IDEAS home Printed from https://ideas.repec.org/a/bla/jorssa/v165y2002i3p549-566.html
   My bibliography  Save this article

Mixture models in measurement error problems, with reference to epidemiological studies

Author

Listed:
  • Sylvia Richardson
  • Laurent Leblond
  • Isabelle Jaussent
  • Peter J. Green

Abstract

Summary. The paper focuses on a Bayesian treatment of measurement error problems and on the question of the specification of the prior distribution of the unknown covariates. It presents a flexible semiparametric model for this distribution based on a mixture of normal distributions with an unknown number of components. Implementation of this prior model as part of a full Bayesian analysis of measurement error problems is described in classical set‐ups that are encountered in epidemiological studies: logistic regression between unknown covariates and outcome, with a normal or log‐normal error model and a validation group. The feasibility of this combined model is tested and its performance is demonstrated in a simulation study that includes an assessment of the influence of misspecification of the prior distribution of the unknown covariates and a comparison with the semiparametric maximum likelihood method of Roeder, Carroll and Lindsay. Finally, the methodology is illustrated on a data set on coronary heart disease and cholesterol levels in blood.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:jorssa:v:165:y:2002:i:3:p:549-566
    DOI: 10.1111/1467-985X.00252
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/1467-985X.00252
    Download Restriction: no
    File URL: https://libkey.io/10.1111/1467-985X.00252?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. Sylvia. Richardson & Peter J. Green, 1997. "On Bayesian Analysis of Mixtures with an Unknown Number of Components (with discussion)," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(4), pages 731-792.
    3. Daniel W. Schafer & Jay H. Lubin & Elaine Ron & Marilyn Stovall & Raymond J. Carroll, 2001. "Thyroid Cancer Following Scalp Irradiation: A Reanalysis Accounting for Uncertainty in Dosimetry," Biometrics, The International Biometric Society, vol. 57(3), pages 689-697, September.
    4. 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. Hansen, Karsten T. & Heckman, James J. & Mullen, K.J.Kathleen J., 2004. "The effect of schooling and ability on achievement test scores," Journal of Econometrics, Elsevier, vol. 121(1-2), pages 39-98.
    2. Mark P Little & Alexander G Kukush & Sergii V Masiuk & Sergiy Shklyar & Raymond J Carroll & Jay H Lubin & Deukwoo Kwon & Alina V Brenner & Mykola D Tronko & Kiyohiko Mabuchi & Tetiana I Bogdanova & Ma, 2014. "Impact of Uncertainties in Exposure Assessment on Estimates of Thyroid Cancer Risk among Ukrainian Children and Adolescents Exposed from the Chernobyl Accident," PLOS ONE, Public Library of Science, vol. 9(1), pages 1-9, January.
    3. Ho, Remus K.W. & Hu, Inchi, 2008. "Flexible modelling of random effects in linear mixed models--A Bayesian approach," Computational Statistics & Data Analysis, Elsevier, vol. 52(3), pages 1347-1361, January.
    4. Cabral, Celso Rômulo Barbosa & Lachos, Víctor Hugo & Zeller, Camila Borelli, 2014. "Multivariate measurement error models using finite mixtures of skew-Student t distributions," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 179-198.
    5. Domingo Benítez & Gustavo Montero & Eduardo Rodríguez & David Greiner & Albert Oliver & Luis González & Rafael Montenegro, 2020. "A Phenomenological Epidemic Model Based On the Spatio-Temporal Evolution of a Gaussian Probability Density Function," Mathematics, MDPI, vol. 8(11), pages 1-22, November.
    6. Anders Skrondal & Sophia Rabe‐Hesketh, 2007. "Latent Variable Modelling: A Survey," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 34(4), pages 712-745, December.
    7. Arana, Jorge E. & Leon, Carmelo J., 2005. "Flexible mixture distribution modeling of dichotomous choice contingent valuation with heterogenity," Journal of Environmental Economics and Management, Elsevier, vol. 50(1), pages 170-188, July.
    8. A. Guolo, 2008. "A Flexible Approach to Measurement Error Correction in Case–Control Studies," Biometrics, The International Biometric Society, vol. 64(4), pages 1207-1214, December.
    9. Duncan J. Mayer & Robert L. Fischer, 2022. "Can a measurement error perspective improve estimation in neighborhood effects research? A hierarchical Bayesian methodology," Social Science Quarterly, Southwestern Social Science Association, vol. 103(5), pages 1260-1272, September.
    10. David M. Zucker & Malka Gorfine & Yi Li & Mahlet G. Tadesse & Donna Spiegelman, 2013. "A Regularization Corrected Score Method for Nonlinear Regression Models with Covariate Error," Biometrics, The International Biometric Society, vol. 69(1), pages 80-90, March.
    11. Tamara Fioroni & Andrea Mario Lavezzi & Giovanni Trovato, 2023. "Organized Crime, Corruption and Economic Growth," Discussion Papers 2023/298, Dipartimento di Economia e Management (DEM), University of Pisa, Pisa, Italy.
    12. Xiaoqiong Fang & Andy W. Chen & Derek S. Young, 2023. "Predictors with measurement error in mixtures of polynomial regressions," Computational Statistics, Springer, vol. 38(1), pages 373-401, 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. Domingo Benítez & Gustavo Montero & Eduardo Rodríguez & David Greiner & Albert Oliver & Luis González & Rafael Montenegro, 2020. "A Phenomenological Epidemic Model Based On the Spatio-Temporal Evolution of a Gaussian Probability Density Function," Mathematics, MDPI, vol. 8(11), pages 1-22, November.
    2. Daniel W. Schafer, 2001. "Semiparametric Maximum Likelihood for Measurement Error Model Regression," Biometrics, The International Biometric Society, vol. 57(1), pages 53-61, March.
    3. Arana, Jorge E. & Leon, Carmelo J., 2005. "Flexible mixture distribution modeling of dichotomous choice contingent valuation with heterogenity," Journal of Environmental Economics and Management, Elsevier, vol. 50(1), pages 170-188, July.
    4. Hartzel, Jonathan & Liu, I-Ming & Agresti, Alan, 2001. "Describing heterogeneous effects in stratified ordinal contingency tables, with application to multi-center clinical trials," Computational Statistics & Data Analysis, Elsevier, vol. 35(4), pages 429-449, February.
    5. Alston, C.L. & Mengersen, K.L. & Robert, C.P. & Thompson, J.M. & Littlefield, P.J. & Perry, D. & Ball, A.J., 2007. "Bayesian mixture models in a longitudinal setting for analysing sheep CAT scan images," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4282-4296, May.
    6. Jamie L. Cross & Lennart Hoogerheide & Paul Labonne & Herman K. van Djik, 2024. "Flexible Negative Binomial Mixtures for Credible Mode Inference in Heterogeneous Count Data from Finance, Economics and Bioinformatics," Working Papers No 09/2024, Centre for Applied Macro- and Petroleum economics (CAMP), BI Norwegian Business School.
    7. Papastamoulis, Panagiotis & Iliopoulos, George, 2009. "Reversible Jump MCMC in mixtures of normal distributions with the same component means," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 900-911, February.
    8. Fisher, Mark & Jensen, Mark J., 2022. "Bayesian nonparametric learning of how skill is distributed across the mutual fund industry," Journal of Econometrics, Elsevier, vol. 230(1), pages 131-153.
    9. 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.
    10. Lee, Sik-Yum & Song, Xin-Yuan, 2008. "On Bayesian estimation and model comparison of an integrated structural equation model," Computational Statistics & Data Analysis, Elsevier, vol. 52(10), pages 4814-4827, June.
    11. Shuang Zhang & Xingdong Feng, 2022. "Distributed identification of heterogeneous treatment effects," Computational Statistics, Springer, vol. 37(1), pages 57-89, March.
    12. Fuentes-García, Ruth & Mena, Ramsés H. & Walker, Stephen G., 2019. "Modal posterior clustering motivated by Hopfield’s network," Computational Statistics & Data Analysis, Elsevier, vol. 137(C), pages 92-100.
    13. Brian Francis & Jiayi Liu, 2015. "Modelling escalation in crime seriousness: a latent variable approach," METRON, Springer;Sapienza Università di Roma, vol. 73(2), pages 277-297, August.
    14. Zhang, Daowen & Davidian, Marie, 2004. "Likelihood and conditional likelihood inference for generalized additive mixed models for clustered data," Journal of Multivariate Analysis, Elsevier, vol. 91(1), pages 90-106, October.
    15. Li, Feng & Kang, Yanfei, 2018. "Improving forecasting performance using covariate-dependent copula models," International Journal of Forecasting, Elsevier, vol. 34(3), pages 456-476.
    16. Panagiotis Papastamoulis & George Iliopoulos, 2013. "On the Convergence Rate of Random Permutation Sampler and ECR Algorithm in Missing Data Models," Methodology and Computing in Applied Probability, Springer, vol. 15(2), pages 293-304, June.
    17. Frangos, Nikolaos & Karlis, Dimitris, 2004. "Modelling losses using an exponential-inverse Gaussian distribution," Insurance: Mathematics and Economics, Elsevier, vol. 35(1), pages 53-67, August.
    18. Sik-Yum Lee, 2006. "Bayesian Analysis of Nonlinear Structural Equation Models with Nonignorable Missing Data," Psychometrika, Springer;The Psychometric Society, vol. 71(3), pages 541-564, September.
    19. Gustavo Alexis Sabillón & Luiz Gabriel Fernandes Cotrim & Daiane Aparecida Zuanetti, 2023. "A data-driven reversible jump for estimating a finite mixture of regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(1), pages 350-369, March.
    20. 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.

    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:jorssa:v:165:y:2002:i:3:p:549-566. 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: https://edirc.repec.org/data/rssssea.html .

    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.