Likelihood-based inference for Tobit confirmatory factor analysis using the multivariate Student-t distribution

Factor analysis models have been one of the most popular multivariate methods for data analysis among psychometricians, behavioral and educational researchers. But these models, originally developed for normally distributed observed variables, can be seriously affected by the presence of influential observations and censored data. Motivated by this situation, in this paper we propose a likelihood-based estimation for a multivariate Tobit confirmatory factor analysis model using the Student-t distribution (t-TCFA model). An EM-type algorithm is developed for computing the maximum likelihood estimates, obtaining as a byproduct the standard errors of the fixed effects and the exact likelihood value. Unlike other approaches proposed in the literature, our exact EM-type algorithm uses closed form expressions at the E-step based on the first two moments of a truncated multivariate Student-t distribution with the advantage that these expressions can be computed using standard statistical software. The performance of the proposed methods is illustrated through a simulation study and the analysis of a real dataset of early grade reading assessment test scores.