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Semiparametric Maximum Likelihood for Measurement Error Model Regression

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  • Daniel W. Schafer

Abstract

Summary. This paper presents an EM algorithm for semiparametric likelihood analysis of linear, generalized linear, and nonlinear regression models with measurement errors in explanatory variables. A structural model is used in which probability distributions are specified for (a) the response and (b) the measurement error. A distribution is also assumed for the true explanatory variable but is left unspecified and is estimated by nonparametric maximum likelihood. For various types of extra information about the measurement error distribution, the proposed algorithm makes use of available routines that would be appropriate for likelihood analysis of (a) and (b) if the true x were available. Simulations suggest that the semiparametric maximum likelihood estimator retains a high degree of efficiency relative to the structural maximum likelihood estimator based on correct distributional assumptions and can outperform maximum likelihood based on an incorrect distributional assumption. The approach is illustrated on three examples with a variety of structures and types of extra information about the measurement error distribution.

Suggested Citation

  • Daniel W. Schafer, 2001. "Semiparametric Maximum Likelihood for Measurement Error Model Regression," Biometrics, The International Biometric Society, vol. 57(1), pages 53-61, March.
    • Handle: RePEc:bla:biomet:v:57:y:2001:i:1:p:53-61
    DOI: 10.1111/j.0006-341X.2001.00053.x
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    References listed on IDEAS

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    1. Murray Aitkin, 1999. "A General Maximum Likelihood Analysis of Variance Components in Generalized Linear Models," Biometrics, The International Biometric Society, vol. 55(1), pages 117-128, March.
    2. Carroll, Raymond J. & Freedman, Laurence & Pee, David, 1997. "Design aspects of calibration studies in nutrition, with analysis of missing data in linear measurement error models," SFB 373 Discussion Papers 1997,12, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    3. Raymond J. Carroll & Kathryn Roeder & Larry Wasserman, 1999. "Flexible Parametric Measurement Error Models," Biometrics, The International Biometric Society, vol. 55(1), pages 44-54, March.
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    Cited by:

    1. Zhang, Jun & Feng, Zhenghui & Zhou, Bu, 2014. "A revisit to correlation analysis for distortion measurement error data," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 116-129.
    2. Marcus Groß, 2016. "Modeling body height in prehistory using a spatio-temporal Bayesian errors-in variables model," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 100(3), pages 289-311, July.
    3. Bani Mallick & F. Owen Hoffman & Raymond J. Carroll, 2002. "Semiparametric Regression Modeling with Mixtures of Berkson and Classical Error, with Application to Fallout from the Nevada Test Site," Biometrics, The International Biometric Society, vol. 58(1), pages 13-20, March.
    4. Taraneh Abarin & Liqun Wang, 2012. "Instrumental variable approach to covariate measurement error in generalized linear models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(3), pages 475-493, June.
    5. Eun-Young Suh & Daniel W. Schafer, 2002. "Semiparametric Maximum Likelihood for Nonlinear Regression with Measurement Errors," Biometrics, The International Biometric Society, vol. 58(2), pages 448-453, June.

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