ABSTRACT
The general approach to modelling binary data that has been described in Chapter 3 is based on the method of maximum likelihood. Parameters in a model of interest are estimated by maximising the likelihood function (Section 3.7), and alternative models are compared using the deviance (Section 3.9). In particular, the significance of adding an explanatory variable to a model can be assessed by comparing the change in deviance due to the addition of that variable with percentage points of the χ2-distribution. This result for the distribution of the deviance is an asymptotic property, the validity of which depends on the number of binary observations in the data base. If this is so small that there are some observed proportions with very small denominators, or proportions close to zero or unity, inferences based on the asymptotic distribution of the change in deviance may be unreliable. Corresponding inferences about the effect that explanatory variables have on the response probability will then be invalid.
