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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