Bayesian methods for an incomplete two-way contingency table with application to the Ohio (Buckeye State) Polls

Abstract

We use a Bayesian method to resolve the boundary solution problem of the maximum likelihood (ML) estimate in an incomplete two-way contingency table, using a loglinear model and Dirichlet priors. We compare five Dirichlet priors in estimating multinomial cell probabilities under nonignorable nonresponse. Three priors among them have been used for an incomplete one-way table, while the remaining two new priors are newly proposed to reflect the difference in the response patterns between respondents and the undecided. The Bayesian estimates with the previous three priors do not always perform better than ML estimates unlike previous studies, whereas the two new priors perform better than both the previous three priors and the ML estimates whenever a boundary solution occurs. We use four sets of data from the 1998 Ohio state polls to illustrate how to use and interpret estimation results for the elections. We use simulation studies to compare performance of the five Bayesian estimates under nonignorable nonresponse.