Evaluating Independent Variables on Binary Response: Logistic versus Probit Regression in Diabetes Data

Abstract

This research investigates how various demographic and physiological variables influence diabetes outcomes through binary response modeling, comparing two widely used statistical approaches: logistic and probit regression. The analysis draws on data from 768 patients who visited Layla Qassim Health Centers over a five-year period spanning 2018 to 2023. Eight predictor variables were examined: glucose levels, body mass index, blood pressure readings, insulin measurements, skin thickness, age, number of pregnancies, and the diabetes pedigree function—a metric capturing hereditary risk. Both regression models were fitted using maximum likelihood estimation. To assess how well each model performed, several diagnostic tools were applied, including McFadden's pseudo-R², the Akaike and Bayesian Information Criteria, mean squared error calculations, and ROC-AUC analysis. Across both modeling frameworks, the same variables emerged as meaningful predictors: elevated glucose concentrations, higher BMI values, a family history of diabetes, and pregnancy count all showed strong statistical associations with diabetes status. In contrast, insulin levels and skin thickness contributed little explanatory value to either model. When comparing the two approaches directly, the probit model demonstrated a slight edge in overall fit and classification accuracy, though the practical difference between them was negligible. These results reinforce that logistic and probit methods yield comparable conclusions when applied to binary health outcomes, while also drawing attention to the metabolic and genetic factors that clinicians and policymakers should prioritize in diabetes screening programs and public health planning