Applied Logistic Regression, 3rd Edition

Chapter 5: Assessing the Fit of the Model

5.1 Introduction

We begin our discussion of methods for assessing the fit of an estimated logistic regression model with the assumption that we are, at least preliminarily, satisfied with our efforts at the model building stage. By this we mean that, to the best of our knowledge, the model contains those variables (main effects as well as interactions) that should be in the model and that variables have been entered in the correct functional form. Now we would like to know whether the probabilities produced by the model accurately reflect the true outcome experience in the data. This is referred to as its goodness of fit.

If we intend to assess the goodness of fit of the model, then we should have some specific ideas about what it means to say that a model fits. Assume that we denote the observed sample values of the outcome variable, in vector form, as y, where . We denote the values estimated by the model, or fitted values, as , where . We conclude that the model fits if: (1) summary measures of the distance between y and are small and (2) the ...