[R-sig-ME] Rasch with lme4

Doran, Harold HDoran at air.org
Tue Jun 9 15:59:00 CEST 2009

> It can be argued that the items are a sample from a 
> population of items which is possibly reasonable for 
> educational testing where there might be a population of 
> questions which can be asked. Even so, assumptions about the 

I think the argument is easily supported, however. If you test my
ability to use R via a single test item (or even a small set of test
questions) isn't that only going to give an extremely myopic
perspective? There would certainly be a lot of variability in the
estimates given that another, exchangeable, set of test items could have
been used, no?

> distribution are optimistic and most items are used because 
> they test something obvious. 

Not sure I follow this, Ken. The distributional assumption about the
random effects in the mixed model is that they are normal. Is that what
you mean by optimistic?

> By an IRT I mean the 2 parameter version where there is a 
> discriminant parameter which varies among items, in contrast 
> to the Rasch where it is constant. It probably gives problems 
> with the other model as well but the second model should have 
> more problems.
> I don't like the idea of assuming a Rasch model at all, its 
> popularity seems to derive from an era when fitting anything 
> else was difficult.  
> Modern software offers proper solutions, unfortunately at a 
> cost but that shouldn't be a consideration.

Wasn't it George Box who said, "Don't fall in love with a model?" I
agree to some extent. I don't think there is such a thing as "a proper
solution". The Bock and Aitkin MML method is perhaps what you mean, but
there are a lot of ways to generate IRT item parameters. 

There are many other reasons why Rasch is chosen in educational testing
situations, not only because of the fact that it is easy to estimate.

But, with different models come different issues that require different
assumptions. For instance, the 3PL estimates a "guessing" parameter.
But, the model cannot be identified without the use of a very strong
gamma prior. Since the variance of the prior is often extremely slim and
the mean is usually 1/k where k is number of options, the posterior is
pretty close to the prior. 

So, I think it's fair to look at all models, criticize the various
assumptions, not only the Rasch model. 

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