IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v121y2018icp71-88.html
   My bibliography  Save this article

Efficient estimation of COM–Poisson regression and a generalized additive model

Author

Listed:
  • Chatla, Suneel Babu
  • Shmueli, Galit

Abstract

The Conway–Maxwell–Poisson (CMP) or COM–Poisson regression is a popular model for count data due to its ability to capture both under dispersion and over dispersion. However, CMP regression is limited when dealing with complex nonlinear relationships. With today’s wide availability of count data, especially due to the growing collection of data on human and social behavior, there is need for count data models that can capture complex nonlinear relationships. One useful approach is additive models; but, there has been no additive model implementation for the CMP distribution. To fill this void, we first propose a flexible estimation framework for CMP regression based on iterative reweighed least squares (IRLS) and then extend this model to allow for additive components using a penalized splines approach. Because the CMP distribution belongs to the exponential family, convergence of IRLS is guaranteed under some regularity conditions. Further, it is also known that IRLS provides smaller standard errors compared to gradient-based methods. We illustrate the usefulness of this approach through extensive simulation studies and using real data from a bike sharing system in Washington, DC.

Suggested Citation

  • Chatla, Suneel Babu & Shmueli, Galit, 2018. "Efficient estimation of COM–Poisson regression and a generalized additive model," Computational Statistics & Data Analysis, Elsevier, vol. 121(C), pages 71-88.
    • Handle: RePEc:eee:csdana:v:121:y:2018:i:c:p:71-88
    DOI: 10.1016/j.csda.2017.11.011
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947317302608
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2017.11.011?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. 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.
    2. Simon N. Wood, 2011. "Fast stable restricted maximum likelihood and marginal likelihood estimation of semiparametric generalized linear models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 73(1), pages 3-36, January.
    3. Simon N. Wood, 2004. "Stable and Efficient Multiple Smoothing Parameter Estimation for Generalized Additive Models," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 673-686, January.
    4. Ramesh Gupta & S. Sim & S. Ong, 2014. "Analysis of discrete data by Conway–Maxwell Poisson distribution," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 98(4), pages 327-343, October.
    5. Simon N. Wood, 2008. "Fast stable direct fitting and smoothness selection for generalized additive models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(3), pages 495-518, July.
    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. Darcy Steeg Morris & Kimberly F. Sellers, 2022. "A Flexible Mixed Model for Clustered Count Data," Stats, MDPI, vol. 5(1), pages 1-18, January.

    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. Longhi, Christian & Musolesi, Antonio & Baumont, Catherine, 2014. "Modeling structural change in the European metropolitan areas during the process of economic integration," Economic Modelling, Elsevier, vol. 37(C), pages 395-407.
    2. Musolesi Antonio & Mazzanti Massimiliano, 2014. "Nonlinearity, heterogeneity and unobserved effects in the carbon dioxide emissions-economic development relation for advanced countries," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 18(5), pages 1-21, December.
    3. Longhi, C. & Musolesi, A. & Baumont, C., 2013. "Modeling the industrial dynamics of the European metropolitan areas during the process of economic integration: a semiparametric approach," Working Papers 2013-10, Grenoble Applied Economics Laboratory (GAEL).
    4. Roland Langrock & Timo Adam & Vianey Leos‐Barajas & Sina Mews & David L. Miller & Yannis P. Papastamatiou, 2018. "Spline‐based nonparametric inference in general state‐switching models," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 72(3), pages 179-200, August.
    5. Sergei Kharin & Zuzana Kapustova & Ivan Lichner, 2023. "Price transmission between maize and poultry product markets in the Visegrád Group countries: What is more nonlinear, egg or chicken?," Agricultural Economics, Czech Academy of Agricultural Sciences, vol. 69(12), pages 510-522.
    6. Rodríguez-Álvarez, María Xosé & Lee, Dae-Jin & Kneib, Thomas & Durbán, María & Eilers, Paul, 2013. "Fast algorithm for smoothing parameter selection in multidimensional generalized P-splines," DES - Working Papers. Statistics and Econometrics. WS ws133026, Universidad Carlos III de Madrid. Departamento de Estadística.
    7. Mazzanti, Massimiliano & Musolesi, Antonio, 2013. "Nonlinearity, Heterogeneity and Unobserved Effects in the CO2-income Relation for Advanced Countries," Climate Change and Sustainable Development 162374, Fondazione Eni Enrico Mattei (FEEM).
    8. Strasak, Alexander M. & Umlauf, Nikolaus & Pfeiffer, Ruth M. & Lang, Stefan, 2011. "Comparing penalized splines and fractional polynomials for flexible modelling of the effects of continuous predictor variables," Computational Statistics & Data Analysis, Elsevier, vol. 55(4), pages 1540-1551, April.
    9. Roberto Basile & Luigi Benfratello & Davide Castellani, 2012. "Geoadditive models for regional count data: an application to industrial location," ERSA conference papers ersa12p83, European Regional Science Association.
    10. E. Zanini & E. Eastoe & M. J. Jones & D. Randell & P. Jonathan, 2020. "Flexible covariate representations for extremes," Environmetrics, John Wiley & Sons, Ltd., vol. 31(5), August.
    11. Daniel Melser & Robert J. Hill, 2019. "Residential Real Estate, Risk, Return and Diversification: Some Empirical Evidence," The Journal of Real Estate Finance and Economics, Springer, vol. 59(1), pages 111-146, July.
    12. Maciej Berȩsewicz & Dagmara Nikulin, 2021. "Estimation of the size of informal employment based on administrative records with non‐ignorable selection mechanism," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 70(3), pages 667-690, June.
    13. Adam R. Pines & Bart Larsen & Zaixu Cui & Valerie J. Sydnor & Maxwell A. Bertolero & Azeez Adebimpe & Aaron F. Alexander-Bloch & Christos Davatzikos & Damien A. Fair & Ruben C. Gur & Raquel E. Gur & H, 2022. "Dissociable multi-scale patterns of development in personalized brain networks," Nature Communications, Nature, vol. 13(1), pages 1-15, December.
    14. Marra, Giampiero & Wood, Simon N., 2011. "Practical variable selection for generalized additive models," Computational Statistics & Data Analysis, Elsevier, vol. 55(7), pages 2372-2387, July.
    15. Daniel Melser, 2017. "Residential Real Estate, Risk, Return and Home Characteristics: Evidence from Sydney 2002-14," ERES eres2017_296, European Real Estate Society (ERES).
    16. Tetsuya Tsurumi & Shunsuke Managi, 2010. "Decomposition of the environmental Kuznets curve: scale, technique, and composition effects," Environmental Economics and Policy Studies, Springer;Society for Environmental Economics and Policy Studies - SEEPS, vol. 11(1), pages 19-36, February.
    17. Jean Chung & Guanchao Tong & Jiayou Chao & Wei Zhu, 2021. "Path Analysis of Sea-Level Rise and Its Impact," Stats, MDPI, vol. 5(1), pages 1-14, December.
    18. Isabel Proença & Stefan Sperlich & Duygu Savaşcı, 2015. "Semi-mixed effects gravity models for bilateral trade," Empirical Economics, Springer, vol. 48(1), pages 361-387, February.
    19. Phung Khanh Lam & Dong Thi Hoai Tam & Nguyen Minh Dung & Nguyen Thi Hanh Tien & Nguyen Tan Thanh Kieu & Cameron Simmons & Jeremy Farrar & Bridget Wills & Marcel Wolbers, 2015. "A Prognostic Model for Development of Profound Shock among Children Presenting with Dengue Shock Syndrome," PLOS ONE, Public Library of Science, vol. 10(5), pages 1-13, May.
    20. Øystein Sørensen & Anders M. Fjell & Kristine B. Walhovd, 2023. "Longitudinal Modeling of Age-Dependent Latent Traits with Generalized Additive Latent and Mixed Models," Psychometrika, Springer;The Psychometric Society, vol. 88(2), pages 456-486, June.

    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:121:y:2018:i:c:p:71-88. 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.