calculation of AIC
I believe the issue is in the output of glm, not the calculation. Take a look at print.glm and consider the following:
format(signif(83245.1,4))
[1] "83250"
format(signif(83249.4,4))
[1] "83250"
I haven't ever encountered this, but looks like the output is rounding to four significant figures. All your degrees of freedom, null deviance, residual deviance, and AIC are rounded to four significant figures. I'd directly call the degrees of freedom, null deviance, and residual deviance (don't know the code, but like you did for AIC(glm object)), and see if they are indeed rounded...
Dear Ben and Ben, Many thanks for your help. (how probable is it that the two responses are from Bens.......?) Indeed, I think you are both correct that the issue is the rounding in glm. For what it is worth, this does speak to how even a well-vetted (and wonderful!) function like glm can generate an "issue". Of course, the "issue" here is that the AIC values are large enough that the default for significant digits generates rounded values that are "equal" even though the "real" values differ by more than 2 support units. The issue is that most people might not go the extra length of wondering about the values and would not proceed to calculate the AIC values separately. Of course, one response is garbage in, garbage out, that is, one should always be wondering about what comes out after the button to start a black-box calculation is pushed and that the user is responsible. True enough, but I can't find any documentation for glm that mentions this rounding OR how one might change the default rounding in glm. Speaking of this, does anybody know how to change the default rounding for glm (and lmer) OR for an R session in general (e.g., so that a regular call to glm would generate AIC values with more digits)? Finally, perhaps you are wondering how meaningful it is to use the 2 support unit change in AIC to decide between models when the AIC values themselves are so large. To this extent, one might think that the rounding convention in glm was implemented with this in mind, i.e., "we, the makers of glm, are making sure that you, the user, does not use a very small difference for model decision-making when the AIC values are so large." Perhaps. But probably not, especially given the explicit discussion in Burnham and Anderson (2002, page 71) of the meaning of relying on small AIC differences when the AIC values themselves are large. They write People are often surprised that [differences of AIC values] of only 1 - 10 are very important, when the associated AIC values that led to the difference are on the order of 97,000 or 243,000. They go to write in bold It is not the absolute size of the AIC values, it is the relative values, and particularly the AIC differences that are important. any help is much appreciated. S.
Steven Orzack The Fresh Pond Research Institute 173 Harvey Street Cambridge, MA. 02140 617 864-4307 www.freshpond.org