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
Complex Sample Survey Analysis 
Data Summary  

Response  Purchase  Response Levels  2 
Weight Variable  wt  Populations  4 
Data Set  LOAN  Total Frequency  234 
Frequency Missing  0  Observations  8 
Population Profiles  

Sample  Education  Income  Sample Size 
1  high  high  77 
2  high  low  53 
3  low  high  77 
4  low  low  27 
Response Profiles  

Response  Purchase 
1  yes 
2  no 
Response Functions and Design Matrix  

Sample  Response Function 
Design Matrix  
1  2  3  
1  0.70130  1  1  1 
2  0.77358  1  1  1 
3  0.45455  1  1  1 
4  0.70370  1  1  1 
Analysis of Variance  

Source  DF  ChiSquare  Pr > ChiSq 
Intercept  1  418.36  <.0001 
Education  1  8.85  0.0029 
Income  1  4.70  0.0302 
Residual  1  1.84  0.1745 
Analysis of Weighted Least Squares Estimates  

Parameter  Estimate  Standard Error 
Chi Square 
Pr > ChiSq  
Intercept  0.6481  0.0317  418.36  <.0001  
Education  high  0.0924  0.0311  8.85  0.0029 
Income  high  0.0675  0.0312  4.70  0.0302 
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
Complex Sample Survey Analysis 
Obs  Education  Income  PredFunction 

1  high  low  0.808034 
2  high  high  0.67294 
3  low  low  0.623204 
4  low  high  0.48811 
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).