Simulation-Extrapolation with Latent Heteroskedastic Error Variance

Lockwood, J. R.; McCaffrey, Daniel F.

doi:10.1007/s11336-017-9556-y

Cited by 9 publications

(9 citation statements)

References 32 publications

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“…The SIMEX approach does not require the true PS model, but relies on assumptions about the functional form between the extent of measurement error and bias. Lockwood and McCaffrey (, ) well describe the use of SIMEX for causal effect estimation within the context of educational research. Further approaches that rely on assumptions about measurement error in covariates are proposed by Huang and Wang (), Kuroki and Pearl (), Stuart () and Yi, Ma, and Carroll ().…”

Section: Discussionmentioning

confidence: 99%

When does measurement error in covariates impact causal effect estimates? Analytic derivations of different scenarios and an empirical illustration

Sengewald

Steiner

Pohl

2018

Brit J Math & Statis

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The average causal treatment effect (ATE) can be estimated from observational data based on covariate adjustment. Even if all confounding covariates are observed, they might not necessarily be reliably measured and may fail to obtain an unbiased ATE estimate. Instead of fallible covariates, the respective latent covariates can be used for covariate adjustment. But is it always necessary to use latent covariates? How well do analysis of covariance (ANCOVA) or propensity score (PS) methods estimate the ATE when latent covariates are used? We first analytically delineate the conditions under which latent instead of fallible covariates are necessary to obtain the ATE. Then we empirically examine the difference between ATE estimates when adjusting for fallible or latent covariates in an applied example. We discuss the issue of fallible covariates within a stochastic theory of causal effects and analyse data of a within-study comparison with recently developed ANCOVA and PS procedures that allow for latent covariates. We show that fallible covariates do not necessarily bias ATE estimates, but point out different scenarios in which adjusting for latent covariates is required. In our empirical application, we demonstrate how latent covariates can be incorporated for ATE estimation in ANCOVA and in PS analysis.Impact of measurement error in covariates 245

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Section: Discussionmentioning

confidence: 99%

When does measurement error in covariates impact causal effect estimates? Analytic derivations of different scenarios and an empirical illustration

Sengewald

Steiner

Pohl

2018

Brit J Math & Statis

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“…Second, in some applications, such as those involving achievement tests, boldΣ U , i may equal v ( normalbold H i ) for a known function v (e.g., Lord, 1980). In such applications, even though v ( normalbold H i ) is not observed for any i because normalbold H i is latent, normalbold Σ true˜ U ( n ) may be specified as an estimator of boldΣ U = E [ v ( normalbold H i ) ] computed from the observed data using deconvolution methods (Lockwood & McCaffrey, 2014, 2017). Third, in many applications, analysts may know the “reliability” of each error-prone covariate (e.g., Crocker & Algina, 1986).…”

Section: Asymptotic Results For Eiv Regression With Surrogacy Violationsmentioning

confidence: 99%

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

Lockwood

McCaffrey

2019

Eval Rev

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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.

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“…Appropriate SIMEX methods for the case of unknown σ 2 i when replicate measures W ij are available for each X i are provided by Carroll and Wang (2008), Devanarayan and Stefanski (2002) and Wang et al (2009), and could be applied in the current setting. As noted in Section 6, applying SIMEX in the heterskedastic case where the ME variance is a known function of X i is addressed by Lockwood and McCaffrey (2015b).…”

Section: Discussionmentioning

confidence: 99%

“…To describe SIMEX, we introduce notation similar to that used by Devanarayan and Stefanski (2002) and Lockwood and McCaffrey (2015b). We consider hypothetical data in which X is measured with ME with variance (1 + λ)σ 2 for λ ≥ −1, where σ 2 is the variance of the ME in the observed data.…”

Section: Review Of Simexmentioning

confidence: 99%

“…It is thus unclear what ME variance to use for each test score during the simulation phase of SIMEX. Lockwood and McCaffrey (2015b) evaluate different plug-in estimators for the unknown variances g math (X i,math ) and g lang (X i,lang ) for their effectiveness in SIMEX applications. Their analyses suggest that treating estimates of E[g math (X i,math )|W i,math ] and E[g lang (X i,lang )|W i,lang ] as the known variance for each test score results in SIMEX estimators with reasonable properties.…”

Section: Example: Estimating Middle School Effectsmentioning

confidence: 99%

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Simulation-Extrapolation for Estimating Means and Causal Effects with Mismeasured Covariates

Lockwood¹,

McCaffrey²

2015

Observational Studies

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Regression, weighting and related approaches to estimating a population mean from a sample with nonrandom missing data often rely on the assumption that conditional on covariates, observed samples can be treated as random. Standard methods using this assumption generally will fail to yield consistent estimators when covariates are measured with error. We review approaches to consistent estimation of a population mean of an incompletely observed variable using error-prone covariates, noting difficulties with applying these methods. We consider the application of Simulation-Extrapolation (SIMEX) as a simple and effective alternative. We provide technical conditions under which SIMEX will lead to a consistent estimator of a population mean and argue why it may function well in common settings. We use a simulation study to demonstrate its potential for removing nearly all of the bias in regression, weighting and doubly robust estimators for a population mean while maintaining precision competitive with what would be obtained without measurement error. We also discuss and evaluate options for estimating the standard error of the SIMEX mean estimator. Finally, we present an empirical example of estimating middle school effects on student achievement.

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Simulation-Extrapolation with Latent Heteroskedastic Error Variance

Cited by 9 publications

References 32 publications

When does measurement error in covariates impact causal effect estimates? Analytic derivations of different scenarios and an empirical illustration

When does measurement error in covariates impact causal effect estimates? Analytic derivations of different scenarios and an empirical illustration

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

Simulation-Extrapolation for Estimating Means and Causal Effects with Mismeasured Covariates

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