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A Bayesian dichotomous model with asymmetric link for fraud in insurance

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  • Bermúdez, Ll.
  • Pérez, J.M.
  • Ayuso, M.
  • Gómez, E.
  • Vázquez, F.J.
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    Abstract

    Standard binary models have been developed to describe the behavior of consumers when they are faced with two choices. The classical logit model presents the feature of the symmetric link function. However, symmetric links do not provide good fits for data where one response is much more frequent than the other (as it happens in the insurance fraud context). In this paper, we use an asymmetric or skewed logit link, proposed by Chen et al. [Chen, M., Dey, D., Shao, Q., 1999. A new skewed link model for dichotomous quantal response data. J. Amer. Statist. Assoc. 94 (448), 1172-1186], to fit a fraud database from the Spanish insurance market. Bayesian analysis of this model is developed by using data augmentation and Gibbs sampling. The results show that the use of an asymmetric link notably improves the percentage of cases that are correctly classified after the model estimation.

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    Bibliographic Info

    Article provided by Elsevier in its journal Insurance: Mathematics and Economics.

    Volume (Year): 42 (2008)
    Issue (Month): 2 (April)
    Pages: 779-786

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    Handle: RePEc:eee:insuma:v:42:y:2008:i:2:p:779-786

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    Web page: http://www.elsevier.com/locate/inca/505554

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    1. Koop, Gary & Poirier, Dale J., 1993. "Bayesian analysis of logit models using natural conjugate priors," Journal of Econometrics, Elsevier, vol. 56(3), pages 323-340, April.
    2. Jean Pinquet & Mercedes Ayuso & Montserrat Guillén, 2007. "Selection Bias and Auditing Policies for Insurance Claims," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 74(2), pages 425-440.
    3. McCulloch, Robert E. & Polson, Nicholas G. & Rossi, Peter E., 2000. "A Bayesian analysis of the multinomial probit model with fully identified parameters," Journal of Econometrics, Elsevier, vol. 99(1), pages 173-193, November.
    4. D. McFadden & J. Hausman, 1981. "Specification Tests for the Multinominal Logit Model," Working papers 292, Massachusetts Institute of Technology (MIT), Department of Economics.
    5. Steven B. Caudill & Mercedes Ayuso & Montserrat Guillén, 2005. "Fraud Detection Using a Multinomial Logit Model With Missing Information," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 72(4), pages 539-550.
    6. El Bachir Belhadji & George Dionne & Faouzi Tarkhani, 2000. "A Model for the Detection of Insurance Fraud*," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan, vol. 25(4), pages 517-538, October.
    7. Belhadji, B. & Dionne, G., 1997. "Development of an Expert System for Automatic Detection of Automobile Insurance Fraud," Ecole des Hautes Etudes Commerciales de Montreal- 97-06, Ecole des Hautes Etudes Commerciales de Montreal-Chaire de gestion des risques..
    8. Amemiya, Takeshi, 1981. "Qualitative Response Models: A Survey," Journal of Economic Literature, American Economic Association, vol. 19(4), pages 1483-1536, December.
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