Efficient Inference in a Generalized Partially Linear Model with Random Effect for Longitudinal Data

In this article, we study the statistical inference for the generalized partially linear model with random effect. We develop the traditional models that can model generalized longitudinal data and treat categorical data as continuous data by using some transformations. We propose a class of semiparametric estimators for the parametric and variance components. The proposed estimators are data adaptive, which does not require any assumption of working likelihood for the random component or model error. We prove that the resulting estimators for the parametric component are consistent and asymptotic normal, but also remain semiparametrically efficient. The asymptotic normality is established for the proposed estimator of variance component. Moreover, we also propose an estimator for the nonparametric component by using the local linear smoother and present their asymptotic normality. Finite sample performance of the proposed procedures is evaluated by Monte Carlo simulation studies. We further illustrate the proposed procedure by an application.