Modeling stunting risk with multicollinear categorical predictors using a CATPCA-based binary logistic spline framework

Abstract

This study integrates categorical principal component analysis (CATPCA) with nonparametric binary logistic spline regression to simultaneously address multicollinearity and predictor heterogeneity. The proposed CATPCA-based binary logistic spline regression approach is designed to handle heterogeneous, categorical, and correlated predictors. Optimal knot selection in the spline component is determined using the minimum generalized cross validation (GCV) criterion. Model performance is evaluated using deviance, accuracy, and the akaike information criterion (AIC). Simulation studies are conducted to compare models with and without CATPCA, followed by an application to real stunting-risk family data consisting of categorical predictors. Model parameters are estimated using maximum likelihood estimation based on CATPCA-derived component scores. Simulation results show that the CATPCA-based binary logistic spline model yields lower deviance and AIC values than the model without CATPCA, indicating improved model fit. Application to family stunting-risk data from South Sulawesi Province, Indonesia, identifies five principal components that capture both linear and nonlinear patterns of predictor influence on the response. The integrated CATPCA-based binary logistic spline regression model effectively explains the influence of heterogeneous and interdependent predictors on the response. The combination of spline-based nonparametric modeling and CATPCA-driven dimensionality reduction enhances the model’s ability to capture complex and detailed relationships between family-level determinants and stunting risk.