Bayesian predictive inference of a finite population mean without specifying the relation between the study variable and the covariates
Articles and reports: 12-001-X202400200004Description: While we avoid specifying the parametric relationship between the study variable and covariates, we illustrate the advantage of including a spatial component to better account for the covariates in our models to make Bayesian predictive inference. We treat each unique covariate combination as an individual stratum, then we use small area estimation techniques to make inference about the finite population mean of the continuous response variable. The two spatial models used are the conditional autoregressive and simple conditional autoregressive models. We include the spatial effects by creating the adjacency matrix via the Mahalanobis distance between covariates. We also show how to incorporate survey weights into the spatial models when dealing with probability survey data. We compare the results of two non-spatial models including the Scott-Smith model and the Battese, Harter, and Fuller model to the spatial models. We illustrate the comparison between the aforementioned models with an application using BMI data from eight counties in California. Our goal is to have neighboring strata yield similar predictions, and to increase the difference between strata that are not neighbors. Ultimately, using the spatial models shows less global pooling compared to the non-spatial models, which was the desired outcome. Issue Number: 2024002Author(s): Lockwood, Ashley; Nandram, BalgobinMain Product:Survey Methodology
