IDEAS home Printed from https://ideas.repec.org/a/spr/stpapr/v58y2017i2d10.1007_s00362-015-0708-9.html
   My bibliography  Save this article

A conditional count model for repeated count data and its application to GEE approach

Author

Listed:
  • Rajib Dey

    (Hajee Mohammad Danesh Science & Technology University)

  • M. Ataharul Islam

    (East West University)

Abstract

In this article, a conditional model is proposed for modeling longitudinal count data. The joint density is disintegrated into the marginal and conditional densities according to the multiplication rule. It allows both positive and negative correlation among variables, which most multivariate count models do not possess. To show the efficiency of the proposed model for count data, we have applied to the generalized estimating equations and the inverse Fisher information matrix is compared with the covariance matrix from estimating equations. A simulation experiment is displayed and an application of the model to divorce data is presented. In addition, a comparison of conditional model and bivariate Poisson model proposed by Kocherlakota and Kocherlakota has shown using simulated data.

Suggested Citation

  • Rajib Dey & M. Ataharul Islam, 2017. "A conditional count model for repeated count data and its application to GEE approach," Statistical Papers, Springer, vol. 58(2), pages 485-504, June.
    • Handle: RePEc:spr:stpapr:v:58:y:2017:i:2:d:10.1007_s00362-015-0708-9
    DOI: 10.1007/s00362-015-0708-9
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00362-015-0708-9
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00362-015-0708-9?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. Gourieroux, Christian & Monfort, Alain & Trognon, Alain, 1984. "Pseudo Maximum Likelihood Methods: Theory," Econometrica, Econometric Society, vol. 52(3), pages 681-700, May.
    2. Arnold, Barry C., 1987. "Bivariate distributions with pareto conditionals," Statistics & Probability Letters, Elsevier, vol. 5(4), pages 263-266, June.
    3. Galit Shmueli & Thomas P. Minka & Joseph B. Kadane & Sharad Borle & Peter Boatwright, 2005. "A useful distribution for fitting discrete data: revival of the Conway–Maxwell–Poisson distribution," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 54(1), pages 127-142, January.
    4. Jung, Robert C & Winkelmann, Rainer, 1993. "Two Aspects of Labor Mobility: A Bivariate Poisson Regression Approach," Empirical Economics, Springer, vol. 18(3), pages 543-556.
    5. Murat K. Munkin & Pravin K. Trivedi, 1999. "Simulated maximum likelihood estimation of multivariate mixed-Poisson regression models, with application," Econometrics Journal, Royal Economic Society, vol. 2(1), pages 29-48.
    6. Gauss Cordeiro & Josemar Rodrigues & Mário Castro, 2012. "The exponential COM-Poisson distribution," Statistical Papers, Springer, vol. 53(3), pages 653-664, August.
    7. Peter Xue‐Kun Song, 2000. "Multivariate Dispersion Models Generated From Gaussian Copula," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 27(2), pages 305-320, June.
    8. Peter Berkhout & Erik Plug, 2004. "A bivariate Poisson count data model using conditional probabilities," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 58(3), pages 349-364, August.
    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. Greene, William, 2007. "Functional Form and Heterogeneity in Models for Count Data," Foundations and Trends(R) in Econometrics, now publishers, vol. 1(2), pages 113-218, August.
    2. Aristidis Nikoloulopoulos & Dimitris Karlis, 2010. "Regression in a copula model for bivariate count data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(9), pages 1555-1568.
    3. Atella, Vincenzo & Deb, Partha, 2008. "Are primary care physicians, public and private sector specialists substitutes or complements? Evidence from a simultaneous equations model for count data," Journal of Health Economics, Elsevier, vol. 27(3), pages 770-785, May.
    4. Tzougas, George & Makariou, Despoina, 2022. "The multivariate Poisson-Generalized Inverse Gaussian claim count regression model with varying dispersion and shape parameters," LSE Research Online Documents on Economics 117197, London School of Economics and Political Science, LSE Library.
    5. Marco Alfò & Giovanni Trovato, 2004. "Semiparametric Mixture Models for Multivariate Count Data, with Application," CEIS Research Paper 51, Tor Vergata University, CEIS.
    6. William Greene, 2007. "Correlation in Bivariate Poisson Regression Model," Working Papers 07-14, New York University, Leonard N. Stern School of Business, Department of Economics.
    7. Lluís Bermúdez & Dimitris Karlis, 2022. "Copula-based bivariate finite mixture regression models with an application for insurance claim count data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(4), pages 1082-1099, December.
    8. Fokianos, Konstantinos, 2024. "Multivariate Count Time Series Modelling," Econometrics and Statistics, Elsevier, vol. 31(C), pages 100-116.
    9. Morris, Darcy Steeg & Raim, Andrew M. & Sellers, Kimberly F., 2020. "A Conway–Maxwell-multinomial distribution for flexible modeling of clustered categorical data," Journal of Multivariate Analysis, Elsevier, vol. 179(C).
    10. Rufin Bidounga & Evrand Giles Brunel Mandangui Maloumbi & Réolie Foxie Mizélé Kitoti & Dominique Mizère, 2020. "The New Bivariate Conway-Maxwell-Poisson Distribution Obtained by the Crossing Method," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 9(6), pages 1-1, November.
    11. Najla Qarmalah & Abdulhamid A. Alzaid, 2023. "Zero-Dependent Bivariate Poisson Distribution with Applications," Mathematics, MDPI, vol. 11(5), pages 1-16, February.
    12. Eugenio Miravete, 2014. "Testing for complementarities among countable strategies," Empirical Economics, Springer, vol. 46(4), pages 1521-1544, June.
    13. George Tzougas & Despoina Makariou, 2022. "The multivariate Poisson‐Generalized Inverse Gaussian claim count regression model with varying dispersion and shape parameters," Risk Management and Insurance Review, American Risk and Insurance Association, vol. 25(4), pages 401-417, December.
    14. Giuliani, Elisa & Martinelli, Arianna & Rabellotti, Roberta, 2016. "Is Co-Invention Expediting Technological Catch Up? A Study of Collaboration between Emerging Country Firms and EU Inventors," World Development, Elsevier, vol. 77(C), pages 192-205.
    15. Bijwaard, G.E. & Franses, Ph.H.B.F., 2006. "Does rounding matter for payment efficiency?," Econometric Institute Research Papers EI 2006-43, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    16. Bettina Becker & Martin Theuringer, 2000. "Macroeconomic Determinants of Contingent Protection: The Case of the European Union," IWP Discussion Paper Series 02/2000, Institute for Economic Policy, Cologne, Germany.
    17. Broze, Laurence & Gourieroux, Christian, 1998. "Pseudo-maximum likelihood method, adjusted pseudo-maximum likelihood method and covariance estimators," Journal of Econometrics, Elsevier, vol. 85(1), pages 75-98, July.
    18. Hallin, Marc & La Vecchia, Davide, 2020. "A Simple R-estimation method for semiparametric duration models," Journal of Econometrics, Elsevier, vol. 218(2), pages 736-749.
    19. Magnus, Jan R., 2007. "The Asymptotic Variance Of The Pseudo Maximum Likelihood Estimator," Econometric Theory, Cambridge University Press, vol. 23(5), pages 1022-1032, October.
    20. Wolfgang Keller & Arik Levinson, 1999. "Environmental Compliance Costs and Foreign Direct Investment Inflows to U.S. States," NBER Working Papers 7369, National Bureau of Economic Research, Inc.

    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:spr:stpapr:v:58:y:2017:i:2:d:10.1007_s00362-015-0708-9. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.