[Rasch] Difficulty & fit

Timothy Pelton tpelton at uvic.ca
Wed Dec 30 04:06:41 EST 2009

If you allow that the  items might have some variation in their discriminations (for convenience I call this independent multidimensionality) then the most difficult and least difficult items tend to exhibit the greatest degree of misfit because the item parameter estimates in such situations are subject to the greatest amount of bias.  Note also that the SE estimates are systematically underestimated by the Rasch Model whenever the data contains deviations from the assumptions.

I presented a paper at IOMW 2002 in which I describe a simulation study that demonstrates some of the limits to the Rasch advantage when the assumptions are not met  (sorry I haven't managed to resubmit it for publication yet).


Tim Pelton
Associate Professor
Faculty of Education
University of Victoria
office: 250-721-7803
fax: 250-721-7598
From: rasch-bounces at acer.edu.au [rasch-bounces at acer.edu.au] On Behalf Of Anthony James [luckyantonio2003 at yahoo.com]
Sent: Tuesday, December 29, 2009 1:45 AM
To: rasch at acer.edu.au
Subject: [Rasch] Difficulty & fit

Dear folks,
In an analysis I have found out that the most and the least difficult items misfit.
Are fit and difficulty related, happened by chance in my analysis or is it an artifact of fit analysis in general?
Why should easy and difficult items misfit.
I have also seen this in principal component analysis of Rasch residulas, where the opposing clusters are easy and difficult items.
These remind me of deficiencies associated with classical factor analysis in which factors cab be merely difficulty factors.


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