Rasch with lme4
On Mon, 8 Jun 2009, Reinhold Kliegl wrote:
Conditional modes (generated from the model parameters and the data) are not independent observations. Therefore, only the second method is valid. Reinhold Kliegl On 08.06.2009, at 13:04, 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?
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
Most people would prefer something like the first model, and in fact would
estimate the correlation between IQ and E estimated (as if without error)
from two measurement models given by the scoring rules for the
instruments (these are essentially BLUPs). Incorporating measurement
error for both measures is the truest way to do it.
You could compare results using the sem and polycor packages to those from
your lmer model.
my 2c, David Duffy.
| David Duffy (MBBS PhD) ,-_|\ | email: davidD at qimr.edu.au ph: INT+61+7+3362-0217 fax: -0101 / * | Epidemiology Unit, Queensland Institute of Medical Research \_,-._/ | 300 Herston Rd, Brisbane, Queensland 4029, Australia GPG 4D0B994A v