chapter  8
16 Pages

## Categorical Covariates

We can, of course, simply estimate these probabilities by the corresponding relative frequency of children with an allergy in each category as shown in Table 8.1. However, our aim is to assess the differences between the categories, that is, we are

Category πˆ(x) logit πˆ(x) 1 0.22 -1.295 2 0.33 -0.720 3 0.28 -0.920 4 0.40 -0.425

k l δˆkl = logit πˆ(l)− logit πˆ(k) 1 2 0.575 1 3 0.375 1 4 0.870 2 3 -0.200 2 4 0.295 3 4 0.495

interested in the six pairwise comparisons and a quantification of the corresponding six differences. We can quantify these differences on the logit scale by introducing the parameters

δkl = logit π(l)− logit π(k) , and using the empirical estimates for π(x) we can, of course, obtain estimates for the parameters δkl as indicated in Table 8.2.