COMPARING MARGINAL DISTRIBUTIONS OF LARGE, SPARSE CONTINGENCY-TABLES

The feasibility of maximum likelihood (ML) analyses of models for marginal distributions of contingency tables diminishes as the numbers of margins and response categories increases. This article describes alternative approaches that are much more feasible. We recommend a "pseudo ML" approach that obtains model parameter estimates by treating repeated responses as independent and uses a jackknife to estimate the covariance matrix of those estimates. We test marginal homogeneity using a Wald statistic, or by adapting the efficient score statistic from the independent-samples case. We illustrate these approaches with a seven-dimensional table having 78125 cells, and we give simulation results that show no substantive loss of efficiency from using pseudo ML estimates.