Department of Statistics, UCLA

We argue that many models for multivariate longitudinal and cross-sectional data analysis have a common ancestry. They all are based on the qualitative idea that if we knew the actual state of the world, the relations between the observed quantities would be truly simple. This is shown to lead directly to factor analysis, IRT, state space models, mixture densities, latent Markov chains, MIMIC, LISREL, and various other common models and techniques. We show how our approach provides a convenient framework for looking at these models. The EM algorithm can be used to estimate the unknown parameters. An additional advantage of our approach is that it can incorporate continuous as well as interval, ordinal and categorical variables .