Asymptotics for the SIMEX Estimator in Nonlinear Measurement Error Models

Carroll, Raymond J.; Küchenhoff, Helmut; Lombard, F.; Stefanski, Leonard A.

doi:10.1080/01621459.1996.10476682

Cited by 150 publications

(102 citation statements)

References 12 publications

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“…Second, the estimates are extrapolated backwards to the point where no measurement error existed (extrapolation step). The method can deal with continuous variables measured with random normal error (the original SIMEX procedure; Carroll, Küchenhoff, Lombard, & Stefanski, 1996;Cook & Stefanski, 1994) and with discrete variables measured with misclassification (the MCSIMEX procedure; Küchenhoff, Lederer, & Lesaffre, 2007;Küchenhoff, Mwalili, & Lesaffre, 2006). Similar to matrix correction and errors-in-variables-models, information about the measurement error must be provided.…”

Section: (Misclassification) Simulation Extrapolation ([Mc]simex)mentioning

confidence: 99%

Some suggestions on dealing with measurement error in linkage analyses

Bachl¹,

Scharkow²

2017

Preprint

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Linkage analysis is a sophisticated media effect research design that reconstructs the likely exposure to relevant media messages of individual survey respondents by complementing the survey data with a content analysis. It is an important improvement over survey-only designs: Instead of predicting some outcome of interest by media use and implicitly assuming what kind of media messages the respondents were exposed to, linkage analysis explicitly takes the media messages into account (de Vreese & Neijens, 2016; Scharkow & Bachl, 2017; Schuck, Vliegenthart, & de Vreese, 2016; Shoemaker & Reese, 1990; Slater, 2016; Valkenburg & Peter, 2013). The design in its modern form has been pioneered by Miller, Goldenberg, and Erbring (1979) and is today considered a “state-of-the art analysis of the impact of specific news consumption” (Fazekas & Larsen, 2015, p. 196). Its widespread use, especially in the field of political communication, and its still increasing popularity demonstrate the relevance of the design. The main advantage of a linkage analysis is the use of one or more message exposure variables which combine information about media use and media content. However, both constitutive sources are often measured with error: Survey respondents are not very good at reporting their media use reliably, and coders will often make some errors when classifying the relevant messages.In this article, we will first give a short overview on the prevalence and consequences of measurement error in both data sources. The arguments are based on a literature review and a simulation study which are published elsewhere in full detail (Scharkow & Bachl, 2017). We continue with a discussion of possible remedies in measurement and data analysis. Beyond the obvious need to improve the measures themselves, we highlight the importance of serious diagnostics of measurement quality. Such information can then be incorporated in the data analysis using estimation or imputation approaches, which are introduced in the main section of this chapter. We conclude by noting that 1) the improvement of measurements and the diagnosis of measurement error in both parts of a linkage analysis must be taken seriously; 2) many tools for correcting measurement error in single parts of a linkage analysis already exist and should be used; 3) methodological research is needed for the development of an integrated analysis workflow which accounts for measurement error and uncertainty in both data sources.

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Section: (Misclassification) Simulation Extrapolation ([Mc]simex)mentioning

confidence: 99%

Some suggestions on dealing with measurement error in linkage analyses

Bachl¹,

Scharkow²

2017

Preprint

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“…The asymptotic distribution theory for the original SIMEX approach has been developed by Carroll et al (1996), hereafter denoted by CKLS. The idea is to view regression estimation as solving unbiased estimating equations, see e.g.…”

Section: Asymptotic Variance Estimationmentioning

confidence: 99%

“…Thus there is a need for a method which is theoretically justified and can calculate the standard errors in a less computer intensive manner allowing for the uncertainty of the estimated misclassification probabilities. The asymptotic variance estimation has been developed for the original SIMEX by Carroll et al (1996). Here we transfer this strategy to the case of the MC-SIMEX approach.…”

Section: Introductionmentioning

confidence: 99%

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Asymptotic variance estimation for the misclassification SIMEX

Küchenhoff

Lederer

Lesaffre³

2007

Computational Statistics & Data Analysis

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Most epidemiological studies suffer from misclassification in the response and/or the covariates. Since ignoring misclassification induces bias on the parameter estimates, correction for such errors is important. For measurement error, the continuous analog to misclassification, a general approach for bias correction is the SIMEX (simulation extrapolation) originally suggested by Cook and Stefanski (1994). This approach has been recently extended to regression models with a possibly misclassified categorical response and/or the covariates by Küchenhoff et al. (2005), and is called the MC-SIMEX approach. To assess the importance of a regressor not only its (corrected) estimate is needed, but also its standard error. For the original SIMEX approach. Carroll et al. (1996) developed a method for estimating the asymptotic variance. Here we derive the asymptotic variance estimators for the MC-SIMEX approach, extending the methodology of Carroll et al. (1996). We also include the case where the misclassification probabilities are estimated by a validation study. An extensive simulation study shows the good performance of our approach. The approach is illustrated using an example in caries research including a logistic regression model, where the response and a binary covariate are possibly misclassified.

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“…It is, however, very computer intensive and it only gives a consistent estimator if the correct extrapolation curve has been used (see Carroll et al, 1996). The quadratic curve may be convenient, but it is rarely the correct curve.…”

Section: Add Random Noise To Thementioning

confidence: 99%

Some Recent Advances in Measurement Error Models and Methods

Schneeweiß

Augustin

Modern Econometric Analysis

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A measurement error model is a regression model with (substantial) measurement errors in the variables. Disregarding these measurement errors in estimating the regression parameters results in asymptotically biased estimators. Several methods have been proposed to eliminate, or at least to reduce, this bias, and the relative efficiency and robustness of these methods have been compared. The paper gives an account of these endeavors. In another context, when data are of a categorical nature, classification errors play a similar role as measurement errors in continuous data. The paper also reviews some recent advances in this field.

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Asymptotics for the SIMEX Estimator in Nonlinear Measurement Error Models

Cited by 150 publications

References 12 publications

Some suggestions on dealing with measurement error in linkage analyses

Some suggestions on dealing with measurement error in linkage analyses

Asymptotic variance estimation for the misclassification SIMEX

Some Recent Advances in Measurement Error Models and Methods

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