Estimating a weighted average of stratum-specific parameters.

@article{citeulike:2942796, abstract = {This article investigates estimators of a weighted average of stratum-specific univariate parameters and compares them in terms of a design-based estimate of mean-squared error (MSE). The research is motivated by a stratified survey sample of Florida Medicaid beneficiaries, in which the parameters are population stratum means and the weights are known and determined by the population sampling frame. Assuming heterogeneous parameters, it is common to estimate the weighted average with the weighted sum of sample stratum means; under homogeneity, one ignores the known weights in favor of precision weighting. Adaptive estimators arise from random effects models for the parameters. We propose adaptive estimators motivated from these random effects models, but we compare their design-based performance. We further propose selecting the tuning parameter to minimize a design-based estimate of mean-squared error. This differs from the model-based approach of selecting the tuning parameter to accurately represent the heterogeneity of stratum means. Our design-based approach effectively downweights strata with small weights in the assessment of homogeneity, which can lead to a smaller MSE. We compare the standard random effects model with identically distributed parameters to a novel alternative, which models the variances of the parameters as inversely proportional to the known weights. We also present theoretical and computational details for estimators based on a general class of random effects models. The methods are applied to estimate average satisfaction with health plan and care among Florida beneficiaries just prior to Medicaid reform. Copyright (c) 2008 John Wiley \& Sons, Ltd.}, address = {Department of Epidemiology and Biostatistics, University of Florida, Gainesville, FL 32611, U.S.A.}, author = {Brumback, Babette A A. and Winner, Larry H H. and Casella, George and Ghosh, Malay and Hall, Allyson and Zhang, Jianyi and Chorba, Lorna and Duncan, Paul }, citeulike-article-id = {2942796}, doi = {http://dx.doi.org/10.1002/sim.3326}, issn = {0277-6715}, journal = {Statistics in medicine}, keywords = {regression, strata}, month = {June}, posted-at = {2008-06-30 04:29:41}, priority = {2}, title = {Estimating a weighted average of stratum-specific parameters.}, url = {http://dx.doi.org/10.1002/sim.3326}, year = {2008} }

TY - JOUR ID - citeulike:2942796 L3 - citeulike-article-id:2942796 TI - Estimating a weighted average of stratum-specific parameters. JF - Statistics in medicine AD - Department of Epidemiology and Biostatistics, University of Florida, Gainesville, FL 32611, U.S.A. SN - 0277-6715 N2 - This article investigates estimators of a weighted average of stratum-specific univariate parameters and compares them in terms of a design-based estimate of mean-squared error (MSE). The research is motivated by a stratified survey sample of Florida Medicaid beneficiaries, in which the parameters are population stratum means and the weights are known and determined by the population sampling frame. Assuming heterogeneous parameters, it is common to estimate the weighted average with the weighted sum of sample stratum means; under homogeneity, one ignores the known weights in favor of precision weighting. Adaptive estimators arise from random effects models for the parameters. We propose adaptive estimators motivated from these random effects models, but we compare their design-based performance. We further propose selecting the tuning parameter to minimize a design-based estimate of mean-squared error. This differs from the model-based approach of selecting the tuning parameter to accurately represent the heterogeneity of stratum means. Our design-based approach effectively downweights strata with small weights in the assessment of homogeneity, which can lead to a smaller MSE. We compare the standard random effects model with identically distributed parameters to a novel alternative, which models the variances of the parameters as inversely proportional to the known weights. We also present theoretical and computational details for estimators based on a general class of random effects models. The methods are applied to estimate average satisfaction with health plan and care among Florida beneficiaries just prior to Medicaid reform. Copyright (c) 2008 John Wiley & Sons, Ltd. KW - regression KW - strata AU - Brumback, Babette A AU - Winner, Larry H AU - Casella, George AU - Ghosh, Malay AU - Hall, Allyson AU - Zhang, Jianyi AU - Chorba, Lorna AU - Duncan, Paul PY - 2008/06/23/ UR - http://dx.doi.org/10.1002/sim.3326 ER -