A criterion for selection log-linear models for contingency tables

A new discrepancy, the Gauss discrepancy of the logarithms of frequencies, is introduced for the selection of log-linear models for contingency tables. Under the assumption of Poisson sampling the log-linear model becomes orthogonal for this discrepancy: the model selection criterion is the sum of the contributions (to the criterion) of the effects in the model. It is, therefore, sufficient for model selection to compute the contributions of the effects in the saturated model. The selected model contains then all effects with negative contributions. It is not necessary to recompute the value of the criterion for all possible models. Two examples are given.