Estimation of mean squared prediction error of empirically spatial predictor of small area means under a linear mixed model

Abstract

Policy decisions regarding allocation of resources to subgroups in a population, called small areas, are based on reliable predictors of their underlying parameters. However, the information is collected at a different scale than these subgroups. Hence, we need to predict characteristics of the subgroups based on the coarser scale data. In view of this, there is a growing demand for reliable small area predictors by borrowing information from other related sources. For this purpose, mixed models have been commonly used in small area estimation assuming independent small areas. There are many situations, however, that the small area parameters are related to their locations. For instance, it is an interest of policy makers (and public) to know the spatial pattern of a chronic disease (e.g., asthma) to identify small areas with high risk of disease for possible preventions. In this paper, we propose small area models in the class of spatial linear mixed models to be able to predict small area parameters and also to obtain corresponding mean squared prediction error (MSPE). We also provide unbiased estimators of MSPE of small area predictors using Taylor series expansion and parametric bootstrap methods. In our simulations, we show that our MSPE estimators using Taylor expansion and parametric bootstrap perform very well in terms of precision of small area predictors. Performance of our proposed approach is also evaluated through a real application of physician visits for Total Respiratory Morbidity conditions in Manitoba, Canada.