A methodological illustration of robust regression for estimating the financial stress-mental health relationship in student populations

The rising prevalence of mental health difficulties among higher education students is a widely documented concern, with financial stress consistently identified as a contributing factor. This study illustrates how outliers can substantially distort the estimated relationship between financial stress and a mental health index using a dataset constructed to demonstrate this problem, since conventional ordinary least squares (OLS) regression is highly sensitive to such observations. A comparative robust regression analysis was conducted, contrasting OLS with M-estimation (bisquare and Huber weighting), S-estimation, and MM-estimation, alongside two outlier-treatment strategies (case deletion and mean imputation), using 2549 student records. The study demonstrates that OLS estimates are severely attenuated by outliers (R²=0.042), whereas robust methods yield substantially stronger associations (R²≈0.17-0.20), with slopes 23-44% steeper than the OLS estimate. M-estimation with bisquare weighting and MM-estimation produced almost identical coefficients, indicating stable estimation. These findings underscore the value of robust regression for accurate inference and caution against overreliance on OLS without outlier diagnostics.

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