Comparing alternative distributional assumptions in mixed models used for small area estimation of income parameter

Linear Mixed Models used in small area estimation usually rely on normality for the estimation of the variance components and the Mean Square Error of predictions. Nevertheless, normality is often inadequate when the target variable is income. For this reason, in this paper we consider Linear Mixed Models for the log-transformed income (which require back-transformation for prediction of means and totals on the variable’s original scale) and a Generalized Linear Mixed Model based on the Gamma distribution. Various prediction methods are compared by means of a simulation study based on the ECHP data. Standard predictors obtained from Linear Mixed Model for the untrasformed income are shown to be preferable to the considered alternatives, confirming their robustness with respect to the failure of the normality assumption.