[R] quasipoisson, glm.nb and AIC values

[ripley@stats.ox.ac.uk]

1) A quasi- mode does not have a likelihood and so does not have an AIC, 
by definition.

2) There is nothing wrong with a negative AIC, but you don't have one.
The value of AIC in your problem is 211.079 + 2*16 + 2.  It is summary.glm 
that is giving you misleading results.  Try the following

logLik.negbin <- function(object, ...)
{
    if (length(list(...)))
        warning("extra arguments discarded")
    p <- object$rank + 1 # for theta
    val <- object$twologlik/2
    attr(val, "df") <- p
    class(val) <- "logLik"
    val

}

then AIC(fit) will work.

3) Don't call methods like summary.negbin directly: they will not be 
user-visible.


On Wed, 12 Mar 2003, 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
> 
> ______________________________________________
> R-help at stat.math.ethz.ch mailing list
> https://www.stat.math.ethz.ch/mailman/listinfo/r-help
> 

-- 
Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595