Bayesian Logistic Regression for Small Areas with Numerous Households

TL;DR

This paper introduces a fast Bayesian hierarchical logistic regression method for small area estimation with large household data, using INNA and parallel computing to improve efficiency over traditional MCMC approaches.

Contribution

It develops a novel computational approach combining INNA and parallel processing for hierarchical Bayesian logistic regression in small area estimation with large datasets.

Findings

The proposed method achieves comparable accuracy to MCMC with significantly reduced computation time.

Application to Nepal Living Standards Survey demonstrates practical utility.

Parallel computing enables scalable analysis of large household datasets.

Abstract

We analyze binary data, available for a relatively large number (big data) of families (or households), which are within small areas, from a population-based survey. Inference is required for the finite population proportion of individuals with a specific character for each area. To accommodate the binary data and important features of all sampled individuals, we use a hierarchical Bayesian logistic regression model with each family (not area) having its own random effect. This modeling helps to correct for overshrinkage so common in small area estimation. Because there are numerous families, the computational time on the joint posterior density using standard Markov chain Monte Carlo (MCMC) methods is prohibitive. Therefore, the joint posterior density of the hyper-parameters is approximated using an integrated nested normal approximation (INNA) via the multiplication rule. This approach provides a sampling-based method that permits fast computation, thereby avoiding very time-consuming MCMC methods. Then, the random effects are obtained from the exact conditional posterior density using parallel computing. The unknown nonsample features and household sizes are obtained using a nested Bayesian bootstrap that can be done using parallel computing as well. For relatively small data sets (e.g., 5000 families), we compare our method with a MCMC method to show that our approach is reasonable. We discuss an example on health severity using the Nepal Living Standards Survey (NLSS).