IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v53y2009i4p1155-1166.html
   My bibliography  Save this article

Power series generalized nonlinear models

Author

Listed:
  • Cordeiro, Gauss M.
  • Andrade, Marinho G.
  • de Castro, Mário

Abstract

We introduce in this paper a new class of discrete generalized nonlinear models to extend the binomial, Poisson and negative binomial models to cope with count data. This class of models includes some important models such as log-nonlinear models, logit, probit and negative binomial nonlinear models, generalized Poisson and generalized negative binomial regression models, among other models, which enables the fitting of a wide range of models to count data. We derive an iterative process for fitting these models by maximum likelihood and discuss inference on the parameters. The usefulness of the new class of models is illustrated with an application to a real data set.

Suggested Citation

  • Cordeiro, Gauss M. & Andrade, Marinho G. & de Castro, Mário, 2009. "Power series generalized nonlinear models," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1155-1166, February.
    • Handle: RePEc:eee:csdana:v:53:y:2009:i:4:p:1155-1166
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-9473(08)00486-6
    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. P.C. Consul & F. Famoye, 1986. "On The Unimodality Of The Generalized Negative Binomial Distribution," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 40(3), pages 141-144, September.
    2. Rigby, R.A. & Stasinopoulos, D.M. & Akantziliotou, C., 2008. "A framework for modelling overdispersed count data, including the Poisson-shifted generalized inverse Gaussian distribution," Computational Statistics & Data Analysis, Elsevier, vol. 53(2), pages 381-393, December.
    3. R. A. Rigby & D. M. Stasinopoulos, 2005. "Generalized additive models for location, scale and shape," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 54(3), pages 507-554, June.
    4. Stasinopoulos, D. Mikis & Rigby, Robert A., 2007. "Generalized Additive Models for Location Scale and Shape (GAMLSS) in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 23(i07).
    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. Katiane S. Conceição & Marinho G. Andrade & Francisco Louzada & Nalini Ravishanker, 2022. "Characterizations and generalizations of the negative binomial distribution," Computational Statistics, Springer, vol. 37(3), pages 1255-1286, July.
    2. José Rodríguez-Avi & María José Olmo-Jiménez, 2017. "A regression model for overdispersed data without too many zeros," Statistical Papers, Springer, vol. 58(3), pages 749-773, September.
    3. Rodríguez-Avi, J. & Conde-Sánchez, A. & Sáez-Castillo, A.J. & Olmo-Jiménez, M.J. & Martínez-Rodríguez, A.M., 2009. "A generalized Waring regression model for count data," Computational Statistics & Data Analysis, Elsevier, vol. 53(10), pages 3717-3725, August.
    4. Marinho G. Andrade & Katiane S. Conceição & Nalini Ravishanker, 2024. "Zero-modified count time series modeling with an application to influenza cases," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 108(3), pages 611-637, September.

    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. Yixuan Wang & Jianzhu Li & Ping Feng & Rong Hu, 2015. "A Time-Dependent Drought Index for Non-Stationary Precipitation Series," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 29(15), pages 5631-5647, December.
    2. Panayi, Efstathios & Peters, Gareth W. & Danielsson, Jon & Zigrand, Jean-Pierre, 2018. "Designating market maker behaviour in limit order book markets," Econometrics and Statistics, Elsevier, vol. 5(C), pages 20-44.
    3. Gauss Cordeiro & Josemar Rodrigues & Mário Castro, 2012. "The exponential COM-Poisson distribution," Statistical Papers, Springer, vol. 53(3), pages 653-664, August.
    4. Christian Kleiber & Achim Zeileis, 2016. "Visualizing Count Data Regressions Using Rootograms," The American Statistician, Taylor & Francis Journals, vol. 70(3), pages 296-303, July.
    5. Matteo Malavasi & Gareth W. Peters & Pavel V. Shevchenko & Stefan Truck & Jiwook Jang & Georgy Sofronov, 2021. "Cyber Risk Frequency, Severity and Insurance Viability," Papers 2111.03366, arXiv.org, revised Mar 2022.
    6. Lucio Masserini & Matilde Bini & Monica Pratesi, 2017. "Effectiveness of non-selective evaluation test scores for predicting first-year performance in university career: a zero-inflated beta regression approach," Quality & Quantity: International Journal of Methodology, Springer, vol. 51(2), pages 693-708, March.
    7. Tong, Edward N.C. & Mues, Christophe & Thomas, Lyn, 2013. "A zero-adjusted gamma model for mortgage loan loss given default," International Journal of Forecasting, Elsevier, vol. 29(4), pages 548-562.
    8. Alexander Silbersdorff & Kai Sebastian Schneider, 2019. "Distributional Regression Techniques in Socioeconomic Research on the Inequality of Health with an Application on the Relationship between Mental Health and Income," IJERPH, MDPI, vol. 16(20), pages 1-28, October.
    9. Tong, Edward N.C. & Mues, Christophe & Brown, Iain & Thomas, Lyn C., 2016. "Exposure at default models with and without the credit conversion factor," European Journal of Operational Research, Elsevier, vol. 252(3), pages 910-920.
    10. Micha{l} Narajewski & Florian Ziel, 2020. "Ensemble Forecasting for Intraday Electricity Prices: Simulating Trajectories," Papers 2005.01365, arXiv.org, revised Aug 2020.
    11. D. Chiru Naik & Sagar Rohidas Chavan & P. Sonali, 2023. "Incorporating the climate oscillations in the computation of meteorological drought over India," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 117(3), pages 2617-2646, July.
    12. Shuhui Guo & Lihua Xiong & Jie Chen & Shenglian Guo & Jun Xia & Ling Zeng & Chong-Yu Xu, 2023. "Nonstationary Regional Flood Frequency Analysis Based on the Bayesian Method," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 37(2), pages 659-681, January.
    13. Maike Hohberg & Katja Landau & Thomas Kneib & Stephan Klasen & Walter Zucchini, 2018. "Vulnerability to poverty revisited: Flexible modeling and better predictive performance," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 16(3), pages 439-454, September.
    14. Kuntz, Laura-Chloé, 2020. "Beta dispersion and market timing," Journal of Empirical Finance, Elsevier, vol. 59(C), pages 235-256.
    15. Epstein, Leonardo D. & Inostroza-Quezada, Ignacio E. & Goodstein, Ronald C. & Choi, S. Chan, 2021. "Dynamic effects of store promotions on purchase conversion: Expanding technology applications with innovative analytics," Journal of Business Research, Elsevier, vol. 128(C), pages 279-289.
    16. Serinaldi, Francesco, 2011. "Distributional modeling and short-term forecasting of electricity prices by Generalized Additive Models for Location, Scale and Shape," Energy Economics, Elsevier, vol. 33(6), pages 1216-1226.
    17. Yolanda M. Gómez & Diego I. Gallardo & Marcelo Bourguignon & Eduardo Bertolli & Vinicius F. Calsavara, 2023. "A general class of promotion time cure rate models with a new biological interpretation," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 29(1), pages 66-86, January.
    18. Christophe Croux & Irène Gijbels & Ilaria Prosdocimi, 2012. "Robust Estimation of Mean and Dispersion Functions in Extended Generalized Additive Models," Biometrics, The International Biometric Society, vol. 68(1), pages 31-44, March.
    19. I. Gijbels & I. Prosdocimi & G. Claeskens, 2010. "Nonparametric estimation of mean and dispersion functions in extended generalized linear models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(3), pages 580-608, November.
    20. Groll, Andreas & Hambuckers, Julien & Kneib, Thomas & Umlauf, Nikolaus, 2019. "LASSO-type penalization in the framework of generalized additive models for location, scale and shape," Computational Statistics & Data Analysis, Elsevier, vol. 140(C), pages 59-73.

    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:53:y:2009:i:4:p:1155-1166. 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.