IRT multigroup SAS example

[Kastchei]

I'm trying to learn IRT, and I'm looking at the following example from the SAS documentation.

http://documentation.sas.com/?docsetId=statug&docsetTarget=statug_irt_examples03.htm&docsetVersion=1...

The last bit of text, preceding the last two tables, says:

"Output 69.3.3 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."

I see how the slope for group 1 items 5-8 are the same: all four are 0.96022.  However, I do not see that the intercept for item1 is the same for group 1 and group 2.  Group 1 item1 difficulty is 0.24624.  Group 2 item1 difficulty is 0.32086.  I'm assuming that difficulty is the intercept the text mentions, but clearly I'm interpreting something wrong.  Does anyone have any idea?

Warm regards,

Michael

[FreelanceReinh · Accepted solution]

Hello @Kastchei,

Let me first say that I'm not familiar with this particular type of analyses and that I've never used PROC IRT.

In the documentation of the OUTMODEL= data set it says that "[f]or computational convenience, the intercept parameters rather than the threshold (or difficulty) parameters are saved in the OUTMODEL= data set." So, intercept and difficulty parameters are not the same, but the wording suggests that there's a fairly close relationship between them. Indeed, in section "Models for Ordinal Response Items" (under "Details") you find the formula bj,k=aj,k/lj (where bj,k is the threshold parameter and lj the slope parameter) and it says that "−aj,k is often called the intercept parameter." This suggests that in Output 69.3.3 the product of Difficulty (i.e. threshold) and Slope, times −1, should yield the intercept parameter. This is indeed confirmed by the values in the "Parameter Estimates" table: For example (for "item1"), −(0.24624*1.89146)=−0.46575... in group 1 and −(0.32086*1.45159)=−0.46575... in group 2. When you specify the OUTMODEL= option, the resulting dataset contains the intercept parameter in variable _EST_ where _SUBTYP_='INTERCEPT' and for item1 it is −0.46575... (in both groups, _GPNUM_=0 and _GPNUM_=1), as it should be. The corresponding values for item2, item3 and item4, respectively, agree similarly.

[Kastchei]

Thank you so much!