Semiparametric Mixed-effects Model for Longitudinal Data with Non-normal Errors

TL;DR

This paper introduces a semiparametric mixed-effects model for longitudinal data with non-normal errors, utilizing a double-penalized GEE approach to identify significant components and improve estimation efficiency.

Contribution

It extends semiparametric mixed-effects modeling to non-normal responses with additive nonparametric components, proposing a novel double-penalized GEE method with oracle properties.

Findings

Effective identification of significant components demonstrated in simulations

Enhanced estimation efficiency through iterative covariance matrix calculation

Model accommodates increasing dimensions with sample size

Abstract

Difficulties may arise when analyzing longitudinal data using mixed-effects models if there are nonparametric functions present in the linear predictor component. This study extends the use of semiparametric mixed-effects modeling in cases when the response variable does not always follow a normal distribution and the nonparametric component is structured as an additive model. A novel approach is proposed to identify significant linear and non-linear components using a double-penalized generalized estimating equation with two penalty terms. Furthermore, the iterative approach provided intends to enhance the efficiency of estimating regression coefficients by incorporating the calculation of the working covariance matrix. The oracle properties of the resulting estimators are established under certain regularity conditions, where the dimensions of both the parametric and nonparametric components increase as the sample size grows. We perform numerical studies to demonstrate the efficacy of our proposal.