The IRT Procedure

This example shows how to use the IRT procedure to do multiple-group analysis. The following DATA step creates the data set IrtGroup:

data IrtGroup;
   input item1-item8 GroupVar @@;
   datalines;
1 0 0 0 1 1 2 1 2 1 1 1 1 1 3 3 3 1 0 1 0 0 1 1 1 1 1 1 0 0 1 0 1 2 3
2 0 0 0 0 0 1 1 1 1 1 0 0 1 0 1 3 3 1 0 0 0 0 0 1 1 3 2 0 0 1 0 0 1 2
2 1 0 1 0 0 1 1 1 2 1 0 0 0 0 0 2 2 3 1 0 1 0 1 0 2 3 3 2 0 0 1 0 1 1
2 3 1 1 1 1 1 1 2 2 3 2 0 0 0 0 1 1 2 2 1 1 0 1 1 1 2 3 3 2 0 1 0 0 1
1 2 3 2 1 0 1 1 1 2 3 3 2 0 1 0 1 1 3 2 3 2 1 1 1 0 0 1 3 3 1 1 1 0 0
1 2 3 3 2 0 1 1 1 1 1 2 1 2 1 0 0 1 1 3 1 1 2 1 0 0 0 1 1 1 3 2 0 0 0
0 1 1 3 3 1 0 0 0 0 0 1 1 1 2 1 0 0 0 0 1 3 3 2 1 1 0 1 1 3 1 1 1 1 0
1 1 1 1 3 1 2 1 1 1 1 1 2 3 2 2 0 0 1 0 0 2 2 2 1 0 0 1 0 1 1 2 3 2 1

   ... more lines ...   

1 0 0 2 1 3 2 1 1 1 1 1 1 3 2 1 1 1 1 0 0 3 3 1 2 1 0 0 1 1 3 3 3 2 0
0 1 0 0 1 1 1 2 0 0 0 0 1 3 1 1 2 1 0 0 1 0 1 3 3 2 0 0 1 1 0 2 2 3 2
1 0 0 0 1 1 1 1 1 0 0 0 0 1 1 1 1 2 0 0 1 1 0 1 1 3 2 0 0 0 0 1 1 1 1
2 0 0 1 0 0 1 1 1 1 
; 

To set up a multiple-group IRT model, you need to specify the grouping variable by using the GROUP statement. Very often you also want to specify cross-group equality constraints for different parameters. You can accomplish this by using the EQUALITY statement.

The model that is specified in the following statements is an extension of the model in Example 53.1. The group variable, GroupVar, is specified in the GROUP statement. It has two values, 1 and 2, to indicate group membership. Equality constraints are specified in the EQUALITY statement.

proc irt data=IrtGroup;
   var item1-item8;
   group GroupVar;
   model item1-item4/resfunc=twop,
         item5-item8/resfunc=graded;
   equality item1-item4/parm=[intercept] between_gp=[1 2],
            _allgr_/parm=[slope] within_gp=[1];
run;

Two different sets of equality constraints have been specified. The first entry specifies equality constraints on the intercept parameters for item1 to item4 between group 1 and group 2:

item1-item4/parm=[intercept] between_gp=[1 2]

Notice that 1 and 2 are the actual values for the group variable GroupVar. The second entry specifies equality constraints on the slope parameters for all the graded response items within group 1:

_allgr_/parm=[slope] within_gp=[1]

Output 53.3.1 shows the "Modeling Information" table and the "Group Information" table for this example. For multiple-group analysis, the "Modeling Information" table contains two extra pieces of information: the group variable and the number of groups. The "Group Information" table contains information about the data for each group. There are 272 observations that have been read and used for group 1; this number for group 2 is 328.

Because there are two groups in this example, the IRT procedure produces two "Item Information" tables. For this example, these two tables contain the same information. That means that all the items have the same levels for the two groups. It is possible that the same item might have different numbers of levels, or maybe the same number of levels but different values. For example, an item has four levels, from 1 to 4, but one group might observe only levels 1 and 2, and the other group might observe only levels 3 and 4.

Output 53.3.3 includes "Item Parameter Estimates" tables for both groups. You can see that the intercept parameters for item1 are the same for both groups. The same applies to item2 to item4. You can also see that the slope parameters have the same value for item5 to item8 in group 1. These results suggest that equality constraints that are specified in the EQUALITY statement have been fulfilled.