Robust Small Area Estimation Based on a Survey Weighted MCMC Solution for the Generalized Linear Mixed Model

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Folsom et al. (1999) developed a survey weighted hierarchical Bayes (SWHB) estimation methodology for fitting unit-level generalized linear mixed models and applied it to the National Household Survey on Drug Abuse (NHSDA). The SWHB solution for the logistic mixed model is robust against model misspecification because the small area estimates (SAEs) for any large sample areas are close to their robust design based analogs. It also assures that national aggregates of the SAEs are design consistent and, therefore, approximately self-calibrated to the robust design based national estimates. The use of unit level models also assures internal consistency of SAEs for different levels of aggregation even when different predictors are used at those levels. However, the Folsom et al. solution assumed that the survey design could be treated as noninformative after inclusion of certain covariates; i.e., the superpopulation model was assumed to hold for the sampled units. In the interest of robustness against model misspecifications, it is desirable to remove this assumption. The first goal of this research project is to improve the uncertainty measures of the SWHB solution by taking full account of the survey design effects. The second project goal is to improve the robustness properties of the enhanced solution by assuring exact calibration of the aggregated SAEs to the design consistent national survey estimate. To achieve these goals an approximate Gaussian likelihood is assumed for the joint sampling distribution of the input vector of survey weighted fixed and random effect estimating functions. In this approximate Gaussian likelihood, a design consistent variance-covariance matrix for the vector of estimating functions will be used to fully account for survey design. The second project goal is achieved by employing a 'calibrated' Markov Chain Monte Carlo (MCMC) algorithm with a Metropolitan Hastings step that exactly benchmarks the SAEs to the robust design based national estimates. Simulated data with fixed and random predictors that are not included in the analysis model will be used to compare the robustness of the calibrated and uncalibrated solutions against model misspecification. Also, the improved SWHB solution will be contrasted with other solutions on one or more large survey data sets, e.g., NHSDA, NHIS, BRFSS.In spite of the wealth of information that is available at the national level, Federal, State and local agencies concerned with program planning face difficulties because of the lack of specific information at the local level. Typically, information is desired for States and for substate planning regions or counties. In principle, surveys that provide national statistics could be expanded so that the needed State and sub-state data were collected; however, government agencies seldom have the economic and infrastructure resources needed to collect this volume of data via a direct survey approach. Fortunately, new advances in statistics and increases in computing power offer a viable, affordable alternative to the prohibitively expensive direct survey approach and now permit the production of valid and reliable estimates for small areas. The goal of this project is to promote wider acceptance of model based SAEs for official statistics by improving the uncertainty measures, by providing robustness against model misspecification, and by assuring the internal consistency of SAEs for different aggregation levels. This research is supported by the Bureau of the Census under the Research on Survey and Statistical Methodology Funding Opportunity.