[R-sig-ME] Lmer with family = quasipoisson

[Douglas Bates]

I wouldn't put too much faith in the values of the AIC etc. for the
quasipoisson family.  I included that family as a convenience and I
believe that the parameter estimates make sense but I don't know about
the deviance and log-likelihood values.  I'm still working out the
effect of the common scale parameter in that family.

On Mon, Aug 25, 2008 at 10:46 AM, Renwick, A. R. <a.renwick at abdn.ac.uk> wrote:
>
> I was wondering if anybody could explain why an AIC can be calucluated for a lmer model with a quasi poisson distriution and not a glm.
> I have also found that the AIC's are extremely sensitive in the lmer model, for example removing a term with very low t-values resulted in an increase in AIC of 284.
> Many thanks,
> Anna
>
> MODEL1:
>
> mix<-lmer(realdis~sex+width+sess+sex:width+sex:sess+sess:width+(1|site),family=quasipoisson,data=move,subset=-52)
>> summary(mix)
> Generalized linear mixed model fit by the Laplace approximation
> Formula: realdis ~ sex + width + sess + sex:width + sex:sess + sess:width +      (1 | site)
>   Data: move
>  Subset: -52
>   AIC   BIC logLik deviance
>  11019 11117  -5490    10979
> Random effects:
>  Groups   Name        Variance Std.Dev.
>  site     (Intercept)  9.1673  3.0278
>  Residual             76.4532  8.7438
> Number of obs: 976, groups: site, 14
>
> Fixed effects:
>             Estimate Std. Error t value
> (Intercept)   2.76589    0.91021  3.0387
> sexm          0.17425    0.41856  0.4163
> widthn        0.26750    0.99495  0.2689
> widthw       -0.47361    0.55549 -0.8526
> sess2        -0.43403    0.64479 -0.6731
> sess3        -0.16228    0.85141 -0.1906
> sess4        -0.40075    0.63427 -0.6318
> sexm:widthn   0.78322    0.63070  1.2418
> sexm:widthw   0.39836    0.44387  0.8975
> sexm:sess2    0.02061    0.51386  0.0401
> sexm:sess3    0.17900    0.52713  0.3396
> sexm:sess4    0.36188    0.53644  0.6746
> widthn:sess2  0.53589    0.83917  0.6386
> widthw:sess2 -0.11500    0.65798 -0.1748
> widthn:sess3 -0.19799    1.03927 -0.1905
> widthw:sess3 -0.99033    0.86773 -1.1413
> widthn:sess4 -0.17498    0.94033 -0.1861
> widthw:sess4 -1.03199    0.75236 -1.3717
>
> REMOVE WIDTH:SESS INTERACTION
>  mix1<-lmer(realdis~sex+width+sess+sex:width+sex:sess+(1|site),family=quasipoisson,data=move,subset=-52)
>> summary(mix1)
> Generalized linear mixed model fit by the Laplace approximation
> Formula: realdis ~ sex + width + sess + sex:width + sex:sess + (1 | site)
>   Data: move
>  Subset: -52
>   AIC   BIC logLik deviance
>  11303 11372  -5638    11275
> Random effects:
>  Groups   Name        Variance Std.Dev.
>  site     (Intercept)  6.8207  2.6117
>  Residual             84.5884  9.1972
> Number of obs: 976, groups: site, 14
>
> Fixed effects:
>            Estimate Std. Error t value
> (Intercept)   3.0503     0.7807   3.907
> sexm          0.1780     0.4249   0.419
> widthn        0.1302     0.7417   0.176
> widthw       -0.7784     0.5217  -1.492
> sess2        -0.4633     0.4770  -0.971
> sess3        -0.9002     0.4859  -1.853
> sess4        -0.9513     0.4733  -2.010
> sexm:widthn   0.7431     0.6553   1.134
> sexm:widthw   0.3856     0.4592   0.840
> sexm:sess2    0.0963     0.5314   0.181
> sexm:sess3    0.2302     0.5511   0.418
> sexm:sess4    0.3524     0.5481   0.643
>
> Change in AIC =  11303 - 11019 = an increase of 284
>
>
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