A new class of semi-mixed effects models and its application in small area estimation

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 requires crucial assumptions, such as that of independence between covariates and the random effects. A new class of semi-mixed effects models introduced here 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, the model selected can be close to the parsimonious random effects case, but far enough away from it to filter out unwanted dependences. The methodology is used for a small area analysis of tourist expenditures in Galicia.