Bayesian Inference on Umbrella Orderings

• Activity Number: 190
• Type: Contributed
• Date/Time: Tuesday, August 10, 2004 : 8:30 AM to 10:20 AM
• Sponsor: General Methodology
• Author(s): Chris Hans*+ and David B. Dunson
• Companies: Duke University and National Institute of Environmental Health Sciences
• Keywords: order constraint ; mixture prior ; variable selection ; downturn order ; shape restriction ; probit model

Abstract

In regression applications with categorical predictors, interest often focuses on comparing the null hypothesis of homogeneity to an ordered alternative. We propose a Bayesian approach for addressing this problem in the setting of normal linear and probit regression models. The regression coefficients are assigned a conditionally conjugate prior density consisting of mixtures of point masses at zero and truncated normal densities, with a (possibly unknown) changepoint parameter included to accommodate umbrella ordering. The investigator specifies the prior probability assigned to the global null hypothesis and to subhypotheses of no difference in specific groups, with default values suggested to account for multiple comparisons. A single Gibbs sampling chain can be used to obtain posterior probabilities for the different hypotheses and for estimation of regression coefficients and predictive quantities, either by model averaging or under the preferred hypothesis. The methods are applied to data from a carcinogenesis study.