Binary Regression Using an Extended Beta-Binomial Distribution, with Discussion of Correlation Induced by Covariate Measurement Errors

Abstract

Abstract The beta-binomial distribution is extended to allow negative correlations among binary variates within an experimental unit. Regression models are proposed for both the binary variate response rate and for the pairwise correlation between binary variates, and corresponding likelihood estimation procedures are described. Binary regression problems are also considered, in which measurement errors in the regression variables represent the sole source of overdispersion. Some corresponding response rate estimation procedures are described and illustrated.