Flexiblity of Using Com-Poisson Regression Model for Count Data

  • Esin AVCI Giresun University
Keywords: Poisson regression, COM-Poisson regression, under-dispersed count data

Abstract

The Poisson regression model is the most common model for fitting count data. However, it is suitable only for modeling equi-dispersed distribution. The Conway-Maxwell-Poisson (COM-Poisson) regression model allows modeling over and under-dispersion distribution. The purpose of this study is to demonstrate the flexibility of the Conway-Maxwell-Poisson (COM-Poisson) regression model on simulation and alg data.

Author Biography

Esin AVCI, Giresun University
Assistant Professor,Department of statistics

References

Aitkie, M., Anderson, D., Francis, B., Hinde, J., Statistical modeling in GLIM. New York: Oxford University Press, (1990).

Cameron, A.C., Trivedi, P.K., Regression analysis of countdata, New York: Cambridge University Press, 53, (2013).

Consul, P.C., Famoye, F.,Generalized Poisson regression model, Communications in Statistics (Theory & Method), 2(1): 89-

,(1992).

Consul, P.C., Generalized Poisson Distribution: Properties and Application. New York: Marcel Dekker (1989).

Conway, R.W., Maxweal, W.L.,A queuing model with state dependent service rates, Journal of Industrial Engineering, 12:132-

,(1962).

Famoye, F., Restricted generalized Poissonregression models, Commun.Statist.Theor. Meth,22:1335-1354, (1993).

Famope, F., Wulu, J.o., Singh, K.P.,On the generalized Poisson regression model with an application to accident data, Journal of Data Science, 2: 287-295, (2004).

Frime, E.L., The analysis of rates using Poisson regression models, Biometrics, 39: 665-674, (1983).

Hidbe, J.M., Negative Binomialregressio , Second edition, Cambridge University Press,(2011).

Ismail, N., Zamani, H., Estimation of Claim Count Data using Negative Binomial, Generalized Poisson, Zero-Inflated Negative Binomial and Zero-Inflated Generalized Poisson Regression Models, Casualty Actuarial Society E-Forum(Spring 2013).

Khan, N.M. and Khan, M.H., Model for analysing count with over-, equi-and under-dispersion in actuarial statistics, Journal of Mathematics and Statistics, 6(2):92-95, (2010).

Lord, D., Modelling motor vehicle crashesusing Poisnon-Gamma models: Examining the effects of low sample mean values and small sample size on the estimation of the fixed dispersion parameter, Accident Analysis&Prevention, 38(4): 751-766, (2006).

Lord, D., Geedipally, S.R., Guikema, S.D.,Extension of the application of Conway-Maxwell-Poisson models: analyzing traffic crash data exhibiting under-dispersion, Risk Analysis, 30(8): 1268-1276, (2010).

Lord, D., Guikema, S.D., Geedipally, S.R.,Application of the Conway–Maxwell–Poisson generalized linear model for analyzing motor vehicle crashes, Accident Analysns & Preventioi, 40(3): 1123–1134, (2008).

McLachlan, G.J., On the EM algorithm for overdispersed count data, Statistical methods in Medical Research, 6: 76-98, (1997).

Minka, T.P., Shmueli, G., Kadane, J.B., Borle, S., Boatwright, P.,Computing with the COM-Poisson distribution. Technical Report Series, Carnegie Mellon University Department of Statistics, Pennsylvania, (2003).

Myers, R.H., Montgomery, D.C., Vining, G.G., Generalized Linear Models with Applications in Engineering and the Science, John Wiley & Sons INC,(2001).

Oh, J., Washington, S.P., Nam, D., Accident prediction model cor railway-highway interfaces, Accident Analysis&Prevention, 38(2): 346-356, (2006).

Renshaw, A. E., Modelling the claims process in the presence of covariates. ASTIN Bulletin, 24(2): 265-285, (1994).

Riphahn, R., Wambach, A., Million, A., Incentive effect in the demand for health care: a bivariate panel count data estimation, Journal of Applied Econometrics, 18(4): 387-405, (2003).

Sellers, K.F., Shmueli, G.,A Flexible Regression Model for Count Data, The Annals of Applied Statletics, 4(2): 943-961, (2010).

Sellers, K.F.,Shmueli, G.,Data Dispersion: Now you see it...Now you don’t, Communication in Statistics: Theory and Methods, 42(17):3134-47, (2013).

Shmueli, G., Minka, T.P., Kadane, J.B., Borle, S., Boatwright, P.,A Useful Distribution for Fitting Discrete Data: Revival of the Conway–Maxwell–Poisson Distribution, Journal of The Royal Statistical Society. Series C (Applied Statistics), 54(1): 127-142,

(2005).

Wang, W., Famoye, F.,Modeling household fertility decisions with generalized Poisson regression,Journay of Population Economics, 10: 273-283, (1997).

Wedderburn, R.W.M.,Quasi-likelihood functions, generalized linear models, and the Gauss-Newton method, Biometrika, 61: 439–

, (1974).

Wimmer, G. and Altmann, G., Thesaurus of univariate discrete probability distributions, Essen: Stamn. www.stamn.de/thesaurus/,

(1999).

Zeileis, A., Kleiber, C., Jaskman, S.,Regression Models for Count Data in R, Journal of Statistical Software, 27(8): 1-25, (2008).

Published
2018-06-24
How to Cite
AVCI, E. (2018). Flexiblity of Using Com-Poisson Regression Model for Count Data. Statistics, Optimization & Information Computing, 6(2), 278-285. https://doi.org/10.19139/soic.v6i2.278
Section
Research Articles