Corrected AIC for binary response variables? (Landis, R Matthew)

Matt Landis asked
I'm using logistic regression to investigate mortality of trees.  I'm using AIC to compare models, and I'm wondering if I should use AICc instead of  AIC.  Burnham and Anderson [1] recommend using AICc when n/K < 40.  But what do I consider for n?  The logistic regression is based on 2811 observations (334 trees observed annually for <= 10 yr), but I've only observed 32 deaths.  Harrell [2] would consider 32 to be the "limiting sample size" for determining the feasible number of predictor variables.  Is AIC the same?  Should I use 2811, 334, or 32 to figure out AICc?
You may be interested in an exchange on this topic that I initiated on www.phidot.org/forum MARK Statistics & analysis help on 30 September. I found the outcome quite unsatisfactory, and it seems the experts don't know. 334 seems safe to me, and of course it will make little numerical difference.

Murray Efford

[I'm sorry that I have this through the Digest & my reply may not conform]
Murray - thanks for pointing me to that discussion - I found it stimulating, if inconclusive in the end.  The discussion of Bernoulli trials (1 per individual per time step) reminds me of something I once read by Paul Allison [1] in an introduction to the use of logistic regression for event data.  He discussed the notion of pseudoreplication of repeated observations on a single individual (p. 223), and concluded that it wasn't applicable because of the something to do with a conditional probability involved in factoring the likelihood function.  I don't quite understand it, but it does seem to imply that using the number of tree*years (2811 in my case), might be justifiable.

In any case, it sounds like the number of individuals (334 here) is certainly justifiable and acceptable to most of the people who responded.  I'll probably go with that.

Many thanks to all who responded with thoughts on my question...and apologies for the lack of specific R content.  The analyses _are_ all being done in R ;-)

Happy New Year!

Matt

[1] Allison, P. 1995. Survival analysis using the SAS system: a practical guide SAS Institute, Inc.

-----Original Message-----
From: r-sig-ecology-bounces at r-project.org [mailto:r-sig-ecology-bounces at r-project.org] On Behalf Of Murray Efford
Sent: Friday, December 19, 2008 3:09 PM
To: r-sig-ecology at r-project.org
Subject: [R-sig-eco] Corrected AIC for binary response variables? (Landis, R Matthew)

Matt Landis asked
I'm using logistic regression to investigate mortality of trees.  I'm using AIC to compare models, and I'm wondering if I should use AICc instead of  AIC.  Burnham and Anderson [1] recommend using AICc when n/K < 40.  But what do I consider for n?  The logistic regression is based on 2811 observations (334 trees observed annually for <= 10 yr), but I've only observed 32 deaths.  Harrell [2] would consider 32 to be the "limiting sample size" for determining the feasible number of predictor variables.  Is AIC the same?  Should I use 2811, 334, or 32 to figure out AICc?
You may be interested in an exchange on this topic that I initiated on www.phidot.org/forum MARK Statistics & analysis help on 30 September. I found the outcome quite unsatisfactory, and it seems the experts don't know. 334 seems safe to me, and of course it will make little numerical difference.

Murray Efford

[I'm sorry that I have this through the Digest & my reply may not conform]

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