Empirical Best Prediction for Small Area Estimation of categorical variables using Finite Mixtures of Multinomial Logistic Models

Many survey variables are categorical in nature and SAE methods based on generalised linear mixed models represent a frequent tool of analysis for prediction. Jiang (2003) developed an empirical Best Prediction (EBP) method for responses in the Exponential Family, based on the use of area-specific, Gaussian, random effects. However, a major drawback of this approach is the computational burden required to derive estimates, compute the EBP and, in particular, provide the corresponding measure of reliability. Here, we introduce a semiparametric EBP for categorical outcomes by extending the approach proposed by Marino et al. (2019) for univariate responses belonging to the Exponential Family of distributions. This approach leaves the mixing distribution (that is, the distribution of the area-specific random effects) unspecified and estimate it from the observed data via a NonParametric Maximum Likelihood approach. This estimate is known to be a discrete distribution defined over a finite number of locations and leads to the definition of a finite mixture specification. Finite sample properties of the proposal are tested via a simulation study.