title: Comparing AIC for different types of models (beta and normal)
body: <p>I have responses which are proportions mainly centered around 0.6-0.7, and not many of them are close to 0 or 1. I have tried fitting both normal and beta models, and the normal models yield lower AIC than the beta models. I use the lm package for fitting the normal model, and betareg for the beta model. 
  But I wonder it if it really possible to compare AIC values for different model types like that? I do of course use the same response variables and the same data for both regressions. </p>
  
  <p>Note: I tried to read about Kullback-Leibler divergence here: <a href="http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=4049836" rel="nofollow noreferrer">http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=4049836</a> (name: The AIC Criterion and Symmetrizing the Kullback–Leibler Divergence), but got confused by this sentence on page two: "It is also assumed as in [12] that the search is carried out in a parametric family of distribution including the true model.", where [12] refers to Akaikes article from 1974. Does this imply that I cannot compare the AIC from a beta and a normal model, as the true model cannot be both beta and normal?<br>
  Note 2: I tried to logit-transform the responses and then fit a normal model, but that just made the residual plots look worse.</p>