This article develops a full maximum likelihood method for obtaining joint estimates of variances and correlations among continuous and polytomous variables with incomplete data which are missing at random with an ignorable missing mechanism. The approach for obtaining the maximum likelihood estimate of the covariance matrix is via a simple confirmatory analysis model with a fixed identity loading matrix and a fixed diagonal matrix with small of unique variances. A Monte Carlo Expectation-Maximization (MCEM) algorithm is constructed to obtain the solution, in which the E-step is approximated by observations simulated by the Gibbs sampler. Results from a simulation study and a real example are provided to illustrate the methodology.
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