I have repeated-measures accelerometer data that quantifies minutes of moderate-to-vigorous physical activity (MVPA) across days. I recently submitted a paper in which I estimated a mixed-effects hurdle model for MVPA using a truncated negative binomial distribution for MVPA >0. A reviewer questioned this approach stating that MVPA should have been modeled as continuous and suggested I instead estimate a mixed-effects two-part model using a gamma distribution for MVPA >0.
We can argue back-and-forth about whether the MVPA process is continuous or count (I think there is justification for either), but in my response I would like to include empirical evidence indicating whether the negative binomial hurdle fits "better" than the two-part gamma. I have estimated both models in PROC NLMIXED (thus, ML estimation was used) using the same outcome with the same number of fixed and random effects. The hurdle model had lower AIC and BIC (AIC = 3115.9 vs. 3245.7; BIC = 3122.9 vs. 3252.7, for hurdle vs. two-part, respectively).
With that said, in reading other posts found here, here, here, and here (among others), I am still confused about whether AIC and/or BIC are appropriate for model selection in my situation. I believe they are (as reported here), but a colleague of mine is of the opinion that AIC/BIC can only be used to compare distributions within the same family. I do not think distribution family is an explicit assumption. I just want to make sure I don't make any mistakes, so thoughts/insights are appreciated.