Modeling Small Area Estimation Problems With Latent Spatial Processes. A Proposal For Business Surveys

This work proposes a class of latent process models which extend the customary hierarchical Bayesian (HB) small areal-level models in order to address typical prob-lems arising in small area estimation (SAE). Our approach envisions, for the entire re-gion under study, an underlying intensity surface which is block-averaged to the areal units relevant to the study. This framework encompasses all the main instances of pa-rameters being considered in SAE studies. E.g., we can think of an incidence surface when the characteristics of interest are area counts or totals, a probability surface when they are percentages, a proper intensity surface when they are continuous vari-ates. Such intensities are commonly used for explaining spatial point patterns and are generally modeled as realizations of (functions) of latent Gaussian processes. The proposed class of models allows for integrating multiple sources of potentially relevant information, even if available on a spatial scale different from that of small areas. These supplementary sources may consist either in auxiliary data or in survey data collected on planned or major domains. Moreover, in the proposed class bench-marking to large area estimates is automatically satisfied. To illustrate our approach we consider the problem of estimating parameters re-lated to firms’ activity and performance (such as the turnover or value added, which typically have a skewed distribution) as well as indicators of innovation efforts under-taken by enterprises (such as the percentage of firms investing in innovation) at Local Labour Market level. The parameters of interest are thus non-continuous or, if con-tinuous, non-symmetrical, as business statistics frequently are. Our proposal will then consider opportune specifications of unmatched models where the sampling error is non-normally distributed as standardly is in SAE problems. We carried out a simulation to compare the performance of our proposed model to that of customary small area models. The simulation is based on the sampling de-sign adopted in business surveys which typically is one-stage stratified. Predictive error of the Bayesian models under comparison is evaluated in terms of standardly used frequentist properties.