Hi all,
I'm analysing data with the following structure:828 students nested
within 138 schools. Every student supplied 13 items (wright/wrong).
The data set contains 13 lines for every student. I consider a random
effect for items as well. The model was set-up as follows, with the
resulting output are presented at the bottom. My question now is
whether setting-up the model like this implies that ITEM and IDSTUD
are crossed and IDSTUD's are nested within SCHOOLS. Or do I make a
mistake here?
> Model1<-lmer(SCORE~1+(1|IDSCHOOL)+(1|IDSCHOOL:IDSTUD)+(1|
ITEM),data=Items, family=binomial)
> summary(Model1)
Generalized linear mixed model fit using Laplace
Formula: SCORE ~ 1 + (1 | IDSCHOOL) + (1 | IDSCHOOL:IDSTUD) + (1 | ITEM)
Data: Items
Family: binomial(logit link)
AIC BIC logLik deviance
10761 10790 -5376 10753
Random effects:
Groups Name Variance Std.Dev.
IDSCHOOL:IDSTUD (Intercept) 0.772882 0.87914
IDSCHOOL (Intercept) 0.076846 0.27721
ITEM (Intercept) 1.727892 1.31449
number of obs: 10764, groups: IDSCHOOL:IDSTUD, 828; IDSCHOOL, 138;
ITEM, 13
Estimated scale (compare to 1 ) 0.9272256
Fixed effects:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 0.8852 0.3676 2.408 0.0160 *
---
With kind regards,
Sven De Maeyer
University of Antwerp
complex cross classified model
2 messages · Sven De Maeyer, Douglas Bates
On Thu, Oct 1, 2009 at 3:49 PM, Sven De Maeyer <sven.demaeyer at ua.ac.be> wrote:
Hi all, I'm analysing data with the following structure:828 students nested within 138 schools. Every student supplied 13 items (wright/wrong). The data set contains 13 lines for every student. I consider a random effect for items as well. The model was set-up as follows, with the resulting output are presented at the bottom. My question now is whether setting-up the model like this implies that ITEM and IDSTUD are crossed and IDSTUD's are nested within SCHOOLS. Or do I make a mistake here?
Model1<-lmer(SCORE~1+(1|IDSCHOOL)+(1|IDSCHOOL:IDSTUD)+(1|ITEM),data=Items, family=binomial) summary(Model1)
Generalized linear mixed model fit using Laplace Formula: SCORE ~ 1 + (1 | IDSCHOOL) + (1 | IDSCHOOL:IDSTUD) + (1 | ITEM) ? Data: Items ?Family: binomial(logit link) ? AIC ? BIC logLik deviance ?10761 10790 ?-5376 ? ?10753 Random effects: ?Groups ? ? ? ? ?Name ? ? ? ?Variance Std.Dev. ?IDSCHOOL:IDSTUD (Intercept) 0.772882 0.87914 ?IDSCHOOL ? ? ? ?(Intercept) 0.076846 0.27721 ?ITEM ? ? ? ? ? ?(Intercept) 1.727892 1.31449 number of obs: 10764, groups: IDSCHOOL:IDSTUD, 828; IDSCHOOL, 138; ITEM, 13 Estimated scale (compare to ?1 ) ?0.9272256 Fixed effects: ? ? ? ? ? ?Estimate Std. Error z value Pr(>|z|) (Intercept) ? 0.8852 ? ? 0.3676 ? 2.408 ? 0.0160 * ---
That model specification seems fine to me. If the student labels are 828 unique labels (that is, if it is not the case that different schools can each have a student with the same IDSTUD) then the specification (1|IDSCHOOL:IDSTUD) could be shortened to (1|IDSTUD). However, specifying (1|IDSCHOOL:IDSTUD) is not harmful in any way and is safer so I would stay with that. When random effects are associated with different factors, lmer does not distinguish between nested and non-nested factors. It just uses the factors as they are specified. In fact, the calculations are identical for nested or non-nested. The only thing that happens with nested factors is that some of the model structures are simpler but that is a side-effect, not an assumed property. I think I am running the risk of over-explaining, a common fault of mine. The short answer is that you have got it right.