Fitting large recursive models of categorical variables by model-splitting and information loss

Abstract

A new EM algorithm was proposed in Kim (2000) that is available for modelling a large recursive model of categorical variables which is too large to handle as a single model. An improvement on that algorithm is proposed in this thesis. The difference between the two algorithms is that while the marginal of a set of observed variables as obtained based on the estimates from an E-step may not be the same as the observed marginal in the former algorithm, the marginal from an E-step and the observed marginal are the same in the latter algorithm. As a consequence, the M-step in the latter algorithm becomes simpler than that in the former. This improvement still undergoes an information loss due to model-splitting. It is proved in the thesis that as we do more splitting on a model, we lose more information from data about the parameters of the model. Thus, it is strongly recommended that a model be split as little as possible for estimating parameters of the model with as much accuracy as possible.