A Note on the Selection of Log-Linear Models

A recent paper in the Consultant's Forum by Benedetti and Brown (1978) discusses possible strategies for the choice of an appropriate log-linear model for a comples contingency table. The methods considered do not invariably choose the same model, but the authors favour the tests of marginal and partial association due to Brown (1976). The authors point out difficulties with the simultaneous test of all pooled effects of the same order and, in a final sentence, note that the significance levels of multiple tests of the data are merely guidelines and should not be interpreted as formal tests of significance.' It is the purpose of this note to point out that a formal simultaneous test may be applied to the entire model selection procedure, including the testing of models chosen after inspection of the data. The simultaneous test will generally use Type I error rates that are much higher than those typically used in discussions of model choice. The choice of a parsimonious model may then become a systematic procedure generally requiring only a small number of explicit fits of models.