Dataset for: Modeling the random effects covariance matrix for longitudinal data with covariates measurement error

2018-08-07T06:29:53Z (GMT) by Erfanul Hoque Mahmoud Torabi
Longitudinal data occur frequently in practice such as medical studies and life sciences. Generalized linear mixed models (GLMMs) are commonly used to analyze such data. It is typically assumed that the random effects covariance matrix is constant across the subject (and among subjects) in these models. In many situations, however, this correlation structure may differ among subjects and ignore this heterogeneity can cause the biased estimate of model parameters. Recently, Lee et al. (2012) developed a heterogeneous random effects covariance matrix for GLMMs for error-free covariates. Covariates measured with an error also happen frequently in the longitudinal data set-up (e.g., blood pressure, cholesterol level). Ignoring this issue in the data may produce bias in model parameters estimate and lead to wrong conclusions. In this paper, we propose an approach to properly model the random effects covariance matrix based on covariates in the class of GLMMs where we also have covariates measured with error. The resulting parameters from the decomposition of random effects covariance matrix have a sensible interpretation and can easily be modeled without the concern of positive definiteness of the resulting estimator. Performance of the proposed approach is evaluated through simulation studies which show that the proposed method performs very well in terms of bias, mean squared error, and coverage rate. An application of the proposed method is also provided using a longitudinal data from Manitoba Follow-up study.