuscriptTitle":"Bridging the Digital Divide: Machine Learning Analysis of Internet Access Effects on Subjective Well-Being","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-04-27 11:35:14","doi":"10.21203/rs.3.rs-8160157/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"bc81fd43-ba03-4d5e-b509-73ed58b6c184","owner":[],"postedDate":"April 27th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":67014210,"name":"Health sciences/Health care"},{"id":67014211,"name":"Physical sciences/Mathematics and computing"}],"tags":[],"updatedAt":"2026-04-28T07:09:56+00:00","versionOfRecord":[],"versionCreatedAt":"2026-04-27 11:35:14","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8160157","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8160157","identity":"rs-8160157","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}