[Rasch] DIF studies for polytomous items

Mike Linacre (RMT) rmt at rasch.org
Sat Apr 17 21:02:06 EST 2010

Thank you for your question, Kenji.

DIF analyses are complicated, and often difficult to interpret.

The items are "polytomous" (= many cuts), not "polychromous" (= many colors).

Anchoring is always done with Rasch-Andrich thresholds, because they 
produce a simpler expression of the Rasch model. Conversion between 
Rasch-Andrich and Rasch-Thurstone thresholds requires some algebra, 

With the Facets software,

For uniform DIF, in your step 1: Models = ?B,..,?B produces the DIF 
estimates. Step 2 is not needed. One "?" is for the group-identifying facet.

For non-uniform DIF, perform your step 1. Output an Anchorfile=.
In your step 2, do not anchor the thresholds or the item difficulties, but 
do anchor the person measures in the two group analyses at their step 1 
values. The person measures are in the step 1 Anchorfile=.


Mike L.

At 4/16/2010, you wrote:
Dear colleagues,

Thank you all very much for your supports for my previous question 
regarding DIF studies for polychromous items.  Today, I would like to ask 
another question that is partly related to the previous question that I asked.

The question is about which threshold values--Rasch-Andrich threshold or 
Rasch-Thurston threshold--I should use to investigate DIF of polytomous 

My understanding of a DIF analysis process is like this.  Step 1,  given 
that there are two groups—-reference and focal groups--for DIF 
investigation, I need to combine the data of these groups as one to 
estimate a set of category threshold values.  The step 2 will be that I use 
this set of threshold values as anchors to recalibrate item difficulties 
for the two groups separately (and so on$B!D(B).

My question is regarding the step 2.  Which threshold values--Rasch-Andrich 
threshold or Rasch-Thurston threshold—I should use?  I use FACETS program 
to conduct this investigation based on the rating scale model.  In my 
situation, I think I need to use the Rasch-Thurston threshold values, but 
it seems that I am not able to use them as anchor values.

So, my question is about the following two issues:
(1)    Is it correct to use the Rasch-Thurston threshold values as anchors 
to make item difficulties comparable across two groups in a DIF investigation?
(2)    If the first question is true, does FACETS have a capability to make 
Rasch-Thurston threshold values as anchors?

Thank you very much.

Kenji Yamazaki

Mike Linacre
Editor, Rasch Measurement Transactions
rmt at rasch.org www.rasch.org/rmt/ Latest RMT:  23:4 Spring 2010
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