A couple of weeks back I posted a query about extractAIC( ) returning
negative values when used with the MASS library function glm.nb( ) for
fitting glms with negative binomial error distributions. Many thanks to
the illuminating answers from Brian Ripley and Bill Venables.
In summary, the negative AIC values arise from leaving a large negative
constant out of the log likelihood. As per Brian Ripley's suggestion
inserting the missing term makes the AIC's positive. However, as all
model selection inference is relative to the model with the minimum AIC,
the differences between the AIC's for the models are identical whether
the constant is in or not.
Bill Venables asked whether the results made sense. The short answer is
yes, with two caveats. First, for some models the iteration that
estimates theta (the dispersion parameter) shoots off wildly and forces
theta towards zero which produces nonsense. These cases are readily
identifiable afterwards! Second, some negative coefficients get very
large, with large standard errors - this seems to occur in the same
context described for problems with binomial glms in MASS (pg 225, the
Hauck-Donner phenomenon), where a group of values is all zero and the
glm is trying to set the linear predictor to minus infinity. At the
moment I'm interpreting this to indicate that particular combination of
samples is unlikely to be a result of sampling from a negative binomial
distribution with a positive mean, which, if true, will be a good thing
for my application.
Thanks again!
Cheers,
Drew
--
Drew Tyre, The Ecology Centre
Dept. of Zoology and Entomology,
Goddard Building, University of Queensland,
St Lucia, 4072 QLD, Australia
phone: +61 7 3365 3539 fax: +61 7 3365 1655
email: dtyre@zen.uq.edu.au
http://www.geocities.com/drew_tyre (personal)
http://www.ecology.uq.edu.au (The Ecology Centre)
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