# Example 3.7 Infection after caesarian birth

As an example of multinomial logistic analysis, consider data from Fahrmeier and Tutz (1994) involving categorical predictors and an unordered categorical response relating to infection in 251 births involving Caesarian section; namely no infection, type I infection, and type II infection. The risk factors are defined as NOPLAN = 1 (if theCaesarian is unplanned, 0 otherwise), ANTIB = 1 if antibiotics were given as prophylaxis, and FACTOR = 1 (if risk factors were present, 0 otherwise). Of the eight possible predictor combinations, seven were observed. The numbers of maternities under the possible combinations range from 2 (for NOPLAN = 0, ANTIB = 1, FACTOR = 0) to 98 (NOPLAN = 1, ANTIB = 1, FACTOR = 1). N(0,10) priors are assumed for the impacts of the binary predictors on outcomes , and a multinomial logistic model is adopted with

The estimates for this MNL model show antibiotic prophylaxis as decreasing the relative risk of infection type I more than type II. Hence is more highly negative than . By contrast, the presence of risk factors ...