Rasch with lme4

On ?, 2009-06-09 at 08:04 +1000, Ken Beath wrote:

The model treats item as a random effect and should be a fixed  
effect.

Hmm. In Doran, Bates, Bliese and Dowling (2007), the authors treat the
item as random.

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 distribution are optimistic and most items are  
used because they test something obvious. Maybe others have a  
different philosophy. A more pedantic argument is that this isn't the  
model Rasch used.

[snip]

Another question to ask is whether the Rasch model is appropriate. If
an IRT is more sensible it would cause some problems with the second
model.

Sorry, but I don't understand this at all.

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.

Ken

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