AIC vs qq-plot for deciding the best model

I’ve been playing with some simulated data in preparation for analysis of a stepped wedge randomised control trial. I will be using a mixed model (and the lmer() function in R). The response variable is length of stay in ED (LOS). When I compare a model with a “log” link with one where I first natural log LOS (“identity” link) and with one where I first log to the base 2 LOS (“identity” link) I find that my AIC is lowest with one method, but qq-plot best with another. In trying to choose a best model specification, which should I prioritise - AIC or qq-plot? [or is there something in how either are calculated/drawn that means I can’t compare them between these scenarios?]

I would use a semiparametric model for LOS as it can have a very strange distribution. On the other issues you can’t compare AIC for different model forms. qq plots are useful here though.


Thanks Frank. That was exactly the type of advice I was hoping to get.