ABSTRACT
This chapter focuses on conditionally specified hierarchical and random effect models, and on Markov chain Monte Carlo (MCMC) estimation via conditional likelihood with random effects as part of the parameter set. Longitudinal studies often feature an intervention or treatment comparison, with intervention studies including both observational studies and controlled clinical trials with random treatment assignment. Estimation of variance components and convergence of MCMC samplers for longitudinal data may be sensitive to the assumed prior interlinkages between multiple sources of random variation. Longitudinal data on multiple outcomes raise the possibility of shared random effects across outcomes, instead of outcome-specific effects. In item analysis and psychometric longitudinal applications, a measurement model might involve both constant and time-varying common factors. Attrition and intermittently missing data are frequently found in longitudinal data, and disregarding the process underlying such missingness may lead to biased and inefficient estimates of parameters in the outcome model, though different mechanisms may apply for attrition as opposed to intermittent missingness.
