[R-sig-ME] Rasch with lme4

[Jeroen Ooms]

2009/6/9 David Duffy <David.Duffy at qimr.edu.au>
>
> Aside from Reinhold's comment, which is not a showstopper (you could bootstrap etc), they are quite different models. In the first model, the estimated IQ-extraversion correlation is disattenuated for measurement error -- the equivalent SEMs are something like (I think ;)):
>
>
> IQ <-----> E  v.   E
> | \                | \
> v  v               v  v
> i1 i2              i1 i2
>                   ^  ^
>                   | /
>                   IQ
>

I am not convinced the second SEM model correclty represents the
second lme model. In the sem model the effect of IQ on y seems to be
conditional on the effect of Extraversion, and vice versa. However,
the fixed effect of extraversion on y does not seem to change
tremendously whether a random effect of subjects is included in the
model or not. I think this is because 'IQ' is only represented by a
random effect in the multilevel model, and the sem model seems to
imply a fixed effect.