[R] using "logLik" with AIC to compare models with different error

[kyoung]

Hi there, I’d like to use AIC to compare between models with different
error distributions (eg: Dick 2004, Sileshi 2004, Burnham and Anderson
2002), namely a normal, Poisson and negative binomial.  I realize there
are differing views whether this is valid or not from reading past R help
postings; however, for my purpose I think AIC is more appropriate rather
than something such as a Chi-sq or G-statistic as I don’t need to know
whether the fit is statistically significant or not, rather I want to know
which model is the best given my data.

The data I’m working on are counts per station (7 stations in total for
each model), and originally I used a simplistic glm model:

Model.p<-glm(count~station,poisson)
Model.n<-glm(count~station,gaussian)

And from the MASS package (v 7.2-30)

Model.nb<-glm.nb(count~station)

I then extracted the log-likelihood using “logLik(model)”, from which I
calculated AIC (by hand).  However, after reviewing more of the R help
postings and associated help pages for the functions, I have the following
questions:

1- the “glm” function doesn’t use MLE to fit the model, so is the
associated “logLik” extracted valid?

2- If it is valid, does it calculate the full likelihood, or are the
constants dropped? (this is not clear in the ?glm or ?loglik files)

3- if neither are valid, are there alternatives? For example, I’ve seen
that the MASS package also has a “fit.distr” function with an associated
“logLik” method, but can I use the log-likelihood extracted using this
method to calculate AIC and compare between distributions (in the manner
that I want using the “glm” function)?  if so, are the log-likelihood
given complete or have the constants been dropped?

Any help and suggestions would be appreciated!


Kelly Young
kyoung at uvic.ca
M.Sc Candidate, Dept. Biology
Fisheries Oceanography Research Lab
University of Victoria
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