Abstract

In multi-level regression, using a fixed effect for each cluster leads to models that are flexible but that have poor estimation accuracy. In small area studies for example, fixed effects models are typically over-parameterized. Regarding region as a random effect reduces the number of parameters, and hence the flexibility, but needs crucial assumptions, such as that of independence between covariates and the random effects. A new class of semi-mixed effects models is introduced that includes random and fixed effects models as extreme cases. This class of models constitutes a continuum of models, indexed by a "slider", that determines the position of the model between these two extremes. Thus, a model can be selected that is close to the parsimonious random effects case, but far enough away from it to filter out unwanted dependencies. The methodology is used for a small area analysis of tourist expenditures in Galicia.