Bayesian Goodness-of-Fit Test and Semiparametric Generalization with Measurement Data

• Activity Number: 536
• Type: Contributed
• Date/Time: Wednesday, August 4, 2010 : 10:30 AM to 12:20 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Angela Schoergendorfer*+ and Adam J. Branscum and Timothy Edward Hanson
• Companies: University of Kentucky and University of Kentucky and University of Minnesota
• Keywords: Polya tree ; logistic regression ; risk estimation ; Bayes factors ; goodness of fit

Abstract

With continuous response data, it is common to create a dichotomous outcome for logistic regression analysis by specifying a threshold for positivity. Fitting a linear regression via least-squares to the non-dichotomized response assuming a logistic error distribution has been shown to yield more efficient estimators of odds ratios than ordinary logistic regression of the dichotomized endpoint variable. However, odds ratios are not constant across covariate values if the assumption of a logistic distribution is violated, leading to biased inferences. We propose novel Bayesian semiparametric methodology for assessing goodness of fit of logistic regression using any threshold that simultaneously provides risk predictions. We develop an empirical Bayes approach that is computationally efficient and present methods for semiparametric estimation of risks when logistic regression fails.