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. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    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. 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.
    2. 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.
    3. Daniel W. Schafer, 2001. "Semiparametric Maximum Likelihood for Measurement Error Model Regression," Biometrics, The International Biometric Society, vol. 57(1), pages 53-61, March.
    4. 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.
    5. Shuang Zhang & Xingdong Feng, 2022. "Distributed identification of heterogeneous treatment effects," Computational Statistics, Springer, vol. 37(1), pages 57-89, March.
    6. Li, Feng & Kang, Yanfei, 2018. "Improving forecasting performance using covariate-dependent copula models," International Journal of Forecasting, Elsevier, vol. 34(3), pages 456-476.
    7. 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.
    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. 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.
    10. Cai, Jing-Heng & Song, Xin-Yuan & Lam, Kwok-Hap & Ip, Edward Hak-Sing, 2011. "A mixture of generalized latent variable models for mixed mode and heterogeneous data," Computational Statistics & Data Analysis, Elsevier, vol. 55(11), pages 2889-2907, November.
    11. N. T. Longford & Pierpaolo D'Urso, 2011. "Mixture models with an improper component," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(11), pages 2511-2521, January.
    12. 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.
    13. Ungolo, Francesco & Kleinow, Torsten & Macdonald, Angus S., 2020. "A hierarchical model for the joint mortality analysis of pension scheme data with missing covariates," Insurance: Mathematics and Economics, Elsevier, vol. 91(C), pages 68-84.
    14. 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.
    15. Conti, Gabriella & Frühwirth-Schnatter, Sylvia & Heckman, James J. & Piatek, Rémi, 2014. "Bayesian exploratory factor analysis," Journal of Econometrics, Elsevier, vol. 183(1), pages 31-57.
    16. 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.
    17. Zhengyi Zhou & David S. Matteson & Dawn B. Woodard & Shane G. Henderson & Athanasios C. Micheas, 2015. "A Spatio-Temporal Point Process Model for Ambulance Demand," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(509), pages 6-15, March.
    18. 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.
    19. Park, Byung-Jung & Zhang, Yunlong & Lord, Dominique, 2010. "Bayesian mixture modeling approach to account for heterogeneity in speed data," Transportation Research Part B: Methodological, Elsevier, vol. 44(5), pages 662-673, June.
    20. 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.

    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.