This study investigates the application of cumulative link models with alternative distributions (hyperbolic secant, Laplace, and Cauchy) to model ordinal outcomes of depressive severity using 2022 National Health Interview Survey data. The primary objective was to assess whether these models provide a better fit to ordinal response data and more accurate predictions than their traditional counterparts with the logit link function. The results indicate that the logit model achieved the highest classification accuracy, correctly classifying 83.54% of the cases. The Cauchy model demonstrated the best model fit, i.e., the lowest AIC and BIC values. This study highlights the importance of considering both classification accuracy and model fit when selecting a statistical model.
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