Bayesian Estimation Methods for Two-Way Contingency Tables

Summary Estimation methods are proposed for the row, column and interaction effects in two-way contingency tables, the one-way table being treated as a special case. The methods are appropriate when the parameters are thought a priori to be related to each other. The posterior estimates have the practical effects of smoothing the contingency table, and are valid even if some of the cell frequencies are zero. The main case treated is where particular assumptions of exchangeability are reasonable a priori for the unknown parameters. Some possible relaxations of the exchangeability assumptions are discussed. The methods are used to provide a numerical analysis of a mobility table originally due to Karl Pearson, and to measure the association between the occupations of fathers and sons in this table.