Can AIC values be combined?

Hello! I have hunted far and wide on the net in an attempt to answer this. Essentially, I'm trying to combine two AIC scores from different parts of a single data set. I have two models (of the same type: nonlinear least squares fitting a growth curve to population data) that each predict about half of the data (imagine two logistic growth curves attached end to end), each half with a different AIC. For reasons inherent in the study, the fitting process is split at a particular time point. I am interested in finding the combined AIC of both curves to represent the single, total AIC of the combined models. I have been told that this is possible, but I don't know how. Any suggestions are much appreciated!


Global Moderator
Yes. This is fine.

\( AIC_{1+2} = [-log P(data | m1+m2) ] + 2(k_1+k_2) = LL_1 + LL_2 + 2k_1+2k_2 \)

\( LL_1 + LL_2 + 2k_1+2k_2 = (LL_1 + 2k_1) + (LL_2 + 2k_2) = AIC_1 + AIC_2\)

LL = log likelihood model 1 or 2
k = number of parameters 1 or 2
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