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Non nested model selection for spatial count regression models with application to health insurance

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  • Claudia Czado
  • Holger Schabenberger
  • Vinzenz Erhardt

Abstract

In this paper we consider spatial regression models for count data. We examine not only the Poisson distribution but also the generalized Poisson capable of modeling over-dispersion, the negative Binomial as well as the zero-inflated Poisson distribution which allows for excess zeros as possible response distribution. We add random spatial effects for modeling spatial dependency and develop and implement MCMC algorithms in $$R$$ for Bayesian estimation. The corresponding R library ‘spatcounts’ is available on CRAN. In an application the presented models are used to analyze the number of benefits received per patient in a German private health insurance company. Since the deviance information criterion is only appropriate for exponential family models, we use in addition the Vuong and Clarke test with a Schwarz correction to compare possibly non nested models. We illustrate how they can be used in a Bayesian context. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Claudia Czado & Holger Schabenberger & Vinzenz Erhardt, 2014. "Non nested model selection for spatial count regression models with application to health insurance," Statistical Papers, Springer, vol. 55(2), pages 455-476, May.
    • Handle: RePEc:spr:stpapr:v:55:y:2014:i:2:p:455-476
    DOI: 10.1007/s00362-012-0491-9
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    References listed on IDEAS

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    1. Rainer Winkelmann, 2008. "Econometric Analysis of Count Data," Springer Books, Springer, edition 0, number 978-3-540-78389-3, September.
    2. Clarke, Kevin A., 2007. "A Simple Distribution-Free Test for Nonnested Model Selection," Political Analysis, Cambridge University Press, vol. 15(3), pages 347-363, July.
    3. Vuong, Quang H, 1989. "Likelihood Ratio Tests for Model Selection and Non-nested Hypotheses," Econometrica, Econometric Society, vol. 57(2), pages 307-333, March.
    4. Yip, Karen C.H. & Yau, Kelvin K.W., 2005. "On modeling claim frequency data in general insurance with extra zeros," Insurance: Mathematics and Economics, Elsevier, vol. 36(2), pages 153-163, April.
    5. Susanne Gschlößl & Claudia Czado, 2008. "Modelling count data with overdispersion and spatial effects," Statistical Papers, Springer, vol. 49(3), pages 531-552, July.
    6. Bae, S. & Famoye, F. & Wulu, J.T. & Bartolucci, A.A. & Singh, K.P., 2005. "A rich family of generalized Poisson regression models with applications," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 69(1), pages 4-11.
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    Cited by:

    1. Ajiferuke, Isola & Famoye, Felix, 2015. "Modelling count response variables in informetric studies: Comparison among count, linear, and lognormal regression models," Journal of Informetrics, Elsevier, vol. 9(3), pages 499-513.
    2. Karsten Schweikert & Manuel Huth & Mark Gius, 2021. "Detecting a copycat effect in school shootings using spatio‐temporal panel count models," Contemporary Economic Policy, Western Economic Association International, vol. 39(4), pages 719-736, October.
    3. Antonio J. Sáez-Castillo & Antonio Conde-Sánchez, 2017. "Detecting over- and under-dispersion in zero inflated data with the hyper-Poisson regression model," Statistical Papers, Springer, vol. 58(1), pages 19-33, March.

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