IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v87y2003i2p398-412.html
   My bibliography  Save this article

On familial longitudinal Poisson mixed models with gamma random effects

Author

Listed:
  • Sutradhar, Brajendra C.
  • Jowaheer, Vandna

Abstract

Poisson mixed models are used to analyze a wide variety of cluster count data. These models are commonly developed based on the assumption that the random effects have either the log-normal or the gamma distribution. Obtaining consistent as well as efficient estimates for the parameters involved in such Poisson mixed models has, however, proven to be difficult. Further problem gets mounted when the data are collected repeatedly from the individuals of the same cluster or family. In this paper, we introduce a generalized quasilikelihood approach to analyze the repeated familial data based on the familial structure caused by gamma random effects. This approach provides estimates of the regression parameters and the variance component of the random effects after taking the longitudinal correlations of the data into account. The estimators are consistent as well as highly efficient.

Suggested Citation

  • Sutradhar, Brajendra C. & Jowaheer, Vandna, 2003. "On familial longitudinal Poisson mixed models with gamma random effects," Journal of Multivariate Analysis, Elsevier, vol. 87(2), pages 398-412, November.
    • Handle: RePEc:eee:jmvana:v:87:y:2003:i:2:p:398-412
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(03)00062-9
    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. Ludwig Fahrmeir & Stefan Lang, 2001. "Bayesian inference for generalized additive mixed models based on Markov random field priors," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 50(2), pages 201-220.
    2. Sutradhar, Brajendra C. & Rao, R. Prabhakar, 2001. "On Marginal Quasi-Likelihood Inference in Generalized Linear Mixed Models," Journal of Multivariate Analysis, Elsevier, vol. 76(1), pages 1-34, January.
    3. C. Sutradhar, Brajendra & Das, Kalyan, 2001. "A higher-order approximation to likelihood inference in the Poisson mixed model," Statistics & Probability Letters, Elsevier, vol. 52(1), pages 59-67, March.
    4. X. Lin & D. Zhang, 1999. "Inference in generalized additive mixed modelsby using smoothing splines," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(2), pages 381-400, April.
    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. Brajendra C. Sutradhar & Vandna Jowaheer & Gary Sneddon, 2008. "On a Unified Generalized Quasi–likelihood Approach for Familial–Longitudinal Non‐Stationary Count Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 35(4), pages 597-612, December.
    2. Brajendra C. Sutradhar, 2024. "Inferences for Fixed Effects Based Regression Parameters in a Finite Population Setup Using Two-stage Cluster Sample," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 86(2), pages 951-991, August.
    3. Youn Ahn, Jae & Jeong, Himchan & Lu, Yang, 2021. "On the ordering of credibility factors," Insurance: Mathematics and Economics, Elsevier, vol. 101(PB), pages 626-638.

    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. Belitz, Christiane & Lang, Stefan, 2008. "Simultaneous selection of variables and smoothing parameters in structured additive regression models," Computational Statistics & Data Analysis, Elsevier, vol. 53(1), pages 61-81, September.
    2. Tamvada, Jagannadha Pawan, 2010. "The Dynamics of Self-employment in a Developing Country: Evidence from India," MPRA Paper 20042, University Library of Munich, Germany.
    3. Duncan Lee & Gavin Shaddick, 2007. "Time-Varying Coefficient Models for the Analysis of Air Pollution and Health Outcome Data," Biometrics, The International Biometric Society, vol. 63(4), pages 1253-1261, December.
    4. Umlauf, Nikolaus & Adler, Daniel & Kneib, Thomas & Lang, Stefan & Zeileis, Achim, 2015. "Structured Additive Regression Models: An R Interface to BayesX," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 63(i21).
    5. Nadja Klein & Michel Denuit & Stefan Lang & Thomas Kneib, 2013. "Nonlife Ratemaking and Risk Management with Bayesian Additive Models for Location, Scale and Shape," Working Papers 2013-24, Faculty of Economics and Statistics, Universität Innsbruck.
    6. Tutz, Gerhard, 2004. "Generalized semiparametrically structured mixed models," Computational Statistics & Data Analysis, Elsevier, vol. 46(4), pages 777-800, July.
    7. Nicole H. Augustin & Stefan Lang & Monica Musio & Klaus Von Wilpert, 2007. "A spatial model for the needle losses of pine‐trees in the forests of Baden‐Württemberg: an application of Bayesian structured additive regression," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 56(1), pages 29-50, January.
    8. Gamerman, Dani & Moreira, Ajax R. B., 2004. "Multivariate spatial regression models," Journal of Multivariate Analysis, Elsevier, vol. 91(2), pages 262-281, November.
    9. Colin O. Wu & Kai F. Yu, 2002. "Nonparametric Varying-Coefficient Models for the Analysis of Longitudinal Data," International Statistical Review, International Statistical Institute, vol. 70(3), pages 373-393, December.
    10. Simon N. Wood, 2006. "Low-Rank Scale-Invariant Tensor Product Smooths for Generalized Additive Mixed Models," Biometrics, The International Biometric Society, vol. 62(4), pages 1025-1036, December.
    11. Klein, Nadja & Denuit, Michel & Lang, Stefan & Kneib, Thomas, 2013. "Nonlife Ratemaking and Risk Management with Bayesian Additive Models for Location, Scale and Shape," LIDAM Discussion Papers ISBA 2013045, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    12. Denuit, Michel & Lang, Stefan, 2004. "Non-life rate-making with Bayesian GAMs," Insurance: Mathematics and Economics, Elsevier, vol. 35(3), pages 627-647, December.
    13. Thomas Kneib & Ludwig Fahrmeir, 2006. "Structured Additive Regression for Categorical Space–Time Data: A Mixed Model Approach," Biometrics, The International Biometric Society, vol. 62(1), pages 109-118, March.
    14. Brezger, Andreas & Lang, Stefan, 2006. "Generalized structured additive regression based on Bayesian P-splines," Computational Statistics & Data Analysis, Elsevier, vol. 50(4), pages 967-991, February.
    15. Xiao Ni & Daowen Zhang & Hao Helen Zhang, 2010. "Variable Selection for Semiparametric Mixed Models in Longitudinal Studies," Biometrics, The International Biometric Society, vol. 66(1), pages 79-88, March.
    16. Simon N. Wood & Natalya Pya & Benjamin Säfken, 2016. "Smoothing Parameter and Model Selection for General Smooth Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(516), pages 1548-1563, October.
    17. Thomas A. Murray & Brian P. Hobbs & Theodore C. Lystig & Bradley P. Carlin, 2014. "Semiparametric Bayesian commensurate survival model for post-market medical device surveillance with non-exchangeable historical data," Biometrics, The International Biometric Society, vol. 70(1), pages 185-191, March.
    18. Lawrence N Kazembe, 2013. "A Bayesian Two Part Model Applied to Analyze Risk Factors of Adult Mortality with Application to Data from Namibia," PLOS ONE, Public Library of Science, vol. 8(9), pages 1-10, September.
    19. Rouven E. Haschka & Helmut Herwartz, 2022. "Endogeneity in pharmaceutical knowledge generation: An instrument‐free copula approach for Poisson frontier models," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 31(4), pages 942-960, November.
    20. Ding, Hui & Zhang, Jian & Zhang, Riquan, 2022. "Nonparametric variable screening for multivariate additive models," Journal of Multivariate Analysis, Elsevier, vol. 192(C).

    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:87:y:2003:i:2:p:398-412. 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.