Bayesian Posterior Estimation of Logit Parameters with Small Samples

Abstract

When the sample size is small compared to the number of cells in a contingency table, maximum likelihood estimates of logit parameters and their associated standard errors may not exist or may be biased. This problem is usually solved by “smoothing” the estimates, assuming a certain prior distribution for the parameters. This article investigates the performance of point and interval estimates obtained by assuming various prior distributions. The authors focus on two logit parameters of a 2 × 2 × 2 table: the interaction effect of two predictors on a response variable and the main effect of one of two predictors on a response variable, under the assumption that the interaction effect is zero. The results indicate the superiority of the posterior mode to the posterior mean.