[R] quasipoisson, glm.nb and AIC values

[Uwe Ligges]

Vicente Piorno wrote:
> 
> Dear R users,
> I am having problems trying to fit quasipoisson and negative binomials glm.
> My data set
> contains abundance (counts) of a species under different management regimens.
> First, I tried to fit a poisson glm:
> 
>  > summary(model.p<-glm(abund~mgmtcat,poisson))
> 
>        Call:
>        glm(formula = abund ~ mgmtcat, family = poisson)
>        .
>        .
>        .
>        (Dispersion parameter for poisson family taken to be 1)
> 
>              Null deviance: 1904.7  on 19  degrees of freedom
>        Residual deviance: 1154.3  on 16  degrees of freedom
>        AIC: 1275.4
>       Number of Fisher Scoring iterations: 4
> 
> Wich suggests the existence of STRONG overdispersion, so I tried:
> 
>  > summary(model.qp<-glm(abund~mgmtcat,quasipoisson))
> 
>        Call:
>        glm(formula = abund ~ mgmtcat, family = quasipoisson)
>        .
>        .
>        .
>        (Dispersion parameter for quasipoisson family taken to be 73.51596)
> 
>               Null deviance: 1904.7  on 19  degrees of freedom
>        Residual deviance: 1154.3  on 16  degrees of freedom
>        AIC: NA
>       Number of Fisher Scoring iterations: 4
> 
> Here I found the first problem: AIC is not available.
> 
> I know that count data for the studied species usually show aggregation.
> So, I fitted
> a negative binomial glm with the glm.nb in MASS:
> 
>  > summary.negbin(model.nb<-glm.nb(abund~mgmtcat))
> 
>        Call: glm.nb(formula = abund ~ mgmtcat, init.theta =
> 1.23560100958978,  link = log)
>        .
>        .
>        .
>        (Dispersion parameter for Negative Binomial(1.2356) family taken to
> be 1)
> 
>            Null deviance: 33.173  on 19  degrees of freedom
>        Residual deviance: 22.316  on 16  degrees of freedom
>        AIC: -15948
>        Number of Fisher Scoring iterations: 1
> 
>        Correlation of Coefficients:
>                 (Intercept) mgmtcat1 mgmtcat2
>        mgmtcat1     -0.7052
>        mgmtcat2     -0.7053   0.4974
>        mgmtcat3     -0.7005   0.4940    0.494
> 
>                          Theta:  1.236
>                    Std. Err.:  0.362
>         2 x log-likelihood:  -211.079
> 
> And now, I am getting a negative AIC value! I have seen that this problem
> have been discused in the S-news list.
> Much of the discussion there is far beyond my statistical and R knowledge.
> One of the solutions proposed there
> was adding - lgamma(y +1) to the internal function loglik in glm.nb, but I
> have seen that the current version of
> MASS contains that term.
> 
> My problem is that I want to compare the quasipoisson and negative binomial
> models, and I have a NA value and a negative one.
> Can I obtain an AIC for the quasipoisson model? What about the negative
> AIC? Can I use it or do you think that anything is wrong?
> 
> Thanks in advance,
> 
> --
> Vicente Piorno
> Departamento de Ecologia y Biologia Animal - Universidad de Vigo
> EUIT Forestal - Campus Universitario
> 36005 Pontevedra SPAIN
> 
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What's wrong with a negative AIC?
I would vote against comparing different model classes using AIC.
Instead, it's a better idea to think about which model class makes sense
in a given context.

Uwe Ligges