Estimated generalized least squares in spatially misaligned regression models with Berkson error.
Estimated generalized least squares in spatially misaligned regression models with Berkson error.
复制标题
具有伯克森误差的空间失准回归模型中的广义最小二乘估计。
DOI：
10.1093/biostatistics/kxt011
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
Gotway,CarolA
中科院分区：
文献类型：
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作者：
Lopiano,KennethK;Young,LindaJ;Gotway,CarolA
在环境研究中，通常会评估空间上不一致的变量之间的关系。由于数据未对齐，因此克里金法通常用于预测观察到响应的位置处的协变量。使用克里金法预测来估计线性回归模型中的回归参数会引入伯克森误差，从而产生难以估计的协方差结构。此外，如果估计与克里金法相关的参数（例如趋势面参数和空间协方差参数），则会引入额外的不确定性。我们将总测量误差描述为更广泛的 Berkson 误差模型类别的一部分，并使用估计的协方差参数开发估计的广义最小二乘估计器。在使用归纳模型时，我们充分考虑了误差结构并使用基于似然的方法估计协方差参数。我们深入了解何时需要充分考虑由不同误差源引起的协方差结构。我们使用模拟评估估算器的性能，并使用美国环境保护局的公开数据说明该方法。
In environmental studies, relationships among variables that are misaligned in space are routinely assessed. Because the data are misaligned, kriging is often used to predict the covariate at the locations where the response is observed. Using kriging predictions to estimate regression parameters in linear regression models introduces a Berkson error, which induces a covariance structure that is challenging to estimate. In addition, if the parameters associated with kriging (e.g. trend surface parameters and spatial covariance parameters) are estimated, then an additional uncertainty is introduced. We characterize the total measurement error as part of a broader class of Berkson error models and develop an estimated generalized least squares estimator using estimated covariance parameters. In working with the induced model, we fully account for the error structure and estimate the covariance parameters using likelihood-based methods. We provide insight into when it is important to fully account for the covariance structure induced from the different error sources. We assess the performance of the estimators using simulation and illustrate the methodology using publicly available data from the US Environmental Protection Agency.