A0420
Title: Threshold boundary logistic regression for binary data
Authors: ChihHao Chang - National Chengchi University (Taiwan) [presenting]
Shih-Feng Huang - National Central University (Taiwan)
Abstract: The threshold boundary logistic regression (TBLR) model is explored for binary data analysis, integrating multiple covariates into both logistic regression and threshold functions. The threshold function, which can be linear or nonlinear, defines a hyperplane that partitions data for distinct logistic models. To estimate TBLR, an iterative two-stage sample-splitting algorithm is proposed that transforms the non-differentiable maximum likelihood estimation into an optimization framework. The method optimizes a weighted classification error for threshold estimation while maximizing likelihood functions for logistic regression. Under suitable conditions, consistency, optimal convergence rates, and the asymptotic distribution of estimators are established. To enhance computational efficiency, the weighted support vector machine (WSVM) is used for initializing linear threshold estimation via mixed-integer programming (MIP). When MIP struggles with nonlinear threshold functions, WSVM serves as an alternative for constructing nonlinear structures. Extensive simulations and real-data applications highlight the method's superior performance in modeling nonlinear binary data.
