More work in and of itself is fine so long as the work is of the same type, e.g., A calculus test with mostly differentiation and some integration may end up being weakly unidimensional at the upper end given that integration is both more difficult and often in a different class. Unidimensional IRT can usually cope with weak unidimensionality, where you have a dominant dimension but some microstructure. The model could be bettered but it often gets by.
-----Original Message-----
From: "Stas Kolenikov" <[email protected]>
To: [email protected]
Sent: 3/13/2009 11:12 AM
Subject: Re: st: IRT with GLLAMM
Cool. Yeah, my difficult items ask for quite a bit more mental work
than medium or low difficulty ones.
On Fri, Mar 13, 2009 at 10:05 AM, jverkuilen <[email protected]> wrote:
> Stas Kolenikov wrote:
>
> "-I tried Rasch
> model with -xtlogit- (or -xtmelogit-), and the results were
> essentially a slightly curved version of the total number correct."
>
> That's what the Rasch model does as total score is a sufficient statistic for ability. The bending is often useful, though, to show more appropriately how spread the subjects realy are and the fact that the estimated abilities have a more realistic SE than arises fro classical test theory.
>
> The local independence issue puzzles me but I'll hazard a guess. I suspect that very extreme difficulty items will tend to be multidimensional, which would be interpreted as a violation of local independence if one asserts that there is only one latent dimension. One of the reasons for the development of IRT was to handle the problem of "difficulty factors" which occur due to the fact that covariances of binary items are restricted by the marginals, which induces an illusory multidimensionality. An IRT model helps a lot, but extreme items might well not fit on the continuum defined by the other items. For example, on a math test, the hard items may require a qualitative shift in reasoning ability. (There are models for this kind of thing, eg., Mark Wilson's saltus model.)
>
> JV
>
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--
Stas Kolenikov, also found at http://stas.kolenikov.name
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