On modeling repeated binary responses and time-dependent missing covariates

We develop a novel modeling strategy for analyzing data with repeated binary responses over time as well as time-dependent missing covariates. We assume that covariates are missing at random (MAR). We use the generalized linear mixed logistic regression model for the repeated binary responses and then propose a joint model for time-dependent missing covariates using information from different sources. A Monte Carlo EM algorithm is developed for computing the maximum likelihood estimates. We propose an extended version of the AIC criterion to identify the important factors that may explain the binary responses. A real plant dataset is used to motivate and illustrate the proposed methodology.