Background: Analysis of covariance (ANCOVA) is commonly used to adjust for potential confounders in observational studies of intervention effects. Measurement error in the covariates used in ANCOVA models can lead to inconsistent estimators of intervention effects. While errors-in-variables (EIV) regression can restore consistency, it requires surrogacy assumptions for the error-prone covariates that may be violated in practical settings. Objectives: The objectives of this article are (1) to derive asymptotic results for ANCOVA using EIV regression when measurement errors may not satisfy the standard surrogacy assumptions and (2) to demonstrate how these results can be used to explore the potential bias from ANCOVA models that either ignore measurement error by using ordinary least squares (OLS) regression or use EIV regression when its required assumptions do not hold. Results: The article derives asymptotic results for ANCOVA with error-prone covariates that cover a variety of cases relevant to applications. It then uses the results in a case study of choosing among ANCOVA model specifications for estimating teacher effects using longitudinal data from a large urban school system. It finds evidence that estimates of teacher effects computed using EIV regression may have smaller bias than estimates computed using OLS regression when the data available for adjusting for students’ prior achievement are limited.

中文翻译：

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使用协方差分析和错误代数协变量来影响代孕的影响评估。

背景：协方差分析（ANCOVA）通常用于调整干预效果观察研究中的潜在混杂因素。ANCOVA模型中使用的协变量中的测量误差会导致干预效果的估计值不一致。尽管变量错误（EIV）回归可以恢复一致性，但它需要对容易出错的协变量进行替代的假设，而这些变量在实际设置中可能会被违反。目标：本文的目标是（1）当测量误差可能不满足标准代孕假设时，使用EIV回归得出ANCOVA的渐近结果;（2）展示如何将这些结果用于探索来自ANCOVA模型的潜在偏差通过使用普通最小二乘（OLS）回归来忽略测量误差，或者在其所需的假设不成立时使用EIV回归。结果：本文得出了ANCOVA的渐近结果，其易错协变量涵盖了与应用相关的各种情况。然后，它使用结果进行案例研究，从大型城市学校系统的纵向数据中选择ANCOVA模型规范，以评估教师的效果。