[R-sig-ME] glmer and overdispersed Poisson models
Ken Beath
ken at kjbeath.com.au
Tue Sep 16 09:00:22 CEST 2008
On 16/09/2008, at 3:44 PM, David.Ramsey at dse.vic.gov.au wrote:
> Hi All, I have recently upgraded my version of lme4 and redid an old
> analysis. The data are counts and are overdispersed and an offset is
> included. I originally fitted a mixed model in lmer() using
> quasi-likelihood
>
> lme4 version 0.99875-9 Matrix version 0.999375-4
>
>> fit1= lmer(total ~ direction + time + flow + offset(log(effort)) +
> (1|site),family=quasipoisson(link=log),data=data,method="ML")
>> summary(fit1)
> Generalized linear mixed model fit using Laplace
> Formula: total ~ direction + time + flow + offset(log(effort)) + (1 |
> site)
> Data: data
> Family: quasipoisson(log link)
> AIC BIC logLik deviance
> 222622 222637 -111305 222610
> Random effects:
> Groups Name Variance Std.Dev.
> site (Intercept) 3930.7 62.695
> Residual 3544.0 59.531
> number of obs: 80, groups: site, 7
>
My suspicion is that the very high variance of the random effects is
the problem resulting from the sites having an extreme range. This
will give the Laplace approximation some problems so adaptive Gauss-
Hermite may work but this data seems extreme. I'm guessing that each
observation is either small or large.
Ken
> Fixed effects:
> Estimate Std. Error t value
> (Intercept) 1.46436 23.70079 0.062
> directionout -0.22065 0.27874 -0.792
> timenight -1.16554 0.28429 -4.100
> flows 0.01255 0.43394 0.029
> flowf 0.40867 0.55300 0.739
>
> Correlation of Fixed Effects:
> (Intr) drctnt tmnght flows
> directionot -0.005
> timenight -0.008 0.086
> flows -0.011 -0.066 0.072
> flowf -0.011 -0.048 0.041 0.687
>
> So far so good. We have an estimate of the scale of 59.5 (ouch - yes
> pretty bad overdispersion!).
> I redid this analysis recently with the latest version of lme4
>
> lme4 version 0.999375-26: Matrix version 0.999375-14
>
>> fit2= glmer(total ~ direction + time + flow + offset(log(effort)) +
> (1|site),family=quasipoisson(link=log),data=data,REML=F)
>> summary(fit2)
> Generalized linear mixed model fit by the Laplace approximation
> Formula: total ~ direction + time + flow + offset(log(effort)) + (1 |
> site)
> Data: data
> AIC BIC logLik deviance
> 222624 222641 -111305 222610
> Random effects:
> Groups Name Variance Std.Dev.
> site (Intercept) 4019367 2004.8
> Residual 3487254 1867.4
> Number of obs: 80, groups: site, 7
>
> Fixed effects:
> Estimate Std. Error t value
> (Intercept) 1.44981 757.88854 0.00191
> directionout -0.22063 8.74381 -0.02523
> timenight -1.16552 8.91772 -0.13070
> flows 0.01266 13.61242 0.00093
> flowf 0.40877 17.34707 0.02356
>
> Correlation of Fixed Effects:
> (Intr) drctnt tmnght flows
> directionot -0.005
> timenight -0.008 0.086
> flows -0.011 -0.066 0.072
> flowf -0.011 -0.048 0.041 0.687
>
> Yikes!! the estimate of the site random effect and scale are now
> orders of
> magnitude larger.
> Log-likelihood and deviance is the same as are the estimates of fixed
> effects and correlations.
> Obviously the SE of the fixed effects are now a bit larger... This
> complicates
> my inferences from the previous analysis, to say the least.
>
> I guess there has been some changes in the way the scale is
> estimated in
> the latest version of lmer (glmer).
> If I refit these models without the estimation of the scale
> parameter (and
> close my eyes..)
>
> lme4 version 0.99875-9 Matrix version 0.999375-4
>
>> fit3<- lmer(total ~ direction + time + flow + offset(log(effort)) +
> (1|site),family=poisson(link=log),data=data,method="ML")
>> summary(fit3)
> Generalized linear mixed model fit using Laplace
> Formula: total ~ direction + time + flow + offset(log(effort)) + (1 |
> site)
> Data: data
> Family: poisson(log link)
> AIC BIC logLik deviance
> 222622 222637 -111305 222610
> Random effects:
> Groups Name Variance Std.Dev.
> site (Intercept) 1.1131 1.0550
> number of obs: 80, groups: site, 7
>
> Estimated scale (compare to 1 ) 59.53134
>
> Fixed effects:
> Estimate Std. Error z value Pr(>|z|)
> (Intercept) 1.464490 0.398841 3.67 0.000241 ***
> directionout -0.220652 0.004682 -47.12 < 2e-16 ***
> timenight -1.165554 0.004775 -244.07 < 2e-16 ***
> flows 0.012577 0.007289 1.73 0.084456 .
> flowf 0.408721 0.009289 44.00 < 2e-16 ***
>
>
> lme4 version 0.999375-26: Matrix version 0.999375-14
>
>> fit4= glmer(total ~ direction + time + flow + offset(log(effort)) +
> (1|site),family=poisson(link=log),data=data,REML=F)
>> summary(fit6)
> Generalized linear mixed model fit by the Laplace approximation
> Formula: total ~ direction + time + flow + offset(log(effort)) + (1 |
> site)
> Data: data
> AIC BIC logLik deviance
> 222622 222637 -111305 222610
> Random effects:
> Groups Name Variance Std.Dev.
> site (Intercept) 1.1526 1.0736
> Number of obs: 80, groups: site, 7
>
> Fixed effects:
> Estimate Std. Error z value Pr(>|z|)
> (Intercept) 1.449810 0.405848 3.57 0.000354 ***
> directionout -0.220630 0.004682 -47.12 < 2e-16 ***
> timenight -1.165520 0.004775 -244.07 < 2e-16 ***
> flows 0.012655 0.007289 1.74 0.082547 .
> flowf 0.408774 0.009289 44.00 < 2e-16 ***
>
> The results from the two different versions now agree(to within a few
> decimal places).
> I notice the latest version of glmer() now does not output the scale
> in
> the summary.
>
> I guess my question is "which of these is correct ?" I routinely
> have to
> deal with
> overdispersed count data and would appreciate any advice on conducting
> these
> sorts of analyses in lme4.
>
> Thanks in advance
> Dave
>
>
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