[R-sig-ME] Rasch with lme4

Murray Jorgensen maj at stats.waikato.ac.nz
Wed Jun 10 00:08:33 CEST 2009

Fitting some alternative models may help if the normality of the random 
effects in the Rauch model is under doubt. For example the Rauch model 
could be fitted to transformed scores.

A more 'nonparametric' approach might be to use finite mixture models 
(usually called latent class models in this context).

Conclusions that are stable across a range of models can surely be 
trusted more.

Murray Jorgensen

Doran, Harold wrote:
>> 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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Dr Murray Jorgensen      http://www.stats.waikato.ac.nz/Staff/maj.html
Department of Statistics, University of Waikato, Hamilton, New Zealand
Email: maj at waikato.ac.nz    majorgensen at ihug.co.nz      Fax 7 838 4155
Phone  +64 7 838 4773 wk    Home +64 7 825 0441   Mobile 021 0200 8350

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