IDEAS home Printed from https://ideas.repec.org/a/spr/stmapp/v30y2021i4d10.1007_s10260-021-00558-6.html
   My bibliography  Save this article

Transition models for count data: a flexible alternative to fixed distribution models

Author

Listed:
  • Moritz Berger

    (Medizinische Fakultät, Universität Bonn)

  • Gerhard Tutz

    (Ludwig-Maximilians-Universität München)

Abstract

A flexible semiparametric class of models is introduced that offers an alternative to classical regression models for count data as the Poisson and Negative Binomial model, as well as to more general models accounting for excess zeros that are also based on fixed distributional assumptions. The model allows that the data itself determine the distribution of the response variable, but, in its basic form, uses a parametric term that specifies the effect of explanatory variables. In addition, an extended version is considered, in which the effects of covariates are specified nonparametrically. The proposed model and traditional models are compared in simulations and by utilizing several real data applications from the area of health and social science.

Suggested Citation

  • Moritz Berger & Gerhard Tutz, 2021. "Transition models for count data: a flexible alternative to fixed distribution models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(4), pages 1259-1283, October.
    • Handle: RePEc:spr:stmapp:v:30:y:2021:i:4:d:10.1007_s10260-021-00558-6
    DOI: 10.1007/s10260-021-00558-6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10260-021-00558-6
    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/s10260-021-00558-6?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. Cameron,A. Colin & Trivedi,Pravin K., 2013. "Regression Analysis of Count Data," Cambridge Books, Cambridge University Press, number 9781107667273.
    2. Zeileis, Achim & Kleiber, Christian & Jackman, Simon, 2008. "Regression Models for Count Data in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 27(i08).
    3. Mullahy, John, 1986. "Specification and testing of some modified count data models," Journal of Econometrics, Elsevier, vol. 33(3), pages 341-365, December.
    4. Hilbe,Joseph M., 2014. "Modeling Count Data," Cambridge Books, Cambridge University Press, number 9781107028333, November.
    5. Deb, Partha & Trivedi, Pravin K, 1997. "Demand for Medical Care by the Elderly: A Finite Mixture Approach," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 12(3), pages 313-336, May-June.
    6. Ludwig Fahrmeir & Heinz Kaufmann, 1987. "Regression Models For Non‐Stationary Categorical Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 8(2), pages 147-160, March.
    7. Claudia Czado & Tilmann Gneiting & Leonhard Held, 2009. "Predictive Model Assessment for Count Data," Biometrics, The International Biometric Society, vol. 65(4), pages 1254-1261, December.
    8. Michael D. Creel & John B. Loomis, 1990. "Theoretical and Empirical Advantages of Truncated Count Data Estimators for Analysis of Deer Hunting in California," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 72(2), pages 434-441.
    9. 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.
    10. Benjamin Kedem & Konstantinos Fokianos, 2002. "Regression Models for Binary Time Series," International Series in Operations Research & Management Science, in: Moshe Dror & Pierre L’Ecuyer & Ferenc Szidarovszky (ed.), Modeling Uncertainty, chapter 0, pages 185-199, Springer.
    11. Gneiting, Tilmann & Raftery, Adrian E., 2007. "Strictly Proper Scoring Rules, Prediction, and Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 359-378, March.
    12. William H. Greene, 1994. "Accounting for Excess Zeros and Sample Selection in Poisson and Negative Binomial Regression Models," Working Papers 94-10, New York University, Leonard N. Stern School of Business, Department of Economics.
    13. Winfried Pohlmeier & Volker Ulrich, 1995. "An Econometric Model of the Two-Part Decisionmaking Process in the Demand for Health Care," Journal of Human Resources, University of Wisconsin Press, vol. 30(2), pages 339-361.
    14. Ozuna, Teofilo, Jr & Gomez, Irma Adriana, 1995. "Specification and Testing of Count Data Recreation Demand Functions," Empirical Economics, Springer, vol. 20(3), pages 543-550.
    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. Christian Kleiber & Achim Zeileis, 2016. "Visualizing Count Data Regressions Using Rootograms," The American Statistician, Taylor & Francis Journals, vol. 70(3), pages 296-303, July.
    2. Sarker, Rakhal & Surry, Yves R., 2003. "The Fast Decay Process In Recreational Demand Activities And The Use Of Alternative Count Data Models," Working Papers 34147, University of Guelph, Department of Food, Agricultural and Resource Economics.
    3. Teresa Bago d'Uva, 2006. "Latent class models for utilisation of health care," Health Economics, John Wiley & Sons, Ltd., vol. 15(4), pages 329-343, April.
    4. Majo, M.C., 2010. "A microeconometric analysis of health care utilization in Europe," Other publications TiSEM 1cf5fd2f-8146-4ef8-8eb5-e, Tilburg University, School of Economics and Management.
    5. Sisira Sarma & Wayne Simpson, 2006. "A microeconometric analysis of Canadian health care utilization," Health Economics, John Wiley & Sons, Ltd., vol. 15(3), pages 219-239, March.
    6. Taghouti, Ibtissem & Martinez-Gomez, Victor & Coque, José María Garcia Alvarez, 2015. "Exploring Eu Food Safety Notifications On Agro-Food Imports: Are Mediterranean Partner Countries Discriminated?," International Journal of Food and Agricultural Economics (IJFAEC), Alanya Alaaddin Keykubat University, Department of Economics and Finance, vol. 3(2), pages 1-15, April.
    7. Sinclair, Michael & Ghermandi, Andrea & Signorello, Giovanni & Giuffrida, Laura & De Salvo, Maria, 2022. "Valuing Recreation in Italy's Protected Areas Using Spatial Big Data," Ecological Economics, Elsevier, vol. 200(C).
    8. R. Martínez-Espiñeira, 2007. "‘Adopt a Hypothetical Pup’: A Count Data Approach to the Valuation of Wildlife," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 37(2), pages 335-360, June.
    9. Harris, Mark N. & Zhao, Xueyan, 2007. "A zero-inflated ordered probit model, with an application to modelling tobacco consumption," Journal of Econometrics, Elsevier, vol. 141(2), pages 1073-1099, December.
    10. Taghouti, Ibtissem & Martinez-Gomez, Victor & Marti, Luisa, 2017. "Sanitary and Phytosanitary measures in agri-food imports from the European Union: Reputation effects over time," Economia Agraria y Recursos Naturales, Spanish Association of Agricultural Economists, vol. 16(02), January.
    11. Hendrik Schmitz, 2012. "More health care utilization with more insurance coverage? Evidence from a latent class model with German data," Applied Economics, Taylor & Francis Journals, vol. 44(34), pages 4455-4468, December.
    12. Nan-Ting Liu & Feng-Chang Lin & Yu-Shan Shih, 2020. "Count regression trees," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 14(1), pages 5-27, March.
    13. Michael D. Creel & Montserrat Farell, 2001. "Likelihood-Based Approaches to Modeling Demand for Medical Care," UFAE and IAE Working Papers 498.01, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
    14. Antonio Clavero Barranquero & Mª. Luz González Alvarez, 2005. "A survey of econometric models to analyze the demand and utilisation of health care," Hacienda Pública Española / Review of Public Economics, IEF, vol. 173(2), pages 129-162, June.
    15. Sergi Jiménez‐Martín & José M. Labeaga & Maite Martínez‐Granado, 2002. "Latent class versus two‐part models in the demand for physician services across the European Union," Health Economics, John Wiley & Sons, Ltd., vol. 11(4), pages 301-321, June.
    16. Garcia, Serge & Jacob, Julien, 2010. "La valeur récréative de la forêt en France : une approche par les coûts de déplacement," Review of Agricultural and Environmental Studies - Revue d'Etudes en Agriculture et Environnement (RAEStud), Institut National de la Recherche Agronomique (INRA), vol. 91(1).
    17. John Haslett & Andrew C. Parnell & John Hinde & Rafael de Andrade Moral, 2022. "Modelling Excess Zeros in Count Data: A New Perspective on Modelling Approaches," International Statistical Review, International Statistical Institute, vol. 90(2), pages 216-236, August.
    18. Monika Sander, 2008. "Is There Migration-Related Inequity in Access to or in the Utilisation of Health Care in Germany?," SOEPpapers on Multidisciplinary Panel Data Research 147, DIW Berlin, The German Socio-Economic Panel (SOEP).
    19. Sergi Jiménez-Martín & José Labeaga & Maite Martínez-Granado, 2004. "An empirical analysis of the demand for physician services across the European Union," The European Journal of Health Economics, Springer;Deutsche Gesellschaft für Gesundheitsökonomie (DGGÖ), vol. 5(2), pages 150-165, May.
    20. BURNEY, Nadeem A. & ALENEZI, Mohammad & HAMADA, Salwa & AL-MUSALLAM, Nadia, 2019. "The Demand for Public and Private Medical Care Services: Evidence from Kuwait," Economia Internazionale / International Economics, Camera di Commercio Industria Artigianato Agricoltura di Genova, vol. 72(1), pages 107-138.

    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:stmapp:v:30:y:2021:i:4:d:10.1007_s10260-021-00558-6. 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.