[R] lmer estimated scale

[Daniel Ezra Johnson]

I have data consisting of binary responses from a large number of  
subjects on seven similar items. I have been using lmer with  
(crossed) random effects for subject and item. These effects are  
almost always (in the case of subject, always) significant additions  
to the model, testing this with anova. Including them also increases  
the Somers' Dxy value substantially.

Even without those reasons, I feel I'd have to include these random  
effects to account for the correlation between the seven items from  
every subject. Otherwise the fixed between-subject effects like race,  
gender, etc. will seem more significant than they should.

But how should I interpret the fact that without a Subject effect  
included, the "estimated scale" parameter is usually very close to 1,  
while when I include the Subject effect the scale parameter drops,  
usually to around 0.85?

Can I at least conclude something interesting from this? Is it the  
same as saying that the subject effect itself (meaning the 'observed'  
subject BLUPs) is underdispersed with respect to its theoretical  
normal distribution?

To summarize:

a <- lmer(Response~Fixed Effects+(1|Subject)+(1|Item),data,binomial)
b <- lmer(Response~Fixed Effects+(1|Item),data,binomial)

a has a much better fit by any measure, and estimated scale around 0.85.
b has a worse fit, but estimated scale around 1.

Obvious? Interesting? Worrisome?

Thanks,
Dan