R help - Feb 2007 - random effect nested within fixed effects (binomial lmer)

I have a large dataset where each Subject answered seven similar  
Items, which are binary yes/no questions. So I've always used Subject  
and Item random effects in my models, fit with lmer(), e.g.:
model<-lmer(Response~Race+Gender+...+(1|Subject_ID)+(1| 
Item_ID),data,binomial)

But I recently realized something. Most of the variables that I've  
tested as fixed effects are properties of the subject (e.g. Race,  
Gender, etc.). Is it correct to be using a random effect Subject that  
is nested within (partially-crossed) fixed effects like Gender and  
Race? - I hope I'm using the terminology correctly.

So today, I accidentally ran a model without the Subject random  
effect, and the fixed effect of Race was significant for the first  
time. With the Subject effect included, Race is not significant. This  
also happens if Race is treated as random, though the effect is  
smaller then. The following table shows the various pairs of model  
fits, from somers2(), and the p-values given by anova().

Somers' Dxy
			p from anova()		random Subject term	no Subject term
Somers' Dxy

no Race term						0.8487					0.4096
	vs.										0.30					0.00064
fixed Race	 term					0.8483					0.4332

no Race term						0.8487					0.4096
	vs.										0.96					0.0047
random Race term					0.8486					0.4334

Adding the Subject effect always highly improves the fit of the  
model, so I would certainly want to keep it. But if there is a real  
effect of Race, why does adding the Subject effect make it go away?

I thought the Subject random effect would be a sort of residual  
subject effect, once everything else was accounted for by other  
subject properties (some of which do remain significant with Subject  
in there as well).

This must be a common scenario, since people are interested in  
inherent properties of subjects, yet also try to model and 'factor  
out' the random individual variation between people. I'm simply not  
very familiar with the relevant literature, and I hope someone here  
can help.

Thank you,
Daniel

P.S. Also, why does treating Race as a random factor have (very  
slightly) more of an effect on the Somers' Dxy, while judging by anova 
() it's "more significant" as a fixed factor?
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> But I recently realized something. Most of the variables that I've  
> tested as fixed effects are properties of the subject (e.g. Race,  
> Gender, etc.). Is it correct to be using a random effect 
> Subject that is nested within (partially-crossed) fixed effects
> like Gender and Race?
Yes. I would even claim that it is necessary. Only if you use subject as a
random effect, gender and race are correctly attributed as constant within
individuals and are thus treated as 'between-subject' variables. (And
thus, basically, the sample on which you can base your gender and race
comparisons is the number of individuals).
 
> So today, I accidentally ran a model without the Subject random  
> effect, and the fixed effect of Race was significant for the first  
> time. With the Subject effect included, Race is not significant.
In my view, this is not surprising and can be called pseudo-replication. Every
line of your data set is now treated as an independent measure even though the
repetition of race and gender for the same individual is, of course, no new,
indpendent information. (Here, you base your statistics on the number of
observations instead of individuals.)
> This also happens if Race is treated as random, though the effect
> is smaller then.
I do not really see why you would want to do that.
> ... But if there is a real effect of Race, ...
Well, is there? If you conduct your analyses at the proper level, there
obviously is no such effect (at least none that is supported statistically). It
is of course possible, that there is a weak effect which you might pick up in a
larger sample (more individuals tested).

Cheers, Lorenz
- 
Lorenz Gygax
Federal Veterinary Office
Centre for proper housing of ruminants and pigs
T?nikon, CH-8356 Ettenhausen / Switzerland