An incomplete data approach to the analysis of covariance structures

In this paper, linear structural equation models with latent variables are considered. It is shown how many common models arise from incomplete observation of a relatively simple system. Subclasses of models with conditional independence interpretations are also discussed. Using an incomplete data point of view, the relationships between the incomplete and complete data likelihoods, assuming normality, are highlighted. For computing maximum likelihood estimates, the EM algorithm and alternatives are surveyed. For the alternative algorithms, simplified expressions for computing function values and derivatives are given. Likelihood ratio tests based on complete and incomplete data are related, and an example on using their relationship to improve the fit of a model is given.This research forms part of the author's doctoral thesis and was supported by a Commonwealth Postgraduate Research Award. The author also wishes to acknowledge the support of CSIRO during the preparation of this paper and the referees' comments which led to substantial improvements.