Simultaneous variable selection and parameters estimation for longitudinal data subject to missingness and covariates measurement error

Longitudinal studies are indispensable to study the change over time in a response variable. The main challenge of such studies is the presence of missing values. Another challenge in these studies is that covariates may be subject to measurement error. In such studies, variable selection, especially if the data are subject to measurement error and missingness, is crucial. Variable selection may lead to biased results in case of ignoring the missing values. Also, measurement error in covariates can negatively affect the accuracy of the estimates if not treated properly. Variable selection for longitudinal data that suffers from missing values and measurement error in covariates is not well explored in literature. In this article, we propose and develop a simultaneous variable selection and parameter estimation method for longitudinal data that suffers from intermittent missing values and covariates measurement error. The penalized weighted generalized estimating equations is used to account for the missingness in the longitudinal response, and simulation selection extrapolation techniques is used to account for the covariate measurement error. A simulation study is conducted to assess the performance of the proposed method. Also, the applicability of the proposed method is demonstrated using the Longitudinal Internet Studies for Social sciences data.