The hierarchical Tobit model: A case study in Bayesian computing

In this paper we discuss the potentials of a new Bayesian inference tool, called the Gibbs sampler, for the analysis of the censored regression or Tobit model. Tobit models have a wide range of applications in empirical sciences, like econometrics and biometrics. The estimation results of the simple Tobit model will be compared to a hierarchical Tobit model, and the Gibbs sampling approach to the related classical algorithm of expectation-maximisation (EM). The underlying botanical example of this paper is concerned with the censoring mechanism in plant reproduction and proposes the Bayesian Tobit model for the growth relationship between the reproductive part and the rest of the plant.