A growth model for multilevel ordinal data

Multi-indicator growth models were formulated as special three-level hierarchical generalized linear models to analyze growth of a trait latent variable measured by ordinal items. Items are nested within a time-point, and time-points are nested within subject. These models are special because they include factor analytic structure. This model can analyze not only data with item- and time-level missing observations, but also data with time points freely specified over subjects. Furthermore, features useful for longitudinal analyses, "autoregressive error degree one" structure for the trait residuals and estimated time-scores, were included. The approach is Bayesian with Markov Chain and Monte Carlo, and the model is implemented in WinBUGS. They are illustrated with two simulated data sets and one real data set with planned missing items within a scale.