Over the course of one school year, third-graders from three different schools are exposed to three different styles of mathematics instruction: a self-paced computer-learning style, a team approach, and a traditional class approach. The students are asked which style they prefer, and their responses, classified by the type of program they are in (a regular school day versus a regular school day supplemented with an afternoon school program), are displayed in Table 28.3. The data set is from Stokes, Davis, and Koch (2000), and it is also analyzed in the section Nominal Response Data: Generalized Logits Model of Chapter 51, The LOGISTIC Procedure.

The levels of the response variable (self, team, and class) have no essential ordering, so a logistic regression is performed on the generalized logits. The model to be fit is

where is the probability that a student in school and program prefers teaching style , , and style is the class style. There are separate sets of intercept parameters and regression parameters for each logit, and the matrix is the set of explanatory variables for the th population. Thus, two logits are modeled for each school and program combination (population): the logit comparing self to class and the logit comparing team to class.

The following statements create the data set school and request the analysis. Generalized logits are the default response functions, and maximum likelihood estimation is the default method for analyzing generalized logits, so only the WEIGHT and MODEL statements are required. The option ORDER=DATA means that the response variable levels are ordered as they exist in the data set: self, team, and class; the logits are formed by comparing self to class and by comparing team to class. The results of this analysis are shown in Figure 28.6 and Figure 28.7.

   data school;
      length Program $ 9;
      input School Program $ Style $ Count @@; 
      datalines; 
   1 regular   self 10  1 regular   team 17  1 regular   class 26
   1 afternoon self  5  1 afternoon team 12  1 afternoon class 50 
   2 regular   self 21  2 regular   team 17  2 regular   class 26
   2 afternoon self 16  2 afternoon team 12  2 afternoon class 36 
   3 regular   self 15  3 regular   team 15  3 regular   class 16
   3 afternoon self 12  3 afternoon team 12  3 afternoon class 20 
   ; 

   proc catmod order=data;
      weight Count;
      model Style=School Program School*Program;
   run;   

A summary of the data set is displayed in Figure 28.6; the variable levels that form the three responses and six populations are listed in the "Response Profiles" and "Population Profiles" tables, respectively.