based on joint work with María-José Lombardía

 

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.  Related to the estimation procedure used in this context, we discuss the general use of non- and semiparametric analysis in small area estimation and prediction in order to reach valid inference and correct prediction intervals.