Mental Health Risk of Students: an Analysis by Binary Logistic Regression

Bianca Lima Marchionno; Igor Pinheiro de Araújo Costa

DOI: 10.22167/2675-6528-202602722

Article derived from a Course Conclusion Work (TCC), with content based on the student’s original work and adapted to the editorial format of the E&S Magazine with the support of the ResumeAI tool, an artificial intelligence solution developed by Instituto Pecege for textual synthesis and organization.

Summary

Entry into higher education imposes challenges that can generate stress and increase students’ psychological vulnerability, making mental health a central concern. Behavioral and socioeconomic factors associated with mental health risk for incoming students at a Brazilian public university were analyzed, using data from 2022 to 2024. Public data from a socioeconomic survey were subjected to descriptive analyses and binary logistic regression modeling, which allowed estimating the probability of the event’s occurrence and evaluating the influence of explanatory variables through odds ratios. The results indicated that behavioral factors, such as alcohol and tobacco consumption, were associated with a higher probability of mental health risk. Socioeconomic variables, including per capita income and family characteristics, also showed relevant association. In contrast, regular physical activity was associated with reduced risk. The model showed low predictive capacity (AUC of 0.654 and accuracy of 61.2%), but fulfilled its inferential purpose by isolating and quantifying the relative weight of each risk factor. With a cutoff of 0.5, the model achieved a sensitivity of 70.4% in identifying students at risk. The findings reinforced that university mental health is influenced by multiple factors, underscoring the need for integrated approaches and institutional policies to promote psychological well-being and prevent risks.

Keywords: University students; Lifestyle habits; Statistical modeling; Mental health.

1. Introduction

Entry into higher education represents a period of significant transformations in students’ lives, marked by new academic responsibilities, challenges in the job market, and the expansion of social relationships. Such changes can generate stress and increase psychological vulnerability, making mental health a central concern for educational institutions, families, and society. Mental health is an essential pillar of quality of life, directly related to an individual’s ability to perform their daily functions, cope with challenges, and maintain social relationships.

However, exposure to stressful environments and challenging situations can compromise the balance of psychological well-being and contribute to the development of mental disorders. The World Health Organization (2022) highlights that approximately one in eight people live with some mental disorder worldwide, with a 25% increase in cases of anxiety and depression in the first year of the COVID-19 pandemic alone, evidencing a global trend of worsening mental health crisis.

In the Brazilian university context, the reality is also alarming. A recent study with 7,177 university students revealed that 75.81% stated that the university considerably impacted their health or that of their colleagues (Barros and Peixoto, 2023). The same research indicated that most students belonged to low-income families, did not participate in social groups, and practiced physical exercises infrequently. These findings suggest that socioeconomic and behavioral factors may aggravate psychological vulnerability among students.

Furthermore, the consumption of alcohol and other substances is a relevant factor in the university environment, often associated with socialization processes and coping with academic pressures. A 2019 study indicated that 79.8% of students at a university in São Paulo reported consuming alcoholic beverages, and 25% consumed some type of tobacco derivative (Barros and Costa, 2019). Epidemiological evidence reinforces that alcohol consumption is associated with higher risks of physical illnesses and mental disorders (Heckmann and Silveira, 2009), underscoring the importance of analyzing these behaviors in the context of mental health.

Given the complexity of factors influencing the mental health of university students, it becomes essential to identify and understand the determinants of this risk. The analysis of these factors is crucial for the development of integrated approaches and effective institutional policies, aiming to promote psychological well-being and prevent risks. For this purpose, binary logistic regression is a suitable statistical technique, as it allows estimating the probability of a dichotomous event, such as mental health risk, occurring from explanatory variables, evaluating the influence of these variables through odds ratios (Fávero and Belfiore, 2024; Bruce and Bruce, 2019).

This study is justified by the need to deepen the knowledge about the multiple factors that contribute to psychological vulnerability in the academic environment, providing subsidies for data-driven university management and the construction of more targeted preventive strategies. Thus, the present work aims to analyze the determinants of mental health risk among incoming students at a Brazilian public university, considering individual, behavioral, and socioeconomic variables.

2. Material and Methods

The present study adopted a quantitative and explanatory approach, aiming to analyze the determinants of mental health risk among university students. The methodology employed binary logistic regression modeling, preceded by descriptive data analyses. The methodological structure focused on the characterization of the database, treatment of variables, and specification of the statistical model.

The data were obtained from a public dataset, in Excel format, corresponding to the Socioeconomic Report of Students entering the Federal University of São Paulo (UNIFESP). The information, collected annually by questionnaire, covers the period from 2022 to 2024 and includes individual, socioeconomic, financial, and health data. A data dictionary was provided by the institution to aid in understanding.

The initial sample consisted of 7,869 participants. After excluding records with missing data (proportions below 1%), the final dataset for modeling totaled 7,809 observations. Participants were incoming students, with 76.25% in the 17 to 23 age group and 62.82% identifying as female.

For data treatment and preparation, the 2022, 2023, and 2024 databases were consolidated. The selection of variables of interest and processing were performed in Python, using the pandas, statsmodels, and scikit-learn libraries. Microsoft Excel was employed complementarily for organization and visualization.

The binary dependent variable (y) was created to indicate the presence of mental health risk, assuming a value of 1 if the individual presented at least one of the symptoms (insomnia/sleep disturbance, persistent sadness, suicidal thoughts, or panic/anxiety) and 0 otherwise. This variable represents a general indicator of vulnerability, not a clinical diagnosis.

Eight explanatory variables (x) were selected, covering individual, behavioral, and socioeconomic aspects. Per capita income was treated as a continuous quantitative variable, and the number of people in the household as a discrete quantitative variable. The other variables were classified as nominal or ordinal qualitative variables (Bonafini, 2019).

The base treatment included the standardization of the variable number of people in the household (quest24) and the removal of extreme values. Categorical variables were regrouped and recoded into binary format (consumption = 1; no consumption = 0 for alcohol and tobacco). Physical activity was reorganized into None, Sporadic, and Regular, and the presence of children was dichotomized into 0 and 1+.

To mitigate multicollinearity, categorical variables were transformed into “dummies”, excluding the reference category (Fávero and Belfiore, 2024). The references were: female sex, non-consumption of alcohol and tobacco, absence of children, and sporadic physical activity. The multicollinearity diagnosis, via Variance Inflation Factor (VIF), indicated model stability, with all values below 5.4.

Binary logistic regression was employed for model specification, given the dichotomous nature of the dependent variable. This technique, part of Generalized Linear Models (GLM), estimates the probability of an event occurring from explanatory variables (Bruce and Bruce, 2019). The relationship is expressed by the logit (Z), a linear combination of the explanatory variables and their coefficients: Z = α + β1.X1i + β2.X2i + … + βk.Xki. Parameter estimation was performed using the maximum likelihood method (Kleinbaum and Klein, 2010).

For the model refinement, the “stepwise” procedure with backward elimination was used. This method iteratively removes non-significant variables (p-value > 0.05) until only significant ones remain (Hair et al., 2009). The family contribution structure variable (quest22) and the category ‘no physical activity practice’ were removed due to lack of statistical significance.

The model evaluation involved defining three cutoff points (0.3; 0.5 and 0.7) to classify the estimated probabilities. For each point, a classification matrix was constructed, comparing observed and predicted values to identify hits and errors (Hair et al., 2009). Based on this, performance metrics such as accuracy, sensitivity, and specificity were calculated.

Additionally, the “Receiver Operating Characteristic” (ROC) curve was constructed and the area under the curve (AUC) was calculated to evaluate the model’s discriminatory capacity (Bruce and Bruce, 2019). The Gini coefficient was also obtained. Finally, the estimated coefficients were transformed into “odds ratios”, allowing the effect of the explanatory variables on the probability of the event occurring to be interpreted.

3. Results and Discussion

The data analysis began with descriptive statistics, aiming to characterize the sample of incoming students at a Brazilian public university between 2022 and 2024. The final database, after excluding records with missing data, totaled 7,809 observations. This preliminary step was crucial for understanding the distribution of variables before applying the logistic regression model, providing an initial overview of the participants’ behavioral and socioeconomic factors.

Regarding the dependent variable, which indicated mental health risk, a relatively balanced distribution was observed in the sample. Approximately 52.81% of students were classified as at risk, while 47.19% showed no risk. This proportion indicates that the phenomenon of interest is present in a significant portion of the studied population, without a severe imbalance between classes, which is favorable for subsequent statistical modeling.

The demographic profile of the students revealed a predominance of the female sex, representing 62.84% of the sample, while male individuals accounted for 37.16%. This characteristic of the sample is relevant for the interpretation of the results, especially regarding the association between gender and mental health risk, an aspect frequently addressed in the literature on university health.

Regarding the behaviors analyzed, alcohol consumption showed an almost equitable distribution, with 54.16% of students indicating consumption and 45.84% not consuming. In contrast, tobacco consumption was less prevalent, with 90.09% of students reporting not consuming this substance and only 9.91% reporting consumption. These behavioral data are crucial for understanding the lifestyle patterns in the university population.

The practice of physical activity also showed varied patterns among students. It was found that 37.57% of participants practiced activities regularly, which is a positive indicator of healthy habits. However, a considerable portion, 33.87%, declared not practicing any physical activity, and 28.56% carried out activities sporadically, highlighting the need for encouragement towards regular practice.

The students’ family structure showed that the vast majority, 96.38%, had no children, while 3.62% indicated having at least one child. For the quantitative variables, the average per capita income of the students was 1.46 minimum wage, with a standard deviation of 1.03, and the average number of people in the household was 3.42, with a standard deviation of 1.15. These values indicate heterogeneity in the socioeconomic and family composition conditions of the participants.

In summary, the descriptive analysis revealed a predominantly young sample, with a female predominance and low incidence of children. Income and household composition conditions showed variation, and different behavioral patterns were identified regarding alcohol consumption, tobacco, and physical activity. These factors are fundamental for understanding mental health risk and served as the basis for statistical modeling, allowing for the exploration of associations between these variables and the outcome of interest.

For the modeling of mental health risk, binary logistic regression was employed, a technique suitable for dichotomous dependent variables. The variable selection process used the “stepwise” method with backward elimination, which iteratively removed non-significant variables at the 5% level (Hair et al., 2009). This procedure resulted in a more parsimonious and statistically robust model, focusing only on the most relevant predictors.

During the selection, the variable related to family contribution structure (quest22) was excluded due to p-values greater than 0.05 in its categories. Similarly, the category ‘no physical activity practice’ was discarded, as its p-value of 0.0735 indicated that sedentary behavior did not statistically differ from sporadic practice in relation to risk. The income_sm variable was also excluded prior to modeling due to multicollinearity with per capita income, ensuring model stability.

The final model included statistically significant variables (p-value < 0.05), which were: student’s sex, alcohol consumption, tobacco consumption, regular physical activity, presence of children, per capita income, and number of people in the household. The inclusion of these variables, transformed into “dummies” for the categories, allowed for the interpretation of the coefficients in relation to a reference category, facilitating the understanding of the impact of each factor on mental health risk.

The model’s results indicated that behavioral and socioeconomic factors are significantly associated with mental health risk among university students. The confidence intervals of the estimates did not include the value 1, which reinforces the consistency and statistical significance of the identified associations. This finding underscores the multifaceted nature of psychological well-being in the academic environment, as pointed out by Silva et al. (2021).

Regarding gender, male individuals showed a reduction of approximately 50.3% in mental health risk chances, with an odds ratio (OR) of 0.4968, compared to females, with other variables held constant. This finding corroborates the literature that points to a higher prevalence of common mental disorders among women, often associated with psychosocial factors and gender burdens (Barros and Peixoto, 2023).

Regarding behaviors, alcohol and tobacco consumption acted as significant risk factors. Alcohol use increased the chances of the event occurring by 1.79 times (OR=1.79), while tobacco consumption increased this chance by almost double (OR=1.95). The comparison between the two behaviors revealed that tobacco consumption had a stronger effect on mental health risk than alcohol consumption, with a higher odds ratio.

This finding about alcohol and tobacco consumption aligns with the literature, which identifies a relevant prevalence of problematic alcohol consumption among university students, reaching about 23.6% of students (Silva et al., 2021). The association of these behaviors with mental health risk reinforces the need for targeted interventions, considering the university environment as a context of vulnerability.

Regular physical activity, in turn, has been shown to be a protective factor. Students who practiced physical activities regularly showed a reduction in mental health risk, with an odds ratio (OR) of 0.7127, compared to those who practiced sporadically. This result highlights the importance of healthy lifestyle habits as a protective mechanism against the development of mental health problems, a finding consistent with previous studies (Bastos et al., 2024).

Structural and family factors also proved relevant. The presence of children was associated with a strong reduction in mental health risk, with an odds ratio (OR) of 0.54. However, this interpretation should be made with caution, given that only 3.62% of the sample had children, which may influence the stability of the estimate. The low representativeness of this category in the sample may limit the generalization of this finding.

Better socioeconomic conditions and family support also acted as protective elements. Per capita income, with an odds ratio (OR) of 0.9176, indicated that increases of one unit (equivalent to one minimum wage per capita) were associated with a reduction in the chances of mental health risk. Similarly, the number of people in the household, with an OR of 0.909, suggested that an increase in family composition is associated with a decrease in risk, indicating that family support may be a protective factor.

To evaluate the model’s predictive performance, different cutoffs were analyzed, specifically 0.3, 0.5, and 0.7. The choice of the 0.5 cutoff was adopted as the final criterion, as it presented the best balance between accuracy, sensitivity, and specificity metrics. This decision is fundamental for the practical application of the model, as it defines from which probability an observation is classified as an occurrence of the event (Fávero and Belfiore, 2024).

With a cutoff point of 0.5, the model achieved an Accuracy of 0.612, indicating that 61.2% of the classifications were correct. The sensitivity was 0.704, meaning that 70.4% of at-risk students were correctly identified. The specificity was 0.509, indicating that 50.9% of non-risk students were correctly classified. The model correctly classified 2,902 at-risk students (true positives) and 1,877 non-risk students (true negatives), but also generated 1,808 false positives and 1,222 false negatives.

Additionally, the Area Under the Curve (AUC) was calculated at 0.654, and the Gini coefficient at 0.307. The AUC is a measure of the model’s discriminatory capacity, where higher values indicate greater effectiveness in distinguishing between classes. A value of 0.654 suggests a moderate discriminatory capacity, superior to total inefficiency (0.5), but indicating that the model has greater inferential than predictive utility for individual risk cases (Bruce and Bruce, 2019).

Despite the moderate predictive capacity, the results obtained should be interpreted considering the complexity of predicting mental health-related conditions. Studies such as Zhai et al. (2025), which evaluated predictive models for anxiety and depression in university students, obtained AUCs of 0.73 and 0.76, and accuracies of 68% and 70%, respectively. This comparison reinforces that the identification of mental health conditions requires different evaluation metrics and that the AUC of 0.654, in the present study, should be analyzed together with the other metrics and the characteristics of the problem.

Complementary metrics, such as precision (approximately 0.62) and F1-score (approximately 0.66), were also considered in the model’s performance evaluation. These indicators reinforce the model’s ability to identify patterns associated with mental health risk, highlighting the influence of behavioral and socioeconomic factors. The multidetermined nature of the mental health phenomenon is, therefore, consistently evidenced by the findings (Silva et al., 2021).

The results obtained allow us to move from statistical analysis to decision-making in the institutional context. The identification of behavioral factors, such as alcohol and tobacco consumption, associated with an increased risk in mental health, enables the direction of more specific preventive actions. These actions can focus on groups more exposed to these behaviors, promoting an academic environment that prioritizes students’ psychological well-being.

The evidence that regular physical activity acts as a protective factor suggests the need to strengthen institutional policies aimed at promoting student well-being. Continuous health education and prevention programs, including workshops and lectures on the risks of psychoactive substance use, can be implemented. Such initiatives are crucial for raising student awareness and offering coping mechanisms for academic stress, as recommended by Gomes et al. (2023).

Additionally, the relevance of socioeconomic variables, such as per capita income, allows for the identification of students in greater situations of vulnerability, contributing to the prioritization of resources and psychosocial support actions. The model’s main contribution lies in supporting data-driven university management, enabling the construction of more targeted preventive strategies and the strategic use of institutional information to promote well-being and prevent risks (Gaiotto et al., 2021).

In summary, the findings of this study demonstrate that the mental health risk of university students is influenced by a complex interaction of behavioral and socioeconomic factors. Binary logistic regression modeling allowed for the quantification of the relative weight of each factor, revealing that alcohol and tobacco consumption increase the risk, while regular physical activity, the presence of children, per capita income, and the number of people in the household act as protective factors. These results reinforce the need for integrated approaches and institutional policies to promote psychological well-being and prevent risks among incoming students, responding to the objective of analyzing the determinants of mental health risk.

4. Conclusion

This study analyzed the determinants of mental health risk among incoming students at a Brazilian public university, considering individual, behavioral, and socioeconomic variables. It was found that behavioral factors, such as alcohol and tobacco consumption, were associated with a significant increase in the probability of mental health risk, with tobacco being a stronger predictor. In contrast, regular physical activity practice proved to be a protective factor, associated with risk reduction. Additionally, it was identified that socioeconomic and family variables, such as higher per capita income and a large number of people in the household, also acted as protective elements, while males presented a lower chance of risk compared to females. Although the binary logistic regression model exhibited moderate predictive capacity, with an accuracy of 61.2% and an AUC of 0.654, its inferential utility was robust, allowing for the isolation and quantification of the relative weight of each risk factor. The main contribution of this work lies in providing data-driven subsidies for university management, enabling the construction of more targeted preventive strategies and the strategic use of institutional information to promote psychological well-being and prevent risks.

However, the study has limitations due to the use of data from a single institution and a specific time frame, which restricts the generalization of the findings. The combination of distinct psychological symptoms into a single binary dependent variable may have introduced classification errors, justifying the moderate predictive performance observed. It is suggested that future studies explore models that break down psychological symptoms and include academic variables to enhance predictive capacity. Replication of the methodological approach in other universities with similar databases is also recommended, expanding the potential for strategic use of data in formulating psychosocial support policies and mental health management in higher education.

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Article originating from the Final Course Project of the Specialization in Data Science and Analytics of the MBA USP/Esalq

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