Latent variable models with mixed continuous and polytomous data

Owing to the nature of the problems and the design of questionnaires, discrete polytomous data are very common in behavioural, medical and social research. Analysing the relationships between the manifest and the latent variables based on mixed polytomous and continuous data has proven to be difficult. A general structural equation model is investigated for these mixed outcomes. Maximum likelihood (ML) estimates of the unknown thresholds and the structural parameters in the covariance structure are obtained. A Monte Carlo–EM algorithm is implemented to produce the ML estimates. It is shown that closed form solutions can be obtained for the M-step, and estimates of the latent variables are produced as a by-product of the analysis. The method is illustrated with a real example.