I am currently exploring Dirichlet regression models to model fatty acid compositional data. I am using 2 categorical predictors and 1 continuous predictor (treatment group, sex, and total lipids).
When it comes to model selection, according to anova (analysis of deviance) and AIC, the most complex model is the best fitting: Y ~ Trt * Sex * lipids | Trt * Sex + lipids
This 3-way interaction however, is only significant for a few of the response variables, and I'm concerned about overfitting the model for many of the response variables.
My question is: is it possible to continue to take out predictors that aren't relevant for some of the response variables(such as the 3 way interaction term), continue with model selection, and then report separate best fit models for different response variables?
