Estimation of multivariate polychoric and polyserial correlations with missing observations.

The main purpose of this paper is to investigate various approaches in analysing the multivariate polychoric and polyserial correlation model in the presence of incomplete data. For the general case with missing entries in both continuous and polytomous variables, a pseudo maximum likelihood method, and a partition pseudo maximum likelihood are developed. Iterative procedures based on the Fletcher-Powell algorithm and the Newton-Raphson algorithm are implemented to obtain various solutions. For the special case with missing entries only in the polytomous variables, a full maximum likelihood estimate is obtained with the help of an appropriate one-one onto transformation that significantly simplifies the computational burden. The analogous approaches as in the general case are also investigated. Finally, a simulation study is conducted to compare the performances of the various approaches.