IDEAS home Printed from https://ideas.repec.org/a/taf/japsta/v27y2000i8p953-964.html
   My bibliography  Save this article

A note on modelling underreported Poisson counts

Author

Listed:
  • Peter Fader
  • Bruce Hardie

Abstract

In this paper we present a parsimonious model for the analysis of underreported Poisson count data. In contrast to previously developed methods, we are able to derive analytic expressions for the key marginal posterior distributions that are of interest. The usefulness of this model is explored via a re-examination of previously analysed data covering the purchasing of port wine (Ramos, 1999).

Suggested Citation

  • Peter Fader & Bruce Hardie, 2000. "A note on modelling underreported Poisson counts," Journal of Applied Statistics, Taylor & Francis Journals, vol. 27(8), pages 953-964.
    • Handle: RePEc:taf:japsta:v:27:y:2000:i:8:p:953-964
    DOI: 10.1080/02664760050173283
    as

    Download full text from publisher

    File URL: http://www.tandfonline.com/doi/abs/10.1080/02664760050173283
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/02664760050173283?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. David C. Schmittlein & Albert C. Bemmaor & Donald G. Morrison, 1985. "Technical Note—Why Does the NBD Model Work? Robustness in Representing Product Purchases, Brand Purchases and Imperfectly Recorded Purchases," Marketing Science, INFORMS, vol. 4(3), pages 255-266.
    2. Abel P. Jeuland & Frank M. Bass & Gordon P. Wright, 1980. "A Multibrand Stochastic Model Compounding Heterogeneous Erlang Timing and Multinomial Choice Processes," Operations Research, INFORMS, vol. 28(2), pages 255-277, April.
    3. Winkelmann, Rainer, 1996. "Markov Chain Monte Carlo Analysis of Underreported Count Data with an Application to Worker Absenteeism," Empirical Economics, Springer, vol. 21(4), pages 575-587.
    4. van Praag, B M S & Vermeulen, E M, 1993. "A Count-Amount Model with Endogenous Recording of Observations," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(4), pages 383-395, Oct.-Dec..
    5. Francisco Fernando & Ribeiro Ramos, 1999. "Underreporting of purchases of port wine," Journal of Applied Statistics, Taylor & Francis Journals, vol. 26(4), pages 485-494.
    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. Eduardo Fé & Richard Hofler, 2013. "Count data stochastic frontier models, with an application to the patents–R&D relationship," Journal of Productivity Analysis, Springer, vol. 39(3), pages 271-284, June.
    2. Kinshuk Jerath & Anuj Kumar & Serguei Netessine, 2015. "An Information Stock Model of Customer Behavior in Multichannel Customer Support Services," Manufacturing & Service Operations Management, INFORMS, vol. 17(3), pages 368-383, July.
    3. Vidhura Tennekoon, 2017. "Counting unreported abortions: A binomial-thinned zero-inflated Poisson model," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 36(2), pages 41-72.
    4. Michael Braun & Peter S. Fader & Eric T. Bradlow & Howard Kunreuther, 2006. "Modeling the "Pseudodeductible" in Insurance Claims Decisions," Management Science, INFORMS, vol. 52(8), pages 1258-1272, August.
    5. Debjit Sengupta & Tathagata Banerjee & Surupa Roy, 2020. "Estimation of Poisson mean with under‐reported counts: a double sampling approach," Australian & New Zealand Journal of Statistics, Australian Statistical Publishing Association Inc., vol. 62(4), pages 508-535, December.

    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. Kinshuk Jerath & Anuj Kumar & Serguei Netessine, 2015. "An Information Stock Model of Customer Behavior in Multichannel Customer Support Services," Manufacturing & Service Operations Management, INFORMS, vol. 17(3), pages 368-383, July.
    2. Sha Yang & Yi Zhao & Ravi Dhar, 2010. "Modeling the Underreporting Bias in Panel Survey Data," Marketing Science, INFORMS, vol. 29(3), pages 525-539, 05-06.
    3. Trinh, Giang & Wright, Malcolm J., 2022. "Predicting future consumer purchases in grocery retailing with the condensed Poisson lognormal model," Journal of Retailing and Consumer Services, Elsevier, vol. 64(C).
    4. R. Winkelmann, 1998. "Count data models with selectivity," Econometric Reviews, Taylor & Francis Journals, vol. 17(4), pages 339-359.
    5. Michael Braun & Peter S. Fader & Eric T. Bradlow & Howard Kunreuther, 2006. "Modeling the "Pseudodeductible" in Insurance Claims Decisions," Management Science, INFORMS, vol. 52(8), pages 1258-1272, August.
    6. Patrick Bachmann & Markus Meierer & Jeffrey Näf, 2021. "The Role of Time-Varying Contextual Factors in Latent Attrition Models for Customer Base Analysis," Marketing Science, INFORMS, vol. 40(4), pages 783-809, July.
    7. Shi, Ruixia & Chen, Hongyu & Sethi, Suresh P., 2019. "A generalized count model on customers' purchases in O2O market," International Journal of Production Economics, Elsevier, vol. 215(C), pages 121-130.
    8. Park, Chang Hee & Park, Young-Hoon & Schweidel, David A., 2014. "A multi-category customer base analysis," International Journal of Research in Marketing, Elsevier, vol. 31(3), pages 266-279.
    9. Anesbury, Zachary William & Talbot, Danielle & Day, Chanel Andrea & Bogomolov, Tim & Bogomolova, Svetlana, 2020. "The fallacy of the heavy buyer: Exploring purchasing frequencies of fresh fruit and vegetable categories," Journal of Retailing and Consumer Services, Elsevier, vol. 53(C).
    10. Thomas Lux, 2020. "On the distribution of links in financial networks: structural heterogeneity and functional form," Empirical Economics, Springer, vol. 58(3), pages 1019-1053, March.
    11. Trinh, Giang & Dawes, John, 2020. "A comparison of brand loyalty between on the go and take-home consumption purchases," Journal of Retailing and Consumer Services, Elsevier, vol. 53(C).
    12. Jeongwen Chiang & Ching-Fan Chung & Emily Cremers, 2001. "Promotions and the pattern of grocery shopping time," Journal of Applied Statistics, Taylor & Francis Journals, vol. 28(7), pages 801-819.
    13. Francisco Fernando & Ribeiro Ramos, 1999. "Underreporting of purchases of port wine," Journal of Applied Statistics, Taylor & Francis Journals, vol. 26(4), pages 485-494.
    14. Demetrios Vakratsas & Frank M. Bass, 2002. "A segment-level hazard approach to studying household purchase timing decisions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(1), pages 49-59.
    15. S Reader, 1993. "Unobserved Heterogeneity in Dynamic Discrete Choice Models," Environment and Planning A, , vol. 25(4), pages 495-519, April.
    16. Hauser, John R. & Wisniewski, Kenneth J., 1981. "Application, predictive test, and strategy implications for a dynamic model of consumer response to marketing," Working papers 1244-81., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    17. Wu, Couchen & Chen, Hsiu-Li, 2000. "Counting your customers: Compounding customer's in-store decisions, interpurchase time and repurchasing behavior," European Journal of Operational Research, Elsevier, vol. 127(1), pages 109-119, November.
    18. Maier, Erik & Wieringa, Jaap, 2021. "Acquiring customers through online marketplaces? The effect of marketplace sales on sales in a retailer's own channels," International Journal of Research in Marketing, Elsevier, vol. 38(2), pages 311-328.
    19. Ehrenberg, Andrew S. C. & Uncles, Mark D. & Goodhardt, Gerald J., 2004. "Understanding brand performance measures: using Dirichlet benchmarks," Journal of Business Research, Elsevier, vol. 57(12), pages 1307-1325, December.
    20. Wayne DeSarbo & Venkatram Ramaswamy & Peter Lenk, 1993. "A latent class procedure for the structural analysis of two-way compositional data," Journal of Classification, Springer;The Classification Society, vol. 10(2), pages 159-193, December.

    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:taf:japsta:v:27:y:2000:i:8:p:953-964. 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/CJAS20 .

    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.