Regressions with Berkson errors in covariates - a nonparametric approach

Schennach, Susanne M.

doi:10.1920/wp.cem.2013.2213

Cited by 5 publications

(7 citation statements)

References 27 publications

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“…Alternative estimation approaches include the use of instrumental variables (e.g. Schennach, ) the ML method or also Bayesian methods as described and applied in, for example Carroll et al. (), Rosner, Willett, and Spiegelman (), Spiegelman, Rosner, and Logan (), Thoresen and Laake ().…”

Section: Discussionmentioning

confidence: 99%

Mixtures of Berkson and classical covariate measurement error in the linear mixed model: Bias analysis and application to a study on ultrafine particles

Deffner¹,

Küchenhoff²,

Breitner

et al. 2018

Biometrical J

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The ultrafine particle measurements in the Augsburger Umweltstudie, a panel study conducted in Augsburg, Germany, exhibit measurement error from various sources. Measurements of mobile devices show classical possibly individual-specific measurement error; Berkson-type error, which may also vary individually, occurs, if measurements of fixed monitoring stations are used. The combination of fixed site and individual exposure measurements results in a mixture of the two error types. We extended existing bias analysis approaches to linear mixed models with a complex error structure including individual-specific error components, autocorrelated errors, and a mixture of classical and Berkson error. Theoretical considerations and simulation results show, that autocorrelation may severely change the attenuation of the effect estimations. Furthermore, unbalanced designs and the inclusion of confounding variables influence the degree of attenuation. Bias correction with the method of moments using data with mixture measurement error partially yielded better results compared to the usage of incomplete data with classical error. Confidence intervals (CIs) based on the delta method achieved better coverage probabilities than those based on Bootstrap samples. Moreover, we present the application of these new methods to heart rate measurements within the Augsburger Umweltstudie: the corrected effect estimates were slightly higher than their naive equivalents. The substantial measurement error of ultrafine particle measurements has little impact on the results. The developed methodology is generally applicable to longitudinal data with measurement error.

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Section: Discussionmentioning

confidence: 99%

Mixtures of Berkson and classical covariate measurement error in the linear mixed model: Bias analysis and application to a study on ultrafine particles

Deffner¹,

Küchenhoff²,

Breitner

et al. 2018

Biometrical J

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“…For example, relevant covariates may not be surveyed or measured at the level of the household, but are instead approximated by a regional average from an external source. For example, Schennach (2013) documents the bias which may result from ignoring Berkson errors in a nonlinear setting, using the effect of air pollution on respiratory health as application.…”

Section: Examples Of Berkson Errorsmentioning

confidence: 99%

“…Delaigle et al (2006) show the demand function is unidentified nonparametrically unless either the distribution of the Berkson error is known or can be estimated consistently from auxiliary data. Alternatively identification can be delivered if there is an instrument that is related to the true price in a suitable way (Schennach, 2013). We choose to follow the first of these approaches and use auxiliary data from external sources to inform us about the distribution of the Berkson error.…”

Section: Introductionmentioning

confidence: 99%

Estimation of a Heterogeneous Demand Function with Berkson Errors

Blundell

Horowitz²,

Parey

2022

The Review of Economics and Statistics

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Berkson errors are commonplace in empirical microeconomics. In consumer demand this form of measurement error occurs when the price an individual pays is measured by the (weighted) average price paid by individuals in a group (e.g., a county), rather than the true transaction price. We show the importance of Berkson errors for demand estimation with nonseparable unobserved heterogeneity. We develop a consistent estimator using external information on the true price distribution. Examining gasoline demand in the U.S., we document substantial within-market price variability. Accounting for Berkson errors is quantitatively important. Imposing the Slutsky shape constraint reduces sensitivity to Berkson errors.

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“…For more examples, see Carroll et al (2006), Du et al (2011), Schennach (2013), and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Minimum distance model checking in Berkson measurement error models with validation data

Geng

Koul

2018

TEST

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This article studies a minimum distance regression model checking approach in the presence of Berkson measurement errors in covariates without specifying the measurement error density but when external validation data are available. The proposed tests are based on a class of minimized integrated square distances between a nonparametric estimate of the calibrated regression function and the parametric null model being fitted. The asymptotic distributions of these tests under the null hypothesis and against certain alternatives are established. Surprisingly, these asymptotic distributions are the same as in the case of known measurement error density. In comparison, the asymptotic distributions of the corresponding minimum distance estimators of the null model parameters are affected by the estimation of the calibrated regression function. A simulation study shows desirable performance of a member of the proposed class of estimators and tests.

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Regressions with Berkson errors in covariates - a nonparametric approach

Cited by 5 publications

References 27 publications

Mixtures of Berkson and classical covariate measurement error in the linear mixed model: Bias analysis and application to a study on ultrafine particles

Mixtures of Berkson and classical covariate measurement error in the linear mixed model: Bias analysis and application to a study on ultrafine particles

Estimation of a Heterogeneous Demand Function with Berkson Errors

Minimum distance model checking in Berkson measurement error models with validation data

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