Latent Variables, State Spaces, and Mixing
Jan de Leeuw, Catrien C. J. H. Bijleveld, Frits D. Bijleveld · eScholarship (California Digital Library) · 2011
. 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 technique. It provides a convenient framework for looking at these models. With such a framework often comes a "natural" class of algorithms. For the mixture approach to MVA it is the EM algorithm. 1. Introduction Our starting point in this paper is that we want to describe the relationships between (possibly many) variables, and we want to describe this relationship in simple terms. We look for simplicity, not necessarily because we believe the world is simple, but because simple relationships are easier to manipulate and communicate. We do not defi...