Bivariate small-area estimation for binary and gaussian variables based on a conditionally specified model

作     者：Sun, Hao Berg, Emily Zhu, Zhengyuan 

作者机构：Iowa State Univ Dept Stat Ames IA 50011 USA 

出 版 物：《BIOMETRICS》 (生物统计学)

年 卷 期：2022年第78卷第4期

页      面：1555-1565页

核心收录：

学科分类：0710[理学-生物学] 07[理学] 09[农学] 0714[理学-统计学（可授理学、经济学学位）] 

基　　金：National Science Foundation [68-7482-17009] 1733572 

主　　题：bivariate mixed-effects model bootstrap EM algorithm small-area estimation 

摘      要：Many large-scale surveys collect both discrete and continuous variables. Small-area estimates may be desired for means of continuous variables, proportions in each level of a categorical variable, or for domain means defined as the mean of the continuous variable for each level of the categorical variable. In this paper, we introduce a conditionally specified bivariate mixed-effects model for small-area estimation, and provide a necessary and sufficient condition under which the conditional distributions render a valid joint distribution. The conditional specification allows better model interpretation. We use the valid joint distribution to calculate empirical Bayes predictors and use the parametric bootstrap to estimate the mean squared error. Simulation studies demonstrate the superior performance of the bivariate mixed-effects model relative to univariate model estimators. We apply the bivariate mixed-effects model to construct estimates for small watersheds using data from the Conservation Effects Assessment Project, a survey developed to quantify the environmental impacts of conservation efforts. We construct predictors of mean sediment loss, the proportion of land where the soil loss tolerance is exceeded, and the average sediment loss on land where the soil loss tolerance is exceeded. In the data analysis, the bivariate mixed-effects model leads to more scientifically interpretable estimates of domain means than those based on two independent univariate models.