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Measurement error in small area estimation: Functional versus structural versus naieve models

机译：小面积估算中的测量误差：功能模型，结构模型和朴素模型

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摘要

Small area estimation using area-level models can sometimes benefit from covariates that are observed subject to random errors, such as covariates that are themselves estimates drawn from another survey. Given estimates of the variances of these measurement (sampling) errors for each small area, one can account for the uncertainty in such covariates using measurement error models (e.g., Ybarra and Lohr, 2008). Two types of area-level measurement error models have been examined in the small area estimation literature. The functional measurement error model assumes that the underlying true values of the covariates with measurement error are fixed but unknown quantities. The structural measurement error model assumes that these true values follow a model, leading to a multivariate model for the covariates observed with error and the original dependent variable. We compare and contrast these two models with the alternative of simply ignoring measurement error when it is present (naive model), exploring the consequences for prediction mean squared errors of use of an incorrect model under different underlying assumptions about the true model. Comparisons done using analytic formulas for the mean squared errors assuming model parameters are known yield some surprising results. We also illustrate results with a model fitted to data from the U.S. Census Bureau's Small Area Income and Poverty Estimates (SAIPE) Program.
机译：使用面积级别模型进行的小面积估算有时可能会受益于随机变量所观察到的协变量，例如协变量本身就是从另一项调查得出的估算值。给定每个小区域的这些测量（采样）误差的方差估计值，就可以使用测量误差模型来解释此类协变量的不确定性（例如Ybarra和Lohr，2008）。在小面积估算文献中已经研究了两种类型的面积水平测量误差模型。功能测量误差模型假定具有测量误差的协变量的基础真实值是固定的，但数量未知。结构测量误差模型假设这些真实值遵循一个模型，从而导致针对带有误差的协变量和原始因变量的多元模型。我们将这两种模型进行比较和对比，并选择不考虑存在的测量误差（天真的模型），探索在关于真实模型的不同基础假设下使用不正确模型的预测均方误差的后果。假设模型参数已知，使用解析公式对均方误差进行比较，得出一些令人惊讶的结果。我们还使用适合美国人口普查局小面积收入和贫困估计（SAIPE）计划数据的模型来说明结果。

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