Semiparametric Change-Point Regression Model for Longitudinal Observations

• Published in: Journal of the American Statistical Association Vol. 107; no. 500; pp. 1625 - 1637
• Main Authors: Xing, Haipeng, Ying, Zhiliang
• Format: Journal Article
• Language: English
• Published: United States Taylor & Francis Group 01.12.2012; Taylor & Francis Ltd
• Subjects: Analytical estimating; Bayes estimators; Changes; Counting; Counting process; Covariance; data collection; Economic models; Estimating equation; Estimating techniques; Estimation methods; Inference; Longitudinal studies; Modeling; Nonparametric models; Normality; Point estimators; Regression analysis; Regression coefficients; Simulation; Statistical analysis; Statistics; Stochastic processes; Theory and Methods; Time series models; Time-varying coefficient; Change-points; Counting process; Time-varying coefficient
• ISSN: 1537-274X; 0162-1459; 1537-274X
• DOI: 10.1080/01621459.2012.712425

Many longitudinal studies involve relating an outcome process to a set of possibly time-varying covariates, giving rise to the usual regression models for longitudinal data. When the purpose of the study is to investigate the covariate effects when experimental environment undergoes abrupt changes or to locate the periods with different levels of covariate effects, a simple and easy-to-interpret approach is to introduce change-points in regression coefficients. In this connection, we propose a semiparametric change-point regression model, in which the error process (stochastic component) is nonparametric and the baseline mean function (functional part) is completely unspecified, the observation times are allowed to be subject specific, and the number, locations, and magnitudes of change-points are unknown and need to be estimated. We further develop an estimation procedure that combines the recent advance in semiparametric analysis based on counting process argument and multiple change-points inference and discuss its large sample properties, including consistency and asymptotic normality, under suitable regularity conditions. Simulation results show that the proposed methods work well under a variety of scenarios. An application to a real dataset is also given.