When using OLS models, choosing the best one is not a complex task: we have a set of variables that we use, and we just pick whichever model has the lowest Akaike information criterion (AIC) (or any other appropriate metric that we choose).
Mixed models entail an extra level of complexity, as we can define the random effects in many ways. Resuming our previous example of deal_size versus time_spent and salespeople, we could choose a model with random effects only for the deal_size or both the deal_size and salespeople. We can also decide to add a random intercept or not, and we can force the model to assume that the shocks impacting each one of these are either, uncorrelated or correlated.
Choosing models by comparing the AIC is quite hard for mixed models, since we have a random and a fixed part. There are two types of analysis that we might...
