[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.

Mike Linacre

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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