IDEAS home Printed from https://ideas.repec.org/a/bla/biomet/v57y2001i1p53-61.html
   My bibliography  Save this article

Semiparametric Maximum Likelihood for Measurement Error Model Regression

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/j.0006-341X.2001.00053.x
    Download Restriction: no
    File URL: https://libkey.io/10.1111/j.0006-341X.2001.00053.x?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. 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.
    3. 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.
    4. 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.
    5. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Sylvia Richardson & Laurent Leblond & Isabelle Jaussent & Peter J. Green, 2002. "Mixture models in measurement error problems, with reference to epidemiological studies," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 165(3), pages 549-566, October.
    2. Julian P. T. Higgins & Simon G. Thompson & David J. Spiegelhalter, 2009. "A re‐evaluation of random‐effects meta‐analysis," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 172(1), pages 137-159, January.
    3. Malka Gorfine & Nurit Lipshtat & Laurence S. Freedman & Ross L. Prentice, 2007. "Linear Measurement Error Models with Restricted Sampling," Biometrics, The International Biometric Society, vol. 63(1), pages 137-142, March.
    4. Getachew A. Dagne, 2016. "A growth mixture Tobit model: application to AIDS studies," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(7), pages 1174-1185, July.
    5. Gustafson, Paul & Le, Nhu D. & Vallée, Marc, 2000. "Parametric Bayesian analysis of case-control data with imprecise exposure measurements," Statistics & Probability Letters, Elsevier, vol. 47(4), pages 357-363, May.
    6. John Staudenmayer & Donna Spiegelman, 2002. "Segmented Regression in the Presence of Covariate Measurement Error in Main Study/Validation Study Designs," Biometrics, The International Biometric Society, vol. 58(4), pages 871-877, December.
    7. Huixia Judy Wang & Leonard A. Stefanski & Zhongyi Zhu, 2012. "Corrected-loss estimation for quantile regression with covariate measurement errors," Biometrika, Biometrika Trust, vol. 99(2), pages 405-421.
    8. Marino, Maria Francesca & Alfó, Marco, 2016. "Gaussian quadrature approximations in mixed hidden Markov models for longitudinal data: A simulation study," Computational Statistics & Data Analysis, Elsevier, vol. 94(C), pages 193-209.
    9. Suzanne J Carroll & Michael J Dale & Theophile Niyonsenga & Anne W Taylor & Mark Daniel, 2020. "Associations between area socioeconomic status, individual mental health, physical activity, diet and change in cardiometabolic risk amongst a cohort of Australian adults: A longitudinal path analysis," PLOS ONE, Public Library of Science, vol. 15(5), pages 1-16, May.
    10. Francesco BARTOLUCCI & Silvia BACCI & Claudia PIGINI, 2015. "A Misspecification Test for Finite-Mixture Logistic Models for Clustered Binary and Ordered Responses," Working Papers 410, Universita' Politecnica delle Marche (I), Dipartimento di Scienze Economiche e Sociali.
    11. Lluís Bermúdez & Dimitris Karlis & Isabel Morillo, 2020. "Modelling Unobserved Heterogeneity in Claim Counts Using Finite Mixture Models," Risks, MDPI, vol. 8(1), pages 1-13, January.
    12. Marco Alfo & Giovanni Trovato & Robert J. Waldmann, 2008. "Testing for country heterogeneity in growth models using a finite mixture approach," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 23(4), pages 487-514.
    13. Berg, Gerard J. van den & Uhlendorff, Arne & Wolff, Joachim, 2015. "Under heavy pressure : intense monitoring and accumulation of sanctions for young welfare recipients in Germany," IAB-Discussion Paper 201534, Institut für Arbeitsmarkt- und Berufsforschung (IAB), Nürnberg [Institute for Employment Research, Nuremberg, Germany].
    14. Caliendo, Marco & Künn, Steffen & Uhlendorff, Arne, 2016. "Earnings exemptions for unemployed workers: The relationship between marginal employment, unemployment duration and job quality," Labour Economics, Elsevier, vol. 42(C), pages 177-193.
    15. C. Y. Wang & Garnet L. Anderson & Ross L. Prentice, 1999. "Estimation of the Correlation Between Nutrient Intake Measures Under Restricted Sampling," Biometrics, The International Biometric Society, vol. 55(3), pages 711-717, September.
    16. Marco Alfò & Stefano Caiazza & Giovanni Trovato, 2005. "Extending a Logistic Approach to Risk Modeling through Semiparametric Mixing," Journal of Financial Services Research, Springer;Western Finance Association, vol. 28(1), pages 163-176, October.
    17. Antonello Maruotti & Pierfrancesco Alaimo Di Loro, 2023. "CO2 emissions and growth: A bivariate bidimensional mean‐variance random effects model," Environmetrics, John Wiley & Sons, Ltd., vol. 34(5), August.
    18. Bruno Crepon & Marc Ferracci & Grégory Jolivet & Gerard Van Den Berg, 2010. "Analyzing the Anticipation of Treatments with Data on Notification Dates," Working Papers 2010-41, Center for Research in Economics and Statistics.
    19. Staudenmayer, John & Ruppert, David & Buonaccorsi, John P., 2008. "Density Estimation in the Presence of Heteroscedastic Measurement Error," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 726-736, June.
    20. Caffo, Brian & An, Ming-Wen & Rohde, Charles, 2007. "Flexible random intercept models for binary outcomes using mixtures of normals," Computational Statistics & Data Analysis, Elsevier, vol. 51(11), pages 5220-5235, July.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bla:biomet:v:57:y:2001:i:1:p:53-61. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0006-341X .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.