[R-sig-ME] fixed effect testing again (but different)

[Douglas Bates]

On Fri, Aug 29, 2008 at 1:09 PM, Daniel Ezra Johnson
<danielezrajohnson at gmail.com> wrote:
>>> If it seems wrong to take the parameter from m1, is there some way to
>>> change the specification of m0 so as to obtain a separate random
>>> effect for males and females? I've seen that done but I've forgotten
>>> how to do it.
>>>
>>> If I can run something like
>>>
>>> m00 <- lmer(response~(1|subject-females)+(1|subject-males),data)   #
>>> how is this specified?
>
> Off list I was shown a way to supposedly do this, by making a pseudo
> random slope using a dummy variable. It seems promising but it doesn't
> really work properly, as the following example shows.
>
> set.seed(1)
> s <- rep(rnorm(200,0,1),each=100)
> g <- rep(c(-3,3),each=10000)
> p <- inv.logit(s+g)
> obs <- data.frame(response=rbinom(20000,1,p),
>        gender=rep(c("M","F"),each=10000),
>        subject=rep(paste("S",1:200,sep=""),each=100))
> obs$M <- ifelse(obs$gender=="M",1,0)
> obs$F <- ifelse(obs$gender=="F",1,0)
>
> test <- lmer(response~(0+M|subject)+(0+F|subject),obs,binomial)
>
> Random effects:
>  Groups  Name Variance Std.Dev.
>  subject M     0.82563 0.90864       # out of whack
>  subject F    37.79488 6.14775       # out of whack
> Number of obs: 20000, groups: subject, 200
>
> obs.m <- obs[obs$gender=="M",]
> test.m <- lmer(response~(1|subject),obs.m,binomial)
>
> Random effects:
>  Groups  Name        Variance Std.Dev.
>  subject (Intercept) 0.85413  0.9242
> Number of obs: 10000, groups: subject, 100
>
> obs.f <- obs[obs$gender=="F",]
> test.f <- lmer(response~(1|subject),obs.f,binomial)
>
> Random effects:
>  Groups  Name        Variance Std.Dev.
>  subject (Intercept) 0.60097  0.77522
> Number of obs: 10000, groups: subject, 100
>
> Is there, then, any way to implement heteroscedastic-by-group random
> effects in lme4, as opposed to nlme?

At present, no - at least none that I know of (and I am usually
reasonably well informed regarding the capabilities of lme4).

I am currently working on abstracting the role of the parameters in
model-fitting within lme4 by redesigning the classes.  The current
design ties the parameters to a particular representation of the
relative covariance matrix of the random effects and it should be
generalized.  The trick is to generalize the approach without
sacrificing too much in the way of performance.