Estimation Methods for Multivariate Tobit Confirmatory Factor Analysis

D. R. Costa
Víctor H. Lachos
J. L. Bazan
Caio L. N. Azevedo

We propose two methods for estimating multivariate Tobit Confirmatory Factor Analysis (TCFA) with covariates, one from Bayesian and another from likelihood based perspectives. TCFA is particularly useful in analysis of multivariate data with censored information. In contrast with previous developments that utilize Monte Carlo simulations for maximum likelihood estimation, an exact EM-type algorithm is proposed, which uses closed form expressions at the E-step that rely on the mean and variance of a truncated multinormal distribution and can be computed using available software. Through simulation studies, we compare the performance of the proposed algorithm when the censored pattern is ignored for different levels of censoring. Our results suggest that this algorithm has excellent performance, since it recovered the true parameters of the TCFA model much better than did the traditional CFA model. In addition, by considering a hierarchical formulation of the models, we also explore the estimation of the parameters via MCMC techniques by using proper priors. A Bayesian case deletion influence diagnostic based on the q-divergence measure and model selection criteria is also developed and applied to analyze a real dataset from an education assessment. In addition, a simulation study is conducted to compare the performance of the proposed method with the traditional CFA model.

Multivariate Tobit model
Factor analysis
Latent variable
Bayesian analysis
Censored data