Prediction in non-sampled areas under spatial small area models

In this article we study the prediction problem in small geographic areas in the situation where the survey data does not cover a substantial percentage of these areas. In such situation, the application of the Spatial Fay–Herriot model may involve a difficult and subtle process of determining neighboring areas. Ambiguity in definition of neighbors can potentially produce a problem of sensitivity of the conclusions to these definitions. In this article, we attempt to remedy this problem by incorporating random effects for higher level administrative divisions into the model. In this setting, only the higher-level random effects are supposed to have spatial correlations. This may potentially reduce the problem of ambiguity in the definition of spatial neighbors, provided that all higher level administrative divisions are represented in the sample. We also show that predicting in non-sampled areas is considerably more straightforward under the proposed model, as opposed to the case where the Spatial Fay–Herriot model is applied. In addition, we propose two new predictors for out-of-sample areas, under the spatial Fay–Herriot model. In order to compare the performance of the aforementioned models, we use the data from the Demographic and Family Health Survey of the year 2021, and the National Census carried out in 2017.