glmer and overdispersed Poisson models

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

Notice:
This email and any attachments may contain information t...{{dropped: 
14}}

_______________________________________________
R-sig-mixed-models at r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models

glmer and overdispersed Poisson models

Thread (4 messages)