[R-sig-ME] generalized linear mixed models: large differences when using glmmPQL or lmer with laplace approximation
Ken Beath
ken at kjbeath.com.au
Sat Oct 11 07:17:45 CEST 2008
On 08/10/2008, at 8:18 AM, Douglas Bates wrote:
> On Tue, Oct 7, 2008 at 4:07 PM, Ken Beath <ken at kjbeath.com.au> wrote:
>> There is a large difference between the estimated std of the random
>> effect,
>> usually a sign that the glmmPQL approximation isn't working.
>
> Or that there is a mistake in the calculation of the standard errors
> for the random effects, which is more likely in this case.
>
> The actual optimization is with respect to the relative standard
> deviation of the random effects (relative to the scale parameter in
> the conditional standard deviation of the response). For the Poisson
> family or the binomial family that scale parameter is fixed at 1 (you
> could also consider the situation to be that there isn't a scale
> parameter in those cases). For the quasipoisson and quasibinomial
> families you maybe estimate a value there or maybe not. I don't know.
> I believe Ben's simulations showed that I was doing the wrong thing
> there
Definitely something wrong. I did some simulations of my own using
Poisson distributed data. The standard error of the fixed effects also
seems rather large.
> nsubj <- 100
> npersubj <- 20
>
> subject <- factor(rep(1:nsubj,each=npersubj))
>
> means <- exp(rep(10+rnorm(nsubj),each=npersubj))
>
> y <- rpois(nsubj*npersubj,means)
>
> simdata <- data.frame(y,subject)
>
> lmer1 <- lmer(y~(1|subject),data=simdata,family=poisson)
> summary(lmer1)
Generalized linear mixed model fit by the Laplace approximation
Formula: y ~ (1 | subject)
Data: simdata
AIC BIC logLik deviance
3329 3341 -1663 3325
Random effects:
Groups Name Variance Std.Dev.
subject (Intercept) 0.9102 0.95405
Number of obs: 2000, groups: subject, 100
Fixed effects:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 9.9734 0.0954 104.5 <2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
>
> lmer2 <- lmer(y~(1|subject),data=simdata,family=quasipoisson)
> summary(lmer2)
Generalized linear mixed model fit by the Laplace approximation
Formula: y ~ (1 | subject)
Data: simdata
AIC BIC logLik deviance
3331 3348 -1663 3325
Random effects:
Groups Name Variance Std.Dev.
subject (Intercept) 11794 108.60
Residual 12957 113.83
Number of obs: 2000, groups: subject, 100
Fixed effects:
Estimate Std. Error t value
(Intercept) 9.973 10.860 0.9184
>
Ken
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