Bayesian extensions of the Tobit model for analyzing measures of health status

Self-reported health status is often measured using utility indices that provide a score intended to summarize an individual's health. Measurements of health status can be subject to a ceiling effect. Frequently, researchers want to examine relationships between determinants of health and measures of health status. In this article, Bayesian extensions of the classical Tobit model are used to study the relationship between health status and predictors of health. Models where the conditional distribution of health status was either normal or lognormal, and allowed for both homoscedasticity and heteroscedasticity were examined. Bayes factors were then used to compare the evidence for a given model against that for a competing model. There was very strong evidence that the distribution of the Health Utilities Index, conditional on age, gender, income adequacy, and number of chronic conditions, was normal with nonuniform variance, compared to the competing models.