[R-sig-ME] Rasch with lme4

[Ken Beath]

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

A problem with the first model is that the random effect estimates are  
treated as though they were measured without error, when aren't. This  
results in attenuation of the parameter estimate. On teh other hand  
people use it and find it OK. A better method is to use modern SEM  
software that handles binary variables.

At a first glance Model 2 seems sensible.

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.

Ken

On 08/06/2009, at 9:04 PM, Jeroen Ooms wrote:

> I have tried to use lme4 to analyze IRT like datasets, but now I am
> confused. I have a data set with intelligence items (i.e. score 0 or  
> 1), for
> completely crossed subjects and items. Furthermore, the data  
> contains some
> personality scores on the subject level. Actually the data is more
> complicated than this, but let's keep it simple for now. My research
> question is whether a personality charcteristic, say extraversion, is
> related to intelligence. My question is how I should incorporate the
> extraversion variable in the analysis.
> When I analyse this data using the Rasch model, I usually first fit  
> the
> model, then extract the 'latent trait scores', and relate these to the
> extraversion scores. I could do the same with lmer:
>
> myModel <- lmer(y~1+(1|item)+(1|subject),data=mydata,  
> family=binomial);
> intelligence <- ranef(myModel)$subject[[1]];
> lm(intelligence~extraversion);
>
> However, in the context of multilevel analysis, it is also possible to
> incorporate the extraversion variable directly into the model:
>
> myModel2 <- lmer(y~1+(1|item)+(1|subject)+extraversion,data=mydata,
> family=binomial);
>
> Conceptually both methods feel very similar, but they give different
> results. What is the most appropriate method? What are the  
> differences in
> interpretation?
>
> Thank you!
>
> Jeroen
>
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