If I have two samples (n=300) from the same population and I'm fitting a GLMM (Generalised Linear Mixed-effects Model) with a similar response and explanatory variables but with a completely different set of participants,
M.1 <- glmer(y1 ~ x1 + x2 + (1 | id), data = Sample1 , family = binomial)
M.2 <- glmer(y1 ~ x1 + x2 + (1 | id), data = Sample2 , family = binomial)
can I compare the AIC values of these two models?
I understand that AIC = -2ln(Likelihood|data) + 2K and I'm not sure whether the likelihood|data1 and likelihhod|data2 are comparable.
However, I'm confused by the statement in, "AIC MYTHS AND MISUNDERSTANDINGS" by Anderson and Burnham, point 2 which states " Information-theoretic approaches can only be applied when there is one data set" is a myth. https://sites.warnercnr.colostate.edu/anderson/wp-content/uploads/sites/26/2016/11/AIC-Myths-and-Misunderstandings.pdf
I'm confused and any clarification is greatly appreciated. Thanks!!