[R] Negative Binomial Regression

[Prof Brian Ripley]

On Tue, 29 Jul 2008, Ben Bolker wrote:

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> Prof Brian Ripley wrote:
> | On Tue, 29 Jul 2008, Ben Bolker wrote:
> |
> |> jcarmichael <jcarmichael314 <at> gmail.com> writes:
> |>>
> |>> Hello.
> |>>
> |>> I am attempting to duplicate a negative binomial regression in R.
> |>> SAS uses
> |>> generalized estimating equations for model fitting in the GENMOD
> |>> procedure.
> |>>
> |>> proc genmod data=mydata (where=(gender='F'));
> |>> by agegroup;
> |>> class id gender type;
> |>> model count = var1 var2 var3 /dist=NB link=log offset=lregtm;
> |>> repeated subject=id /type=exch;
> |>> run;
> |>>
> |>> Since my dataset has several observations for each subject, I need the
> |>> REPEATED statement in order to indicate dependence among observations
> |>> with
> |>> the same subject ID and independence amongst those with distinct subject
> |>> IDs.  The TYPE statement goes on to specify the structure of the
> |>> correlation
> |>> matrix to be used (exchangeable in this case).
> |>
> |>  I would try glmmPQL in the MASS package.  I don't think you
> |> can *quite* get negative binomial regression this way, but
> |> you can definitely get a quasipoisson model.  I think exchangeable
> |> correlation corresponds to correlation=corCompSymm() in your
> |> glmmPQL command.
> |
> | The problem here is that GLMM and GEE are not fitting the same model --
> | in one the coefficients are subject-specific and in the other
> | population-average (see MASS4 or Diggle, Liang, Zeger +/- Heagarty).
> |
> | There are several R packages for GEE, including gee, yags, geepack.  The
> | documentation of geeglm (geepack) claims it can be used with families as
> | in glm(), so you could try it with MASS's negative.binomial family.
> |
>
> ~  Point taken (although I guess I was pointing the original poster
> to a way to do a reasonable analysis, not necessarily to duplicate
> the SAS analysis as requested).  Will the negative.binomial family
> really work for this, since it seems to require a fixed theta
> (overdispersion) parameter?

I was answering 'I am trying to duplicate': I don't know how SAS estimates 
the parameter by GEE. The best guess I have is that theta is estimated 
from the initial glm fit and fixed in the GEE phase, but that is only 
interpolation from very vague descriptions.

> ~  If I very naively do the following:
>
> library(geepack)
> data(dietox)
> mf2 <- formula(Weight~Cu*Time+I(Time^2)+I(Time^3))
> gee2 <- geeglm(mf2, data=dietox, id=Pig,
> ~   family=poisson("identity"),corstr="ar1")
> library(MASS)
> gee2 <-
> geeglm(mf2,data=dietox,id=Pig,family=negative.binomial(theta=100),corstr="ar1")
>
> ~  gives an error "variance invalid" --
>
> ~  so the whole thing would seem to take a bit of troubleshooting

I wasn't placing much faith on geeglm actually being as general as it says 
it is ('claims' ... 'could try').

> ~  (geeglm also gives warnings about non-integer Poisson values -- I
> don't know why a Poisson link is being used in this example for
> a non-integer Weight value ... ?)

'poisson' _family_, I presume?

-- 
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