[R] Using quasibinomial family in lmer

[r.millar at auckland.ac.nz]

Dear R-Users,

I can't understand the behaviour of quasibinomial in lmer. It doesn't
appear to be calculating a scaling parameter, and looks to be reducing the
standard errors of fixed effects estimates when overdispersion is present
(and when it is not present also)! A simple demo of what I'm seeing is
given below. Comments appreciated?

Thanks,

Russell Millar
Dept of Stat
U. Auckland

PS. I'm using the latest version of lme4 (0.999375-26) with R 2.7.2.

> eta=rnorm(50)
> p=exp(eta)/(1+exp(eta))
> y=rbinom(50,20,p)/20 #IID overdispersed binomial-normal proportions
> #y=rbinom(50,20,0.5)/20 #IID binomial(20,0.5)
>
> Group=rep(c("A","B","C","D","E"),c(10,10,10,10,10))
>
> #library(lme4)
>
> lmer(y~1+(1|Group),weights=rep(20,50),family="binomial")
Generalized linear mixed model fit by the Laplace approximation
Formula: y ~ 1 + (1 | Group)
 AIC   BIC logLik deviance
 211 214.8 -103.5      207
Random effects:
 Groups Name        Variance Std.Dev.
 Group  (Intercept) 0.072891 0.26998
Number of obs: 50, groups: Group, 5

Fixed effects:
            Estimate Std. Error z value Pr(>|z|)
(Intercept)   0.2194     0.1367   1.605    0.108
>
> lmer(y~1+(1|Group),weights=rep(20,50),family="quasibinomial")
Generalized linear mixed model fit by the Laplace approximation
Formula: y ~ 1 + (1 | Group)
 AIC   BIC logLik deviance
 213 218.7 -103.5      207
Random effects:
 Groups   Name        Variance  Std.Dev.
 Group    (Intercept) 0.0032632 0.057125
 Residual             0.0447685 0.211586
Number of obs: 50, groups: Group, 5

Fixed effects:
            Estimate Std. Error t value
(Intercept)  0.21940    0.02892   7.586
>