Likelihood inference in binomial factor analysis with the Monte Carlo EM algorithm

Since its introduction, the classical linear factor model has been central in many fields of application, notably in psychology and sociology, and, assuming continuous and normally distributed observed variables, its likelihood analysis has typically been tackled with the use of the EM algorithm. For the case in which the observed variables are not Gaussian, extensions of this model have been proposed. Here, we present a hierarchical factor model for binomial data for which likelihood inference is carried out through a Monte Carlo EM algorithm. In particular, we discuss some implementations of the estimation procedure with the aim to improve its computational performances. The binomial factor model and the Monte Carlo EM estimation procedure are illustrated on a data set coming from a psychological study on the evaluation of the professional self-efficacy of social workers.