Let's review what was covered in the previous chapter. The logistic model is a useful method that allows us to examine the p parameter of binomial data. In order to keep our estimate of p between 0 and 1, we need to model functions of p. The log odds or log(p/(1 – p)) is called the logit and is modeled as a linear function of covariates. There are other variations on this idea. The probit models the cumulative normal distribution as a linear function of covariates. Both the logit and probit were designed to keep estimates of p between 0 and 1. The link=probit option in the model statement of proc logistic can be used to fit the probit model. There is little difference between the two fitted models, as we see when we look at Figure 8.2.

The SAS output in Table 8.3 provides a statistical significance of the regression slope, but it does not tell us anything about how well the model fits or even whether it is appropriate. In this chapter we want to discuss several diagnostic measures available that allow us to detect outliers and observations with high influence. Many of these have a parallel measure in linear regression, discussed in Chapter 5. There are options in proc logistic to print and plot these. Before we get to that, let's introduce another example.

The data in Table 9.1 is a list of men with prostate cancer. If the cancer is localized, then the disease is still in an early stage.