Well, I stumbled upon this in someone's blog "The problem is that the point estimates of AIC-likecriteria are partially dependent upon the number ofmanifest variables. If different models have differentnumbers of manifest variables, then it would be difficultto meaningfully compare values across models." (

http://zencaroline.blogspot.com/2007/08/non-nested-sem-model.html), but she doesn't have any citations for this particular point, so...I don't know what to make of it.

I also came across this, in a document posted online, which appears to be an information sheet that is used in an SEM class "Models with more variables tend to have larger chi-squares...Akaike’s Information Criterion (AIC), the Bayesian Information Criterion (BIC), the Expected Cross-validation Index (ECVI), the root mean square residual (RMR), and the standardized root mean square residual (SRMR)...have similar problems to those of the chi-square, because they are based on simple variations on chi-square"...again, not sure what to make of that.

When I went to my textbook (Kline, 2011) he starts of the section of comparing nonheirarchical models (I'm assuming nonheirarchical is the same as non-nested?) by saying "Sometimes researchers compare alternative models based on the same variables measured in in the same sample that are not heiracrchically related." The fact that he specified that they contain the "same variables" made me think there was a distinction between models which are non-nested and those that contain different variables (or an additional variable), but I'm not sure...

Thank you for your response, it is possible that it is simply not the case that AIC or BIC are inappropriate for my purposes (I'm not just going to take a random blogs word for it, at least)...I've been having a hard time finding journal articles on this - I think I am going to find any and all textbooks on SEM at our library and see if that helps clear up my question.