Instrumental Variable Estimation in Generalized Linear Measurement Error Models
TL;DR: In this paper, the maximum likelihood estimator for the normal theory, structural linear instrumental variable model is shown to be a solution to the estimating equations derived in this paper, and a simulation study described for the logistic model based on the Framingham Heart Study data.
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Abstract: Instrumental variable estimation in generalized linear measurement error models are studied. For models with canonical link functions, unbiased estimating equations are derived. The maximum likelihood estimator for the normal theory, structural linear instrumental variable model is shown to be a solution to the estimating equations derived herein. Logistic regression is studied in detail. An example is given and a simulation study described for the logistic model based on the Framingham Heart Study data.
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Table 3.5 Correlations between estimates for (31 when CORR(Y, U) = .25. 
Table 4.2 Relative efficiency of the one-step estimator to the conditional estimator. Table . MSE(OS) entrIes are MSE(S) . 
Table 4.3 Performance of the one-step estimator when the conditional estimator did not converge. Note that numerical values in the Converged column are from Table 4.1. An asterisk between two values indicates the difference was significant at the 5% level, see the discussion in Section 4.6 for details. CORR(Y, U) = .15. 
Table 3.3 Relative efficiency of the simple estimator to the optimal simple estimator. Table . MSE os entnes are MSE S 
Table 3.4 Relative efficiency of the maximum likelihood estimator to the optimal simple . T bl . MSE(OS)estimator. a e entnes are MSE(MLE)' 
Table 3.2 Percent coverage of 95% Wald-type confidence intervals for the optimal simple estimator.
Citations
An Introduction To Instrumental Variables For epidemiologists
TL;DR: This paper provides an introduction to developments of non-parametric versions of IV methods that connect IV methods to causal and measurement-error models important in epidemiological applications, illustrated by an application ofIV methods to non- Parametric adjustment for non-compliance in randomized trials.
Limits to Causal Inference based on Mendelian Randomization: A Comparison with Randomized Controlled Trials
Dorothea Nitsch,Mariam Molokhia,Liam Smeeth,Bianca DeStavola,John C. Whittaker,David A. Leon +5 more
TL;DR: The authors conclude that Mendelian randomization is a powerful addition to etiologic research tools, however, care must be taken, because drawing valid causal inferences from its application depends upon more extensive assumptions than are required in randomized controlled trials.
237
Identification and Estimation of Regression Models with Misclassification
TL;DR: In this paper, the problem of identification and estimation in nonparametric regression models with a misclassified binary regressor where the measurement error may be correlated with the regressors is studied.
Identification and Estimation of Regression Models with Misclassification
TL;DR: In this paper, the problem of identification and estimation in nonparametric regression models with a misclassified binary regressor where the measurement error may be correlated with the regressors is studied.
147
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TL;DR: In this article, a taxonomy of the data sets likely to be available in measurement error studies is developed and an asymptotic theory based on this taxonomy is obtained and includes measurement error and Berkson error models as special cases.
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