Estimation of random-effects model for longitudinal data with nonignorable missingness using Gibbs sampling

The missing data problem is common in longitudinal or repeated measurements data. When the missingness mechanism is nonignorable, the distribution of the observed response and indicators of missingness should be modelled jointly using either 'shared random-effects model' or 'correlated random-effects model'. However, computational challenges arise in the model fitting due to intractable numerical integration involved in the log-likelihood function. We provide alternative modeling of 'correlated random-effects model' using latent variables and propose a simple algorithm based on Gibbs sampling for estimation of associated parameters. The method is illustrated through simulation and the analysis of a real data set arising from an autism study.