I want to use AIC to compare three candidate models (labeled by m), each having K_m parameters. However, I have M datasets over which I can make the comparison. My ultimate goal is to report the "relative goodness" of each of the three models for a single fit. How to I make use of the multiple datasets?
One idea is to find the Akaike weights (See Anderson and Burnham, 2002) for each dataset and average the weights over all the M datasets (perhaps, weighting by the number of points in each dataset?).
Another approach would be to say that, for model m, I have a single M*K_m parameter model that I fit over the M datasets. In this case the AIC value, ACIC_net, is the sum of the AIC values for a fit to each of the M datasets. In this case, I would use AIC_net to compare the three models.
How should I proceed?