I am using gls in nlme. My response variable is spatial so I am using gls with correlation structure. I am determining which structure to use based on Zuur 2009, comparing AIC scores of models with all relevent fixed effects and only differing in the correlation structures. I am doing this in REML as at this stage all models have identical fixed effects. Then I am using Likelihood ratio tests in ML to select best model (in terms of fixed effects), again following Zuur 2009. Once the best model is determined, I am re-running it in REML for my unbiased parameter estimates. My problem is that I am attempting to test several hypotheses so ultimately need to compare the best model for several different hypotheses (eg. a prey model compared to a habitat model compared to a topography model). I understand that I cannot compare these using AIC in REML because the fixed effects are different even though the random effects are the same.
Can I compare the AIC scores of the best models as they are determined using ML (ie BEFORE I re-run them in REML for unbiased parameter estimates)? I have read a fair amount of the literature (including some related topics here), but I have not been able to determine once and for all if this is suitable as most comments I have seen are concerned with finding the best model and not comparing different models.