Abstract
Small area estimation (SAE) tackles the problem of providing reliable estimates for small areas, i.e., subsets of the population for which sample information is not sufficient to warrant the use of a direct estimator. Hierarchical Bayesian approach to SAE problems offers several advantages over traditional SAE models including the ability of appropriately accounting for the type of surveyed variable. In this paper, a number of model specifications for estimating small area counts are discussed and their relative merits are illustrated. We conducted a simulation study by reproducing in a simplified form the Italian Labour Force Survey and taking the Local Labor Markets as target areas. Simulated data were generated by assuming population characteristics of interest as well as survey sampling design as known. In one set of experiments, numbers of employment/unemployment from census data were utilized, in others population characteristics were varied. Results show persistent model failures for some standard Fay-Herriot specifications and for generalized linear Poisson models with (log-)normal sampling stage, whilst either unmatched or nonnormal sampling stage models get the best performance in terms of bias, accuracy and reliability. Though, the study also found that any model noticeably improves on its performance by letting sampling variances be stochastically determined rather than assumed as known as is the general practice. Moreover, we address the issue of model determination to point out limits and possible deceptions of commonly used criteria for model selection and checking in SAE context.
Highlights
Small area estimation (SAE) tackles the problem of providing reliable estimates for small areas, i.e., subsets of the population for which sample information is not sufficient to warrant the use of a direct estimator
We address the issue of model determination to point out limits and possible deceptions of commonly used criteria for model selection and checking in SAE context, namely, the deviance information criterion (DIC) and the posterior predictive p-value (PPp)
We know “lights and shades” of the models under comparison from the foregoing external validation: PPp effectively chooses the unmatched models and Gamma-Poisson-logNormal model (GPlN) while rejects Normal-Normal model (NN) and FH. (PlN is clearly picked out only for the employment application, yet we stress that focus is on the unemployment study where models’ performance differs significantly.) PPp is based on a particular measure of discrepancy (the “event” under probability in (19)/(20)), which carries out a model validation relatively to a single aspect of model performance
Summary
Following the HB way of thinking, we independently proposed a Normal-Poisson-logNormal model arguing that this unmatched form could be more appropriate for taking explicitly into account the nature of the variable of interest [9] [10] An application of this model, originally extended to enable the use of multiple data sources possibly misaligned with small areas, is in [11]. Notwithstanding a (proper) informative prior distribution on the hyperparameters would be appropriate for a full Bayesian analysis, for ignorance or because we want inference to be driven solely by the data at hand, noninformative priors are often used (this is still mainstream practice in SAE analyses) In this case, to avoid posterior density to be improper, diffuse yet proper (otherwise said, weakly-informative) priors are routinely assumed.
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