[Rasch] Paired Comparisons and Rasch software
Mike Linacre (RMT)
rmt at rasch.org
Fri Jan 13 08:04:36 EST 2006
Dear Don et al.
Paired comparison with standard Rasch software is straight-forward, e.g.,
www.rasch.org/rmt/rmt113o.htm - There is no requirement for complete
pairings, balanced pairings, etc. But there is a need for a linked network
of pairings, or for constraints on the estimation with an equivalent
effect. This has been applied in many sporting situations, for instance to
College Basketball including in the comparison home court advantage:
www.winsteps.com/ncbrank.htm - this is discussed at
www.rasch.org/rmt/rmt151w.htm - where the paired comparison model is
adjusted to allow for many "real world" aspects of the NCAA competition.
Bradley-Terry is a Rasch model, e.g., www.rasch.org/rmt/rmt92d.htm
Thurstone's methods usually give results similar to Rasch.
At 09:22 AM 1/12/2006 -0700, Donald Bacon wrote:
>I'm working with paired comparison data characterized by small samples and
>a somewhat "naturalistic" design: most respondents compare only a few
>pairs, and I have no control over which pairs they do choose to
>compare. Thus some pairs are never compared while other pairs are
>compared by 20 or 30 respondents (maybe a bit like sporting contests?). I
>know Rasch has been successfully applied to situations like this. I also
>thought that Thurstone's method may be appropriate, but I believe this
>method required equal frequencies of paired comparisons (and of course
>assumes normality). The Bradley Terry model appears to work fairly well
>(Firth's add-on package in R); is this mathematically equivalent to
>Rasch? I'm also wondering if a Bayesian model might work even
>better. Does anyone know a good paper that might compare Rasch,
>Thurstone, Bradley-Terry, and Bayesian approaches, and offer some kind of
>decision rule on when to use what?
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