Chapter 12 - Longitudinal transition models for categorical response data

Abstract

In this chapter, a number of multidimensional transition models are described, which link categorical outcome data to time, a prior state, and other theoretically relevant covariates. I first review the classical methods designed to model multidimensional transitions between just two time points. Next, I delineate some simple Markov chain models in the analysis of multidimensional transitions across more than two time points, using the fixed-effects perspective. Based on a discussion on the strengths and limitations of the fixed-effects techniques, the mixed-effects multinomial logit transition model is introduced. The delineation includes model specifications, statistical inference, nonlinear predictions, and the approximation of the variance-covariance matrix for the predicted transition probabilities. Lastly, an empirical illustration is provided to display how to apply the mixed-effects multinomial logit transition model. All the multidimensional transition models described in this chapter build upon a competing risks framework, and therefore, the transition models for Gaussian or binary outcome data are not included in this text.