Spatial generalized linear mixed models in small area estimation

Abstract

In survey sampling, policy decisions regarding the allocation of resources to sub‐groups of a population depend on reliable predictors of their underlying parameters. However, in some sub‐groups, called small areas due to small sample sizes relative to the population, the information needed for reliable estimation is typically not available. Consequently, data on a coarser scale are used to predict the characteristics of small areas. Mixed models are the primary tools in small area estimation (SAE) and also borrow information from alternative sources (e.g., previous surveys and administrative and census data sets). In many circumstances, small area predictors are associated with location. For instance, in the case of chronic disease or cancer, it is important for policy makers to understand spatial patterns of disease in order to determine small areas with high risk of disease and establish prevention strategies. The literature considering SAE with spatial random effects is sparse and mostly in the context of spatial linear mixed models. In this article, small area models are proposed for the class of spatial generalized linear mixed models to obtain small area predictors and corresponding second‐order unbiased mean squared prediction errors via Taylor expansion and a parametric bootstrap approach. The performance of the proposed approach is evaluated through simulation studies and application of the models to a real esophageal cancer data set from Minnesota, U.S.A. The Canadian Journal of Statistics 47: 426–437; 2019 © 2019 Statistical Society of Canada

Mixed effects models for large-sized clustered extremes

“…The MEM provides reliable estimates even for large-sized clustered data by expressing the clusters as a latent structure. Furthermore, in the field of small area estimation (Torabi 2019; Sugasawa and Kubokawa 2020), the efficiency of the MEM is well known for its so-called "borrowing of strength" property (Dempster et al 1981). Dempster et al (1981) described "borrowing of strength" as follows:…”

Empirical best prediction of small area bivariate parameters

“…Chandra et al (2017, 2018) and Chandra and Salvati (2018) introduced SAE predictors of spatially correlated count data. Torabi (2019) proposed a class of spatial GLMMs to obtain small area predictors of esophageal cancer prevalence. This uncomplete list of contribution shows the high impact that the EBP approach has in SAE.…”

Small Area Estimation Using a Semiparametric Spatial Model with Application in Insurance

“…They used the conditional autoregressive (CAR) model to consider the spatial random effect. Torabi [7] studied the area-level spatial models in the small area. He used the proper CAR model to consider the spatial random effect of the areas and obtained the small area parameters using the spatial generalized linear model.…”