IDEAS home Printed from https://ideas.repec.org/a/bpj/ijbist/v12y2016i1p65-77n8.html
   My bibliography  Save this article

The Orthogonally Partitioned EM Algorithm: Extending the EM Algorithm for Algorithmic Stability and Bias Correction Due to Imperfect Data

Author

Listed:
  • Regier Michael D.

    (Department of Biostatistics, West Virginia University, Morgantown, WV, USA)

  • Moodie Erica E. M.

    (Department of Epidemiology, Biostatistics & Occupational Health, McGill University, Montreal, QC, Canada)

Abstract

We propose an extension of the EM algorithm that exploits the common assumption of unique parameterization, corrects for biases due to missing data and measurement error, converges for the specified model when standard implementation of the EM algorithm has a low probability of convergence, and reduces a potentially complex algorithm into a sequence of smaller, simpler, self-contained EM algorithms. We use the theory surrounding the EM algorithm to derive the theoretical results of our proposal, showing that an optimal solution over the parameter space is obtained. A simulation study is used to explore the finite sample properties of the proposed extension when there is missing data and measurement error. We observe that partitioning the EM algorithm into simpler steps may provide better bias reduction in the estimation of model parameters. The ability to breakdown a complicated problem in to a series of simpler, more accessible problems will permit a broader implementation of the EM algorithm, permit the use of software packages that now implement and/or automate the EM algorithm, and make the EM algorithm more accessible to a wider and more general audience.

Suggested Citation

  • Regier Michael D. & Moodie Erica E. M., 2016. "The Orthogonally Partitioned EM Algorithm: Extending the EM Algorithm for Algorithmic Stability and Bias Correction Due to Imperfect Data," The International Journal of Biostatistics, De Gruyter, vol. 12(1), pages 65-77, May.
    • Handle: RePEc:bpj:ijbist:v:12:y:2016:i:1:p:65-77:n:8
    DOI: 10.1515/ijb-2015-0016
    as

    Download full text from publisher

    File URL: https://doi.org/10.1515/ijb-2015-0016
    Download Restriction: For access to full text, subscription to the journal or payment for the individual article is required.
    File URL: https://libkey.io/10.1515/ijb-2015-0016?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Amy L. Stubbendick & Joseph G. Ibrahim, 2003. "Maximum Likelihood Methods for Nonignorable Missing Responses and Covariates in Random Effects Models," Biometrics, The International Biometric Society, vol. 59(4), pages 1140-1150, December.
    2. James R. Carpenter & Michael G. Kenward & Stijn Vansteelandt, 2006. "A comparison of multiple imputation and doubly robust estimation for analyses with missing data," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 169(3), pages 571-584, July.
    3. D. Oakes, 1999. "Direct calculation of the information matrix via the EM," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(2), pages 479-482, April.
    4. Joseph G. Ibrahim & Ming-Hui Chen & Stuart R. Lipsitz, 1999. "Monte Carlo EM for Missing Covariates in Parametric Regression Models," Biometrics, The International Biometric Society, vol. 55(2), pages 591-596, June.
    5. Erica Moodie & D. Stephens, 2011. "Marginal Structural Models: unbiased estimation for longitudinal studies," International Journal of Public Health, Springer;Swiss School of Public Health (SSPH+), vol. 56(1), pages 117-119, February.
    6. Wei Liu & Lang Wu, 2007. "Simultaneous Inference for Semiparametric Nonlinear Mixed-Effects Models with Covariate Measurement Errors and Missing Responses," Biometrics, The International Biometric Society, vol. 63(2), pages 342-350, June.
    Full references (including those not matched with items on IDEAS)

    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. Chen, Qingxia & Ibrahim, Joseph G. & Chen, Ming-Hui & Senchaudhuri, Pralay, 2008. "Theory and inference for regression models with missing responses and covariates," Journal of Multivariate Analysis, Elsevier, vol. 99(6), pages 1302-1331, July.
    2. G. Y. Yi & W. Liu & Lang Wu, 2011. "Simultaneous Inference and Bias Analysis for Longitudinal Data with Covariate Measurement Error and Missing Responses," Biometrics, The International Biometric Society, vol. 67(1), pages 67-75, March.
    3. James Y. Dai & Michael LeBlanc & Charles Kooperberg, 2009. "Semiparametric Estimation Exploiting Covariate Independence in Two-Phase Randomized Trials," Biometrics, The International Biometric Society, vol. 65(1), pages 178-187, March.
    4. Lan Huang & Ming-Hui Chen & Joseph G. Ibrahim, 2005. "Bayesian Analysis for Generalized Linear Models with Nonignorably Missing Covariates," Biometrics, The International Biometric Society, vol. 61(3), pages 767-780, September.
    5. Yang, Miao & Das, Kalyan & Majumdar, Anandamayee, 2016. "Analysis of bivariate zero inflated count data with missing responses," Journal of Multivariate Analysis, Elsevier, vol. 148(C), pages 73-82.
    6. Shu Yang & Jae Kwang Kim, 2016. "Likelihood-based Inference with Missing Data Under Missing-at-Random," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(2), pages 436-454, June.
    7. Robert D. J. Anderson, 2008. "US Consumer Inflation Expectations: Evidence Regarding Learning, Accuracy and Demographics," Centre for Growth and Business Cycle Research Discussion Paper Series 99, Economics, The University of Manchester.
    8. Creemers, An & Aerts, Marc & Hens, Niel & Molenberghs, Geert, 2012. "A nonparametric approach to weighted estimating equations for regression analysis with missing covariates," Computational Statistics & Data Analysis, Elsevier, vol. 56(1), pages 100-113, January.
    9. Joseph G. Ibrahim & Hongtu Zhu & Ramon I. Garcia & Ruixin Guo, 2011. "Fixed and Random Effects Selection in Mixed Effects Models," Biometrics, The International Biometric Society, vol. 67(2), pages 495-503, June.
    10. Cheng, Hao, 2021. "Importance sampling imputation algorithms in quantile regression with their application in CGSS data," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 188(C), pages 498-508.
    11. Huang Yangxin & Chen Ren & Dagne Getachew, 2011. "Simultaneous Bayesian Inference for Linear, Nonlinear and Semiparametric Mixed-Effects Models with Skew-Normality and Measurement Errors in Covariates," The International Journal of Biostatistics, De Gruyter, vol. 7(1), pages 1-28, January.
    12. Zhou, Lin & Tang, Yayong, 2021. "Linearly preconditioned nonlinear conjugate gradient acceleration of the PX-EM algorithm," Computational Statistics & Data Analysis, Elsevier, vol. 155(C).
    13. Björn Andersson & Tao Xin, 2021. "Estimation of Latent Regression Item Response Theory Models Using a Second-Order Laplace Approximation," Journal of Educational and Behavioral Statistics, , vol. 46(2), pages 244-265, April.
    14. Gerda Claeskens & Fabrizio Consentino, 2008. "Variable Selection with Incomplete Covariate Data," Biometrics, The International Biometric Society, vol. 64(4), pages 1062-1069, December.
    15. Liang, Hua & Su, Haiyan & Zou, Guohua, 2008. "Confidence intervals for a common mean with missing data with applications in an AIDS study," Computational Statistics & Data Analysis, Elsevier, vol. 53(2), pages 546-553, December.
    16. Giorgio Eduardo Montanari & Marco Doretti & Maria Francesca Marino, 2022. "Model-based two-way clustering of second-level units in ordinal multilevel latent Markov models," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 16(2), pages 457-485, June.
    17. Zhiwei Zhang & Zhen Chen & James F. Troendle & Jun Zhang, 2012. "Causal Inference on Quantiles with an Obstetric Application," Biometrics, The International Biometric Society, vol. 68(3), pages 697-706, September.
    18. Lu, Xiaosun & Huang, Yangxin & Zhu, Yiliang, 2016. "Finite mixture of nonlinear mixed-effects joint models in the presence of missing and mismeasured covariate, with application to AIDS studies," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 119-130.
    19. Zhiwei Zhang & Howard Rockette, 2006. "Semiparametric Maximum Likelihood for Missing Covariates in Parametric Regression," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 58(4), pages 687-706, December.
    20. Lingyun Lyu & Yu Cheng & Abdus S. Wahed, 2023. "Imputation‐based Q‐learning for optimizing dynamic treatment regimes with right‐censored survival outcome," Biometrics, The International Biometric Society, vol. 79(4), pages 3676-3689, December.

    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:bpj:ijbist:v:12:y:2016:i:1:p:65-77:n:8. 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: Peter Golla (email available below). General contact details of provider: https://www.degruyter.com .

    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.