Suppose you have collected marketing research data to examine the relationship between a prospect’s likelihood of buying your product and the person’s education and income. Specifically, the variables are as follows:
Variable 
Levels 
Interpretation 


high, low 
Prospect’s education level 

high, low 
Prospect’s income level 

yes, no 
Did prospect purchase product? 
The following statements first create a data set, loan
, that contains the marketing research data. Then the CATMOD procedure fits a model, obtains the parameter estimates, and
obtains the predicted probabilities of interest. These statements produce Output 32.11.1 and Output 32.11.2.
data loan; input Education $ Income $ Purchase $ wt; datalines; high high yes 54 high high no 23 high low yes 41 high low no 12 low high yes 35 low high no 42 low low yes 19 low low no 8 ;
ods output PredictedValues=Predicted (keep=Education Income PredFunction); proc catmod data=loan order=data; weight wt; response marginals; model Purchase=Education Income / pred design; run;
proc sort data=Predicted; by descending PredFunction; run; proc print data=Predicted; run;
Notice that the preceding statements use the Output Delivery System (ODS) to output the parameter estimates instead of the OUT= option, though either can be used.
Output 32.11.1: Marketing Research Data: Obtaining Predicted Probabilities
Predicted Values for Response Functions  

Education  Income  Function Number 
Observed  Predicted  Residual  
Function  Standard Error 
Function  Standard Error 

high  high  1  0.701299  0.052158  0.67294  0.047794  0.028359 
high  low  1  0.773585  0.057487  0.808034  0.051586  0.03445 
low  high  1  0.454545  0.056744  0.48811  0.051077  0.03356 
low  low  1  0.703704  0.087877  0.623204  0.064867  0.080499 
Output 32.11.2: Predicted Probabilities Data Set
You can use the predicted values (values of PredFunction
in Output 32.11.2) as scores representing the likelihood that a randomly chosen subject from one of these populations will purchase the product.
Notice that the "Response Profiles" table in Output 32.11.1 shows you that the first sorted level of Purchase
is 'yes', indicating that the predicted probabilities are for Pr(Purchase
='yes'). For example, someone with high education and low income has an estimated probability of purchase of 0.808. Like any
response function estimate given by PROC CATMOD, this estimate can be obtained by crossmultiplying the row from the design
matrix corresponding to the sample (sample number 2 in this case) with the vector of parameter estimates: .
This ranking of scores can help in decision making (for example, with respect to allocation of advertising dollars, choice of advertising media, choice of print media, and so on).