Categorical Data Analysis Using The SAS® System, 2nd Edition

Appendix A: Statistical Methodology for Dichotomous Logistic Regression

Consider the relationship of a dichotomous outcome variable to a set of explanatory variables. Such situations can arise from clinical trials where the explanatory variables are treatment, stratification variables, and background covariables; another common source of such analyses are observational studies where the explanatory variables represent factors for evaluation and background variables.

The model for θ, the probability of the event, can be specified as follows:

It follows that the odds are written

so the model for the logit is linear:

The exp(β_k) are the odds ...