I have one full model and several partial GLS models that I want to compare using AIC or BIC to select which factors to include in the final model. I use ML to fit each model before comparing their respective AIC or BIC. However, the ML estimator renders false convergence in several of the models. Should I resort to fit the models using REML in that case (it does fit the models in my case)? Which would be the correct approach to solve this problem?
This question is not for automated model selection. I have 5 predictive variables in the full model plus 2 interactions among two of them. I want to infer which of those have stronger effects on my response variable. All variables are continuous but one predictor, which is categorical with three levels. Also, I just discovered that three predictors induce false convergence in the model are far from normal. Elevation looks like an exponential distribution and minimum temperatures seem to be bimodal (its frequency distribution has two humps). Finally, habitat type is categorical with three categories. Besides, I found out that the false convergence is induced only when there is no interaction of these factors with other predictors in the model. I feel I should only include the interactions (i.e. avoid the predictors alone) and fit the model... but unsure about this.
Best regards and thanks in advance
