I am conducting some analysis on my data I found a strange behavior and would greatly appreciate some guidance or suggestions.
I am trying to investigate the effect of a categorical variable ( cl ) to three percentages that sum 1 ( M ). Naturally, I conducted a dirichlet regression on my dataset and a multivariate beta regression , but when compared using loo the beta regression presented a significantly better fit the data than the dirichlet .
Strangely, the predicted variables sum varies between 50% to 150% which is nonsense. However, the fitted variables sum varies 95% to 105% that is an acceptable error.
Is it fair to compare the models? or due to the natural constraints of a Dirichlet model it yields worst fit than a multivariate beta regression ?