Exploratory Tobit Factor Analysis for Multivariate Censored Data

We propose Multivariate Tobit models with a factor structure on the covariance matrix. Such models are particularly useful in the exploratory analysis of multivariate censored data and the identification of latent variables from behavioral data. The factor structure provides a parsimonious representation of the censored data and reduces the dimensionality of the integration required in evaluating the likelihood. In addition, the factor model parameters lend themselves to substantive interpretation and graphical display. The models are estimated with simulated maximum likelihood. Applications to the prescription of pharmaceutical products and the analysis of multi-category buying behavior are provided.