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I'm trying to use IRT to equate scales across 5 datasets. Three of them use the same scale (A); the other ones use different ones (B and C) There are items that overlap between A and C, A and B, but not B and C.

  1. Is it still possible to create commensurate measures across the three datasets?
  2. If I wanted to create a commensurate measure for A and B, I get that I need to use the anchor items...but what exactly is the role of non-anchor items? (that are unique to each dataset)? do they add any information?
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  1. It is entirely possible to equate the test forms if the items common across all three forms contain no response bias (i.e., DIF). All that would be required is to estimate a multiple-group IRT model with equality constraints for the respective anchor items across all test versions (there may be larger blocks of missing data for datasets that did not respond to the respective items, but that's not a statistical issue), as well as freely estimating the scaling parameters for the latent traits in the focal groups. As well, if there is a sufficient number of common items across the forms it may be possible to test for DIF in more suspect items, but more information is needed on how many items are common across the forms.

  2. Yes, non-anchor items add information to the equating process, thereby improving the quality of the equating. You can think of the non-anchor items as adding measurement precision to the respective latent trait estimates for each individual, which in turn helps the accuracy of the equating process by way of borrowing strength from other aspects of the model.

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  • $\begingroup$ Wow Thanks a lot! Re: #1) i think you minght have misunderstood my question... I was wondering if it’s possible to equate them when there is no common item across all three. (i.e., there are common items between test A and B, B and C, but not across A,B,andC) $\endgroup$
    – llbia
    Oct 18, 2020 at 14:22
  • $\begingroup$ @llbia my response is suitable to this situation as well. The idea is that as long as the distinct datasets contain some type of overlap, and the overlapping items are constrained across the groups where applicable (not necessarily across all three forms) then the equating will be fine as the latent variable scales are suitably adjusted and identified relative to a given reference group. $\endgroup$
    – philchalmers
    Oct 18, 2020 at 23:52
  • $\begingroup$ This was super helpful thank you so much! $\endgroup$
    – llbia
    Oct 19, 2020 at 10:09

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