Analysis of structural equation models with Incomplete Polytomous Data

A two-stage estimation procedure is developed to analyze structural equation models of polytomous variables based on incomplete data. At the first stage, the partition maximum likelihood approach is used to obtain the estimates of the elements in the correlation matrix. It will be shown that the asymptotic distribution of these estimates is jointly multivariate normal. The second stage estimates the structural parameters in the correlation matrix by the generalized least squared approach with a correctly specified weight matrix. Asymptotic properties of the second stage estimates are also provided. Extension of the theory to multisample models, and some illustrative examples are also included.