Tobit confirmatory factor analysis is particularly useful in analysis of multivariate data with censored information. Two methods for estimating multivariate Tobit confirmatory factor analysis models with covariates from a Bayesian and likelihood-based perspectives are proposed. In contrast with previous likelihood-based developments that consider Monte Carlo simulations for maximum likelihood estimation, an exact EM-type algorithm is proposed. Also, the estimation of the parameters via MCMC techniques by considering a hierarchical formulation of the model is explored. Bayesian case deletion influence diagnostics based on the q-divergence measure and model selection criteria is also developed and considered in the analysis of a real dataset related to the education assessment field. In addition, a simulation study is conducted to compare the performance of the proposed method with the traditional confirmatory factor analysis. The results show that both methods offer more precise inferences than the traditional confirmatory factor analysis, which ignores the information about the censoring threshold. © 2014 Elsevier B.V. All rights reserved.