Analysis of multivariate reliability structures and the induced bias in linear model estimation.
Analysis of multivariate reliability structures and the induced bias in linear model estimation.
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DOI：
10.1002/(sici)1097-0258(19960815)15:15
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发表时间：
1996-08
影响因子：
2
通讯作者：
Mikel Aickin;Cheryl Ritenbaugh
中科院分区：
文献类型：
--
作者：
Mikel Aickin;Cheryl Ritenbaugh
当 x 的完全准确测量可用时，最小二乘法可以对模型 E[Y [符号：参见文本] x] = beta x 中的回归系数 beta 进行一致的估计。然而，在生物医学研究中，人们必须经常用不可靠的测量值 X 来代替 x。这会导致最小二乘系数估计出现偏差。在单变量情况下，偏差表现为向零收缩，但这个结果并不能概括。当 x 是多元时，实际回归系数和估计回归系数的符号或大小之间不存在可预测的关系。在本文中，我们描述了估计偏差的特征，并回顾了一个相对简单的调整程序来纠正它。我们还表明，一些关于偏见的自然猜想是错误的。我们提出了可靠性系数矩阵的三个定义，概括了单变量情况，并说明了它们在癌症预防研究的膳食摄入数据中的应用。
Least squares provides consistent estimates of the regression coefficients beta in the model E[Y [symbol: see text] x] = beta x when fully accurate measurements of x are available. However, in biomedical studies one must frequently substitute unreliable measurements X in place of x. This induces bias in the least squares coefficient estimates. In the univariate case, the bias manifests itself as a shrinkage toward zero, but this result does not generalize. When x is multivariate, then there are no predictable relationships between the signs or magnitudes of actual and estimated regression coefficients. In this article, we characterize the estimation bias, and review a relatively simple adjustment procedure to correct it. We also show that several natural conjectures about the bias are false. We present three definitions of reliability coefficient matrices that generalize the univariate case, and we illustrate their application to dietary intake data from a cancer prevention study.