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.
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References
Bae S, Famoye F, Wulu JT, Bartolucci AA, Singh KP (2005) A rich family of generalized Poisson regression models. Math Comput Simul 69(1–2):4–11
Clarke KA (2003) Nonparametric model discrimination in international relations. J Confl Resolut 47:72–93
Clarke KA (2007) A simple distribution-free test for nonnested model selection. Polit Anal 15(3):347–363
Consul PC, Famoye F (1992) Generalized poisson regression model. Commun Stat Theor Methods 21(1):89–109
Consul PC, Jain GC (1973) A generalization of the Poisson distribution. Technometrics 15(4):791–799
Czado C, Erhardt V, Min A, Wagner S (2007) Zero-inflated generalized Poisson models with regression effects on the mean, dispersion and zero-inflation level applied to patent outsourcing rates. Stat Model 7(2):125–153
Erhardt, V. (2009). ZIGP: zero-inflated generalized Poisson (ZIGP) models. R package version 3.5
Famoye F (1993) Restricted generalized Poisson regression model. Commun Stat Theor Methods 22(5):1335–1354
Famoye F, Singh KP (2003) On inflated generalized Poisson regression models. Adv Appl Stat 3(2):145–158
Famoye F, Singh KP (2006) Zero-inflated generalized Poisson model with an application to domestic violence data. J Data Sci 4(1):117–130
Gelman A, Carlin JB, Stern HS, Rubin DB (2003) Bayesian data analysis, 2nd edn. Chapman & Hall/CRC, Boca Raton
Gilks W R, Richardson S, Spiegelhalter D (1996) Markov chain Monte Carlo in practice. Chapman & Hall/CRC, Boca Raton
Gschlößl S (2007) Czado C (2007) Spatial modelling of claim frequency and claim size in non-life insurance. Scand Actuar J 3:202–225
Gschlößl S, Czado C (2008) Modelling count data with overdispersion and spatial effects. Stat Papers 49(3):531–552
Gupta PL, Gupta RC, Tripathi RC (2004) Score test for zero inflated generalized Poisson regression model. Commun Stat Theor Methods 33(1):47–64
Hastings WK (1970) Monte carlo sampling methods using Markov chains and their applications. Biometrika 57(1):97–109
Joe H, Zhu R (2005) Generalized Poisson distribution: the property of mixture of Poisson and comparison with negative binomial distribution. Biometr J 47(2):219–229
Lambert D (1992) Zero-inflated poisson regression, with an application to defects in manufacturing. Technometrics 34(1):1–14
McCullagh P, Nelder JA (1989) Generalized linear models, 2nd edn. Chapman & Hall, London
Metropolis N, Rosenbluth A, Rosenbluth M, Teller A, Teller E (1953) Equations of state calculations by fast computing machines. J Chem Phys 21:1087–1091
Pettitt AN, Weir IS, Hart AG (2002) A conditional autoregressive gaussian process for irregularly spaced multivariate data with application to modelling large sets of binary data. Stat Comput 12(4):353–367
Schabenberger H (2009a) Spatcounts: spatial count regression. R package version 1.1
Schabenberger H (2009b) Spatial count regression models with applications to health insurance data. Master’s thesis, Technische Universität München, München. http://www-m4.ma.tum.de/lehre/abschlussarbeiten/abgeschlossene-diplomarbeiten/
Spiegelhalter DJ, Best NG, Carlin BP, van der Linde A (2002) Bayesian measures of model complexity and fit. J R Stat Soc Ser B 64(4):583–639
Vuong QH (1989) Likelihood ratio tests for model selection and non-nested hypotheses. Econometrica 57(2):307–333
Winkelmann R (2008) Econometric analysis of count data, 5th edn. Springer, Berlin
Yip KC, Yau KK (2005) On modeling claim frequency data in general insurance with extra zeros. Insur Math Econ 36(2):153–163
Acknowledgments
C. Czado is supported by DFG (German Science Foundation) Grant CZ 86/1-3.
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Czado, C., Schabenberger, H. & Erhardt, V. Non nested model selection for spatial count regression models with application to health insurance. Stat Papers 55, 455–476 (2014). https://doi.org/10.1007/s00362-012-0491-9
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DOI: https://doi.org/10.1007/s00362-012-0491-9