I have a technical question concerning calculating AICc for two possible models.
For the data set I am working with there are 12 subjects and 10 phases of the experiment. Two different models, a Gamma distribution and an Inverse Gaussian distribution were fit to the data of each individual subject for each phase. Using a function I've found useful in exploratory unimodal distribution fitting (downloaded it off of Matlab's File Exchange) I got AICc values for each subject for each phase.
Thus, within each phase of the experiment there are 12 AICc values for each model, one per subject. My question is as follows:
Given the AICc values are already calculated for each individual subject, is it okay to sum the AICc values across subjects for each phase to yield to AICc values, one for the gamma distribution and one for the Inverse Gaussian and then calculate the difference or weights based off those two sums?
The alternative is to get the Log-likelihood for each animal, sum across animals, and then calculate AICc for each model within each phase. However, it seems to me that this is equivalent to my first solution...
Additionally, to determine the best model for the entire dataset (i.e. across phases) does the summing seem appropriate?
Does anyone have any insight into this situation (getting the Log-likelihoods is doable, I'd need to edit the function, but the AICc are the default output of the function).