IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v102y2011i1p61-72.html
   My bibliography  Save this article

Semiparametric analysis of longitudinal zero-inflated count data

Author

Listed:
  • Feng, Jiarui
  • Zhu, Zhongyi

Abstract

In this article, we consider a semiparametric zero-inflated Poisson mixed model that postulates a possible nonlinear relationship between the natural logarithm of the mean of the counts and a particular covariate in the longitudinal studies. A penalized log-likelihood function is proposed and Monte Carlo expectation-maximization algorithm is used to derive the estimates. Under some mild conditions, we establish the consistency and asymptotic normality of the resulting estimators. Simulation studies are carried out to investigate the finite sample performance of the proposed method. For illustration purposes, the method is applied to a data set from a pharmaceutical company where the variable of interest is the number of episodes of side effects after the patient has taken the treatments.

Suggested Citation

  • Feng, Jiarui & Zhu, Zhongyi, 2011. "Semiparametric analysis of longitudinal zero-inflated count data," Journal of Multivariate Analysis, Elsevier, vol. 102(1), pages 61-72, January.
    • Handle: RePEc:eee:jmvana:v:102:y:2011:i:1:p:61-72
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(10)00160-0
    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. Yu Y. & Ruppert D., 2002. "Penalized Spline Estimation for Partially Linear Single-Index Models," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 1042-1054, December.
    2. D. Böhning & E. Dietz & P. Schlattmann & L. Mendonça & U. Kirchner, 1999. "The zero‐inflated Poisson model and the decayed, missing and filled teeth index in dental epidemiology," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 162(2), pages 195-209.
    3. Lin X. & Carroll R. J., 2001. "Semiparametric Regression for Clustered Data Using Generalized Estimating Equations," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1045-1056, September.
    4. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521785167.
    5. Yuan, Ke-Hai & Jennrich, Robert I., 1998. "Asymptotics of Estimating Equations under Natural Conditions," Journal of Multivariate Analysis, Elsevier, vol. 65(2), pages 245-260, May.
    6. Daniel B. Hall, 2000. "Zero-Inflated Poisson and Binomial Regression with Random Effects: A Case Study," Biometrics, The International Biometric Society, vol. 56(4), pages 1030-1039, December.
    7. Guo You Qin & Zhong Yi Zhu, 2009. "Robustified Maximum Likelihood Estimation in Generalized Partial Linear Mixed Model for Longitudinal Data," Biometrics, The International Biometric Society, vol. 65(1), pages 52-59, March.
    8. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521780506.
    9. K. F. Lam & Hongqi Xue & Yin Bun Cheung, 2006. "Semiparametric Analysis of Zero-Inflated Count Data," Biometrics, The International Biometric Society, vol. 62(4), pages 996-1003, December.
    10. Annie Qu & Runze Li, 2006. "Quadratic Inference Functions for Varying-Coefficient Models with Longitudinal Data," Biometrics, The International Biometric Society, vol. 62(2), pages 379-391, 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. Timothy K.M. Beatty & Erling Røed Larsen, 2005. "Using Engel curves to estimate bias in the Canadian CPI as a cost of living index," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 38(2), pages 482-499, May.
    2. Ferraccioli, Federico & Sangalli, Laura M. & Finos, Livio, 2022. "Some first inferential tools for spatial regression with differential regularization," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    3. Tousifur Rahman & Partha Jyoti Hazarika & M. Masoom Ali & Manash Pratim Barman, 2022. "Three-Inflated Poisson Distribution and its Application in Suicide Cases of India During Covid-19 Pandemic," Annals of Data Science, Springer, vol. 9(5), pages 1103-1127, October.
    4. Li, Jinqing & Ma, Jun, 2019. "Maximum penalized likelihood estimation of additive hazards models with partly interval censoring," Computational Statistics & Data Analysis, Elsevier, vol. 137(C), pages 170-180.
    5. M. Taavoni & M. Arashi, 2021. "Kernel estimation in semiparametric mixed effect longitudinal modeling," Statistical Papers, Springer, vol. 62(3), pages 1095-1116, June.
    6. Yazhao Lv & Riquan Zhang & Weihua Zhao & Jicai Liu, 2015. "Quantile regression and variable selection of partial linear single-index model," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 67(2), pages 375-409, April.
    7. Cao, Yanrong & Lin, Haiqun & Wu, Tracy Z. & Yu, Yan, 2010. "Penalized spline estimation for functional coefficient regression models," Computational Statistics & Data Analysis, Elsevier, vol. 54(4), pages 891-905, April.
    8. Sumanta Adhya & Tathagata Banerjee & Gaurangadeb Chattopadhyay, 2012. "Inference on finite population categorical response: nonparametric regression-based predictive approach," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 96(1), pages 69-98, January.
    9. Wu, Chaojiang & Yu, Yan, 2014. "Partially linear modeling of conditional quantiles using penalized splines," Computational Statistics & Data Analysis, Elsevier, vol. 77(C), pages 170-187.
    10. Wu, Ximing & Sickles, Robin, 2018. "Semiparametric estimation under shape constraints," Econometrics and Statistics, Elsevier, vol. 6(C), pages 74-89.
    11. Zou, Yubo & Zhang, Jiajia & Qin, Guoyou, 2011. "A semiparametric accelerated failure time partial linear model and its application to breast cancer," Computational Statistics & Data Analysis, Elsevier, vol. 55(3), pages 1479-1487, March.
    12. Lai, Peng & Li, Gaorong & Lian, Heng, 2013. "Quadratic inference functions for partially linear single-index models with longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 118(C), pages 115-127.
    13. Ma, Shujie & Liang, Hua & Tsai, Chih-Ling, 2014. "Partially linear single index models for repeated measurements," Journal of Multivariate Analysis, Elsevier, vol. 130(C), pages 354-375.
    14. Tang, Nian-Sheng & Duan, Xing-De, 2012. "A semiparametric Bayesian approach to generalized partial linear mixed models for longitudinal data," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 4348-4365.
    15. Kauermann Goeran & Krivobokova Tatyana & Semmler Willi, 2011. "Filtering Time Series with Penalized Splines," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 15(2), pages 1-28, March.
    16. Holland, Ashley D., 2017. "Penalized spline estimation in the partially linear model," Journal of Multivariate Analysis, Elsevier, vol. 153(C), pages 211-235.
    17. Huang, Lei & Jiang, Hui & Wang, Huixia, 2019. "A novel partial-linear single-index model for time series data," Computational Statistics & Data Analysis, Elsevier, vol. 134(C), pages 110-122.
    18. Muggeo, Vito M.R. & Ferrara, Giancarlo, 2008. "Fitting generalized linear models with unspecified link function: A P-spline approach," Computational Statistics & Data Analysis, Elsevier, vol. 52(5), pages 2529-2537, January.
    19. Tang, Nian-Sheng & Duan, Xing-De, 2014. "Bayesian influence analysis of generalized partial linear mixed models for longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 126(C), pages 86-99.
    20. Jia Chen & Jiti Gao & Degui Li, 2013. "Estimation in Partially Linear Single-Index Panel Data Models With Fixed Effects," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 31(3), pages 315-330, July.

    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:jmvana:v:102:y:2011:i:1:p:61-72. 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/wps/find/journaldescription.cws_home/622892/description#description .

    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.