[R-sig-ME] Bootstrapping glmer random effects

[David Duffy]

On Fri, 15 Jun 2012, Joe King wrote:

> Dear all
>
> I am attempting to obtain a bootstrap confidence interval for the random 
> effect in a simple (random intercept) model using glmer.
>
> The problem I have is that the interval I obtain consistently does not 
> contain the value I am trying to get an interval for !
>
> There are no missing data. This is the code I have used to obtain the interval:
>
> for (i in 1:k) {
>   sam <- dt[sample(nrow(dt), replace=T, size=nrow(dt)), ]
>   m1<- glmer(wg~(1|city), data=sam, family=binomial)
>   bs[i] <- VarCorr(m1)$city[1]
> }
> quantile(bs,c(0.025,0.975))
>
> Could anyone suggest why this is happening, and what I might be able to do about it ?

Have a look at how it is done by glmmML's glmmboot (or by merboot).  Your 
resampling has to correctly mimic the mechanism by which your 
data are generated.  I liked Shao J, Tu D (1995): The jackknife and 
bootstrap.