IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v54y2010i1p193-207.html
   My bibliography  Save this article

Joint analysis of mixed Poisson and continuous longitudinal data with nonignorable missing values

Author

Listed:
  • Yang, Ying
  • Kang, Jian

Abstract

Regression models are proposed for joint analysis of Poisson and continuous longitudinal data with nonignorable missing values under fully parametric framework. Our primary interest is to evaluate the influence of the covariates on both Poisson and continuous responses. First, we form the full likelihood with complete data using the multivariate Poisson model and conditional multivariate normal distribution and then construct an ECM algorithm to find the maximum likelihood estimates of the model parameters. Then, under the assumption that the missingness mechanisms for the two responses are independent but nonignorable, namely, dependent on both observed and missing data of the two responses, we choose the logit model for the missingness mechanisms and selection model for the full likelihood. Also, we build two implementations of the Monte Carlo EM algorithm for estimating the parameters in the model. Wald test is employed to test the significance of covariates. Finally, we present the results of the Monte Carlo simulation to evaluate the performance of the proposed methodology and an application to the interstitial cystitis data base (ICDB) cohort study. To the best of our knowledge, our model is the first parametric model for joint analysis of Poisson and continuous longitudinal data with nonignorable missing value.

Suggested Citation

  • Yang, Ying & Kang, Jian, 2010. "Joint analysis of mixed Poisson and continuous longitudinal data with nonignorable missing values," Computational Statistics & Data Analysis, Elsevier, vol. 54(1), pages 193-207, January.
    • Handle: RePEc:eee:csdana:v:54:y:2010:i:1:p:193-207
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-9473(09)00277-1
    Download Restriction: Full text for ScienceDirect subscribers only.
    ---><---

    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. Dimitris Karlis, 2003. "An EM algorithm for multivariate Poisson distribution and related models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 30(1), pages 63-77.
    2. Joseph G. Ibrahim & Ming-Hui Chen & Stuart R. Lipsitz & Amy H. Herring, 2005. "Missing-Data Methods for Generalized Linear Models: A Comparative Review," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 332-346, March.
    3. Roy J. & Lin X., 2002. "Analysis of Multivariate Longitudinal Outcomes With Nonignorable Dropouts and Missing Covariates: Changes in Methadone Treatment Practices," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 40-52, March.
    4. J. G. Booth & J. P. Hobert, 1999. "Maximizing generalized linear mixed model likelihoods with an automated Monte Carlo EM algorithm," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(1), pages 265-285.
    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. Xuerong Chen & Guoqing Diao & Jing Qin, 2020. "Pseudo likelihood‐based estimation and testing of missingness mechanism function in nonignorable missing data problems," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(4), pages 1377-1400, December.
    2. Wenqiong Xue & Jian Kang & F. DuBois Bowman & Tor D. Wager & Jian Guo, 2014. "Identifying functional co-activation patterns in neuroimaging studies via poisson graphical models," Biometrics, The International Biometric Society, vol. 70(4), pages 812-822, December.

    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. Hemant Kulkarni & Jayabrata Biswas & Kiranmoy Das, 2019. "A joint quantile regression model for multiple longitudinal outcomes," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 103(4), pages 453-473, December.
    2. Brent A. Coull & Alan Agresti, 2000. "Random Effects Modeling of Multiple Binomial Responses Using the Multivariate Binomial Logit-Normal Distribution," Biometrics, The International Biometric Society, vol. 56(1), pages 73-80, March.
    3. J. E. Mills & C. A. Field & D. J. Dupuis, 2002. "Marginally Specified Generalized Linear Mixed Models: A Robust Approach," Biometrics, The International Biometric Society, vol. 58(4), pages 727-734, December.
    4. Ryo Kato & Takahiro Hoshino, 2020. "Semiparametric Bayesian multiple imputation for regression models with missing mixed continuous–discrete covariates," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(3), pages 803-825, June.
    5. Li Cai & Lijie Gu & Qihua Wang & Suojin Wang, 2021. "Simultaneous confidence bands for nonparametric regression with missing covariate data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(6), pages 1249-1279, December.
    6. Jan Pablo Burgard & Patricia Dörr & Ralf Münnich, 2020. "Monte-Carlo Simulation Studies in Survey Statistics – An Appraisal," Research Papers in Economics 2020-04, University of Trier, Department of Economics.
    7. McDonough, Ian K. & Millimet, Daniel L., 2017. "Missing data, imputation, and endogeneity," Journal of Econometrics, Elsevier, vol. 199(2), pages 141-155.
    8. J. Andrew Royle, 2009. "Analysis of Capture–Recapture Models with Individual Covariates Using Data Augmentation," Biometrics, The International Biometric Society, vol. 65(1), pages 267-274, March.
    9. Jiang, Depeng & Zhao, Puying & Tang, Niansheng, 2016. "A propensity score adjustment method for regression models with nonignorable missing covariates," Computational Statistics & Data Analysis, Elsevier, vol. 94(C), pages 98-119.
    10. Harding, Matthew & Lamarche, Carlos, 2019. "A panel quantile approach to attrition bias in Big Data: Evidence from a randomized experiment," Journal of Econometrics, Elsevier, vol. 211(1), pages 61-82.
    11. J. F. Lawless, 2018. "Two-phase outcome-dependent studies for failure times and testing for effects of expensive covariates," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 24(1), pages 28-44, January.
    12. Hui Yao & Sungduk Kim & Ming-Hui Chen & Joseph G. Ibrahim & Arvind K. Shah & Jianxin Lin, 2015. "Bayesian Inference for Multivariate Meta-Regression With a Partially Observed Within-Study Sample Covariance Matrix," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(510), pages 528-544, June.
    13. Yi Qian & Hui Xie, 2011. "No Customer Left Behind: A Distribution-Free Bayesian Approach to Accounting for Missing Xs in Marketing Models," Marketing Science, INFORMS, vol. 30(4), pages 717-736, July.
    14. Jiang, Wei & Josse, Julie & Lavielle, Marc, 2020. "Logistic regression with missing covariates—Parameter estimation, model selection and prediction within a joint-modeling framework," Computational Statistics & Data Analysis, Elsevier, vol. 145(C).
    15. Patricia Dörr & Jan Pablo Burgard, 2019. "Data-driven transformations and survey-weighting for linear mixed models," Research Papers in Economics 2019-16, University of Trier, Department of Economics.
    16. An, Xinming & Bentler, Peter M., 2012. "Efficient direct sampling MCEM algorithm for latent variable models with binary responses," Computational Statistics & Data Analysis, Elsevier, vol. 56(2), pages 231-244.
    17. Hongbin Zhang & Lang Wu, 2018. "A non‐linear model for censored and mismeasured time varying covariates in survival models, with applications in human immunodeficiency virus and acquired immune deficiency syndrome studies," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 67(5), pages 1437-1450, November.
    18. Baojiang Chen & Xiao-Hua Zhou, 2011. "Doubly Robust Estimates for Binary Longitudinal Data Analysis with Missing Response and Missing Covariates," Biometrics, The International Biometric Society, vol. 67(3), pages 830-842, September.
    19. Tortora, Cristina & Franczak, Brian C. & Bagnato, Luca & Punzo, Antonio, 2024. "A Laplace-based model with flexible tail behavior," Computational Statistics & Data Analysis, Elsevier, vol. 192(C).
    20. Zhuoer Sun & Suojin Wang, 2019. "Semiparametric estimation in regression with missing covariates using single-index models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(5), pages 1201-1232, October.

    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:eee:csdana:v:54:y:2010:i:1:p:193-207. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    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.