It is well known that the AIC can be used to compare nested models.
Additionally, I believe I am correct in saying that you can also use the AIC to compare non-nested models on the same dataset (please correct me if I am in fact wrong). However, it is not correct to use the AIC to compare between different data sets.
In my scenario, I have 5 measurements on individuals over time plus an outcome variable. If I was to regress the outcome variable linearly on all the measurements over time, I would be able to obtain an AIC for this model which uses the entire dataset.
Now I want to consider only 2 of the measurements of all individuals plus the outcome variable. Technically, I am now using a subset of the original dataset as I have lost information on the other three measurements. However, isn't this the same as fitting a nested model since I kept all individuals but lost 3 explanatory variables? So is it justified to compare the AIC I get from this model with that obtained from the full model?