Summary: BAYESIAN RESIDUAL ANALYSIS
FOR BINARY RESPONSE
REGRESSION MODELS
Jim Albert
Department of Mathematics and Statistics
Bowling Green State University, Bowling Green, 43403 USA
Siddhartha Chib
Olin School of Business
Washington University, St. Louis 63130 USA
March, 1994
Summary
In a binary response regression model, classical residuals are difficult to
define and interpret due to the discrete nature of the response variable. In con­
trast, Bayesian residuals have continuous­valued posterior distributions which
can be graphed to learn about outlying observations. Two definitions of Bayesian
residuals are proposed for binary regression data. Plots of the posterior dis­
tributions of the basic ``observed \Gamma fitted'' residual can be helpful in outlier
detection. Alternatively, the notion of a tolerance random variable can be used
to define latent data residuals that are functions of the tolerance random vari­
ables and the parameters. In the probit setting, these residuals are attractive

Source: Albert, James H. - Department of Mathematics and Statistics, Bowling Green State University

Collections: Mathematics