[Rasch] [BULK] Re: Rasch Digest, Vol 66, Issue 1

Stuart Luppescu slu at ccsr.uchicago.edu
Wed Jan 5 08:57:54 EST 2011

On Tue, 2011-01-04 at 02:12 -0500, Stemler, Steven wrote:
> Suppose that out of 100 test-takers, only 2 people actually answer
> item 20 (your theoretically hardest item on the test). One of those
> two gets it right and the other gets it wrong. If you don't treat the
> other test-takers who didn't make it to that hard item as answering it
> incorrectly (and you are not working with anchored item statistics),
> the logit estimate for the item difficulty will be 0.

This certainly isn't true, is it? The item difficulty would depend on
the ability of the people who responded to that item. If the only people
who answered item 20 were high ability people, the item difficulty would
be near the average ability of those people. If they got most of the
other items correct, and had an ability of, say, 2.0, then the
difficulty of item 20 would be near 2.0. Or am I confused?

I have found significant problems in treating these missing data as
incorrect. I was working on a timed test; there were some items that no
students at all reached. The items later in the test were answered by
only a few students. Treating responses by students who did not reach
those items as incorrect produced huge misfit and very peculiar patterns
in the person measures. (Sorry, but I don't have time right now to look
up the specifics.) The fits and the person measures were much more
reasonable when non-reached item data were treated as missing.

Another thing to consider in this case is that the items near the end of
the test are probably way too difficult for the students with long
strings of preceding incorrect responses, and thus will not provide much
information anyway. In principle, I don't think making the missing data
incorrect will change the person measure appreciably, but will increase
the precision, a result that is probably unwarranted.
Stuart Luppescu -=- slu .at. ccsr.uchicago.edu        
University of Chicago -=- CCSR 
才文と智奈美の父 -=-    Kernel 2.6.36-gentoo-r5                
Friends don't let friends use Excel for statistics!
 -- Jonathan D. Cryer (about problems with using
 Microsoft Excel for       statistics)       JSM
 2001, Atlanta (August 2001)  

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