Bayesian sampling‐based approach for factor analysis models with continuous and polytomous data

Factor analysis is an important technique in behavioural science research in explaining the interdependence and assessing causations and correlations of the observed variables and the latent factors. Recently, generalization of the model to handle polytomous variables has received a lot of attention. In this paper, a Bayesian approach to analysing the model with continuous and polytomous variables is developed. In the posterior analysis, the observed continuous and polytomous data are augmented with the latent factor scores and the unobserved measurements underlying the polytomous variables. Random observations from the posterior distributions are simulated via the Gibbs sampler algorithm. It is shown that the conditional distributions involved in the implementation of the algorithm are the familiar distributions, hence the simulation is rather straightforward. Joint Bayesian estimates of the unknown thresholds, structural parameters and the factor scores are produced simultaneously. The efficiency and accuracy of our approach are demonstrated by a real‐life example and a simulation study.