[Rasch] Polytomous data difficulty parameter

Trevor Bond trevor.bond at jcu.edu.au
Mon Sep 1 08:00:11 EST 2008

Dear Mark
Which polytomous model did you use?
The RSM usually gives a difficulty estimate for each individual item plus one set 
of threshold estimates common to all items.(ie problem solved)
The PCM usually gives four threshold estimates (for 5 cats) for each item.
Depending on the software you use, you can specify the item diff + threshold 
ests as output from the PCM as well
c.f. Fig 6.3 (Quest) and Fig 6.4 Winsteps in B&F 2

BUT, why just  the rank order of subscale items? Rasch measurement is designed 
exactly for giving interval scales to mere orders


I am working with data from a 5-category questionnaire. I'd like to present a 
table that indicates the rank order of subscale items by ease of endorseability. 
>From what I have learned, polytomous data have difficulty parameters per 
threshold, but not an overall item-level difficulty parameter. I have heard from 
some that I should just a priori declare which threshold indicates endorsement, 
and use that difficulty parameter. I have heard from others that I should average 
all the threshold difficulties together to calculate an overall difficulty. First, is it 
correct that there is no such thing as an overall difficulty parameter for 
polytomous data (per item)? If no, how is it calculated. If yes, what is the best 
approach to deriving a statistic that could meet my purpose mentioned above? 
Gratefully yours, Mark

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