# Are very large log likelihood and delta AIC values problematic for model selection?

I am using AICc for small sample sizes to compare 8 a priori models (including null model). I fitted my models using a GLMM due to the nested nature of my data and defined the family as 'poisson' based on a visual inspection of the error structure from my residual vs fitted values plot.

After running my analysis using lmer from the lme4 package in R, I obtain very large log likelihood values, e.g., LL = -120995125, which makes the delta AICc values very large as well, e.g., difference between 'best' fit model and second ranking model is 12422654. This makes comparison within the model set rather dubious.

I was wondering if anyone has encountered a similar problem or if there is something I am missing when using family=poisson for lmer in my model fitting.

-
I suspect Poisson isn't the best choice of family. Is your dependent variable non-negative integer-valued? You might want to try "Gamma", which at least allows var != mean, just to see what happens. You can still put in "link=log" if you want to retain the log link function that's default with the Poisson family. –  jbowman May 7 '12 at 16:56
Thanks for your comment. Yes my dependent variable is non-negative integer-valued. I have followed your suggestion adding family=Gamma(link="log") but received an error: Error in asMethod(object) : matrix is not symmetric [1,2]. Do you know why this may be the case? Currently checking other threads to see what others may have come across. –  jlsh May 8 '12 at 7:01
Huh, I've never seen that error. Could you post a histogram of the dependent variable, or if the range (upper bound) is not large, a table? –  jbowman May 8 '12 at 14:12
Unfortunately I do not have enough reputation to upload images as a newbie. However, the histogram of the response variable looks like a mirror image of an exponential curve, i.e., high frequency of low x values and steep drop as x values increases. I hope the verbal illustration was clear. –  jlsh May 9 '12 at 9:37
I would not be so quick to withdraw a Poisson distribution. LogLikelihood my be huge do to other reasons. For example consider $X \sim Poisson(t \lambda)$. If $t=10^9$, $X=1000$, $\lambda = 2$, then the log-likelihood would be equal to 2000015504. So, do you have in your data very large values? –  Tomas Sep 12 '12 at 12:40