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

• DOI: 10.1111/biom.13552
• Publication Date: 2021-09-10T18:58:33Z
• Authors: Hao Sun; Emily Berg; Zhengyuan Zhu
• Keywords: Small Area Estimation; Binary data

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