A goodness of fit test for sparse 2(p) contingency tables

When a model is fitted to data in a 2p contingency table many cells are likely to have very small expected frequencies. This sparseness invalidates the usual approximation to the distribution of the chi-squared or log-likelihood tests of goodness of fit. A solution to this problem is presented by proposing a test based on a comparison of the observed and expected frequencies of the second-order margins of the table.