Nonparametric Regression Estimator of Multivariable Truncated Spline For Categorical Data

Recent years have witnessed significant interest in truncated spline estimators for nonparametric regression with quantitative data. However, the applicability of these estimators is limited by the frequent occurrence of categorical response variables in real-world applications. A paucity of nonparametric estimators exists for handling categorical response data. This necessitates a method capable of modeling relationships between variables exhibiting pattern shifts across sub-intervals with categorical outcomes. This article thus introduces a novel multivariate truncated spline nonparametric regression estimator for categorical data, developed through a synthesis of literature and theoretical research. The developed method was applied to Indonesia's 2023 poverty depth index data and East Java's 2020 gender development index data. A comparative analysis of the Truncated Spline nonparametric regression model and the binary logistic regression model for estimating categorical data revealed that the Truncated Spline approach yielded superior estimations. Some of the highlights of the proposed method are: 1) This study employs truncated spline nonparametric regression to model categorical response data, 2) Optimal knot placement is determined using the Akaike Information Criterion (AIC), 3) The method's overall performance is demonstrated through its application to two established datasets, and 4) This study compares truncated spline nonparametric regression and logistic regression.