Example 88.7 Domain Analysis

Recall the example in the section Getting Started: SURVEYREG  Procedure, which analyzed a stratified simple random sample from a junior high school to examine how household income and the number of children in a household affect students’ average weekly spending for ice cream. You can use the same sample to analyze the average weekly spending among male and female students. Because student gender is unrelated to the design of the sample, this kind of analysis is called domain analysis (subgroup analysis).

This example shows how you can use PROC SURVEYREG  to perform domain analysis. The data set follows:

data IceCreamDataDomain;
   input Grade Spending Income Gender$ @@;
   datalines; 
7   7  39  M   7   7  38  F   8  12  47  F 
9  10  47  M   7   1  34  M   7  10  43  M
7   3  44  M   8  20  60  F   8  19  57  M
7   2  35  M   7   2  36  F   9  15  51  F
8  16  53  F   7   6  37  F   7   6  41  M
7   6  39  M   9  15  50  M   8  17  57  F
8  14  46  M   9   8  41  M   9   8  41  F
9   7  47  F   7   3  39  F   7  12  50  M
7   4  43  M   9  14  46  F   8  18  58  M
9   9  44  F   7   2  37  F   7   1  37  M
7   4  44  M   7  11  42  M   9   8  41  M 
8  10  42  M   8  13  46  F   7   2  40  F
9   6  45  F   9  11  45  M   7   2  36  F
7   9  46  F
;

data IceCreamDataDomain; 
   set IceCreamDataDomain; 
   if Grade=7 then Prob=20/1824;
   if Grade=8 then Prob=9/1025;
   if Grade=9 then Prob=11/1151;
   Weight=1/Prob;
run;

In the data set IceCreamDataDomain, the variable Grade indicates a student’s grade, which is the stratification variable. The variable Spending contains the dollar amount of each student’s average weekly spending for ice cream. The variable Income specifies the household income, in thousands of dollars. The variable Gender indicates a student’s gender. The sampling weights are created by using the reciprocals of the probabilities of selection, as follows:

data StudentTotals;
   input Grade _TOTAL_; 
   datalines;
7 1824
8 1025
9 1151
;

In the data set StudentTotals, the variable Grade is the stratification variable, and the variable _TOTAL_ contains the total numbers of students in the strata in the survey population.

The following statements demonstrate how you can analyze the relationship between spending and income among male and female students:

title1 'Ice Cream Spending Analysis';
title2 'Domain Analysis by Gender';
proc surveyreg data=IceCreamDataDomain total=StudentTotals;
   strata Grade; 
   model Spending = Income; 
   domain Gender;
   weight Weight;
run;

Output 88.7.1 gives a summary of the domains.

Output 88.7.2 shows the parameter estimates for the model within each domain.

For this particular example, the effect Income is significant for both models built within subgroups of male and female students, and the models are quite similar. In many other cases, regression models vary from subgroup to subgroup.