Impact Evaluation Using Analysis of Covariance With Error-Prone Covariates That Violate Surrogacy

Area of Science:

• Statistical modeling
• Observational study analysis

Background:

• Analysis of covariance (ANCOVA) is frequently used to control for confounders in intervention studies.
• Measurement error in covariates within ANCOVA can yield inconsistent intervention effect estimates.
• Errors-in-variables (EIV) regression can correct for measurement error but relies on potentially violated surrogacy assumptions.

Purpose of the Study:

• Derive asymptotic results for ANCOVA with EIV regression under relaxed surrogacy assumptions.
• Investigate potential bias in ANCOVA when ignoring measurement error (OLS) or misapplying EIV regression.

Main Methods:

• Developed asymptotic theory for ANCOVA with error-prone covariates, accommodating various error scenarios.
• Applied derived results to a case study on estimating teacher effects using longitudinal data.
• Compared ANCOVA model specifications, including OLS and EIV regression.

Main Results:

• Derived general asymptotic results for ANCOVA with error-prone covariates.
• Demonstrated application in a real-world educational data analysis.
• Found that EIV regression may offer reduced bias compared to OLS regression, particularly when prior achievement data is limited.

Conclusions:

• The derived asymptotic results provide a framework for analyzing ANCOVA with measurement error under broader conditions.
• EIV regression shows potential for mitigating bias in intervention effect estimation when covariate measurement error is present.
• Careful consideration of model specification is crucial for accurate estimation in observational studies with error-prone covariates.