A Factor Analysis Model for a Mixture of Various Types of Variables

A factor analysis model is proposed for the case of a mixture of various types of discrete and continuous manifest variables. It is indicated that the likelihood of parameters can be described for a mixture of different types of distributions by assuming local independence. For estimation of the parameters of interest, the method of marginal maximum likelihood is used, where scores of latent factors are integrated out from the likelihood. A kind of the EM algorithm is utilized for optimization. As an example, the case of a mixture of normal, binomial and Poisson distributions is provided.