Model Selection Analysis for Predicting Students Mental Health from Academic and Psychological Variables

Abstract

This paper proposes a complete model selection analysis in order to predict mental health index based on 15 predictor variables taken from student mental health and burnout dataset (N = 2,549). The approach uses the stepwise regression method, which includes forward, backward and bidirectional selection procedures along with the FWDselect method for predictor selection with maximal information content. The results show that the entire 15-predictor model provides perfect goodness of fit (R² = 1.0), having near-zero residuals (10⁻¹⁰), which means that the mental health index in the given case is entirely defined by the predictor variables as a linear combination of stress level, anxiety score, and depression score. Stepwise regression allows reducing the entire model down to six core predictors (stress level, anxiety score, depression score, sleep hours, dropout risk and study hours per day) without any loss of predictive power. The FWDselect procedure proves stress level as the only necessary predictor, providing nearly 90.7% of variance, while three mental health subscales are selected at the first positions across all model sizes. There is no problem with multicollinearity (all VIF < 10) despite the perfect fit, since the latter is quite high and does not affect the reliability of the model. Thus, one can conclude that the mental health index in the dataset is primarily constructed from psychological distress measures, raising important questions about the construct validity of composite mental health indices and the implications for predictive modelling in mental health research.