Logistic Regression, Categorical Predictors, and Goodness-of-Fit: It Depends on Who You Ask

The assessment of goodness-of-fit for logistic regression models using categorical predictors is made complicated by the fact that there are different ways of defining the saturated model. Three distinct approaches have been suggested: the casewise approach, the contingency table approach, and the collapsing approach. Assessments of goodness-of-fit using χ2 statistics are very different depending on which of these approaches is used, and different statistical packages do different things (often depending on how the data are entered into the package). In this article the different approaches are outlined, and the functionality of different statistical packages is described. Cautions for the unwary data analyst are offered, and suggestions for improvements to statistical software that would make logistic regression analysis easier for the data analyst are made. Some advice for data analysts using current versions of such software is also provided.