Variable selection and inference procedures for marginal analysis of longitudinal data with missing observations and covariate measurement error

In contrast to extensive attention on model selection for cross-sectional data, research on model selection for longitudinal data remains largely unexplored. This is particularly the case when data are subject to missingness and measurement error. To address this important problem, we propose marginal methods that simultaneously carry out model selection and estimation for longitudinal data with missing responses and error-prone covariates. Our methods have several appealing features: the applicability is broad because the methods are developed for a unified framework with marginal generalized linear models; model assumptions are minimal in that no full distribution is required for the response process and the distribution of the true covariates is left unspecified; and the implementation is straightforward. To justify the proposed methods, we provide both theoretical properties and numerical assessments.