Effect of Akaike Information Criterion on Model Selection in Analyzing Auto-crash Variables

Osuji G.A, Okoro C. N, Obubu M, Obiora-Ilouno H. O

Abstract

Count data has become widely available in many disciplines. The mostly used distribution for modeling count data is the Poisson distribution (Horim and Levy; 1981) which assume equidispersion (Variance is equal to the mean). Since observed count data often exhibit over or under dispersion, the Poisson model becomes less ideal for modeling. To deal with a wide range of dispersion levels, Generalized Poisson regression, Poisson regression, and lately Conway-Maxwell-Poisson (COM-Poisson) regression can be used as alternative regression models. We compared the Generalized Poisson regression, Poisson Regression Model and Conway- Maxwell- Poisson. Data on road traffic crashes from the Anambra State Command of the Federal Road Safety Commission (FRSC), Nigeria were analyzed using these three methods, the results from the three methods are compared using the Akaike Information Criterion (AIC) with Poisson showing an AIC value of 2325.8 and GPR having an AIC value of 896.0278 and COM-Poisson showing an AIC value of 951.01. The GPR was considered a better model when analyzing road traffic crashes in Anambra State, Nigeria.

Keywords

Over-dispersion; Road Traffic; Crashes; Discrete; Akaike Information Criterion; equidispersion.

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References

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

J.M. Hilbe,"Negative Binomial Regression". 2nd edition. Cambridge University Press, London (2011).

G.J. McLachlan, On the EM Algorithm for Overdispersed Count Data, Statistical Methods in Medical Reseach.6, 76-98 (1997).

G. Shmueli, T.P. Minka, J.B. Kadane, S. Borle, P. Boatwright, A Useful Distribution for Fitting Discrete Data: Revival of the ConwayMaxwellPoisson Distribution, Journal of The Royal Statistical Society. Series C (Applied Statistics). 54, Issue 1, 127-142 (2005).

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

Bozdogan, H. (2000). Akaike's Information Criterion and Recent Developments in Information Complexity. Mathematical Psychology, 44 , 62-91.

Famoye (1993), Wang and Famoye (1997), Restricted Generalized Poisson Regression Model. Communication in statistics -Theory and Methods. 01/1993; 22(5): 1335-1354. DOI: 10.1080/03610929308831089

Wikipedia.org

Cameron, A.C and Trivedi, P. K (1998), Regression analysis of count data. Cambridge University press Cambridge, UK.

Consul P. C. and Famoye F. (1992), Generalized Poisson regression model, communications in statistics (theory and methodology) vol. 2, no.1, 89-109.

S.D. Guikema, J.P. Coffelt, A Flexible Count Data Regression Model for Risk Analysis, Risk Analysis. 28, Issue 1, 213-223 (2008).

D. Lord, S.R. Geedipally, S.D. Guikema, Extension of the Application of Conway-Maxwell-Poisson Models: Analyzing Traffic Crash Data Exhibiting Under-Dispersion, Risk Analysis. 30, Issue 8, 1268-1276 (2010).

Famoye F, John T. W. and Karan P. S. (2004), On the generalized Poisson regression model with an application to accident data. Journal of data science 2 (2004), 287-295.

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