Analyzing Highly Dispersed Crash Data Using the Sichel Generalized Additive Models for Location , Scale and Shape

This paper documents the application of the Sichel (SI) generalized additive models for location, scale and shape (GAMLSS) for modeling highly dispersed crash data. The Sichel distribution is a compound Poisson distribution, which mixes the Poisson parameter with the generalized inverse Gaussian distribution. This distribution is particularly useful as a model for highly dispersed count data and has provided satisfactory fits in many cases where other models have proved to be inadequate. The objectives of this study were to evaluate the application of the Sichel GAMLSS for analyzing highly dispersed crash data and compare the results with the traditional Negative Binomial (NB) generalized linear model (GLM). To accomplish the objectives of the study, the NB, zero-inflated NB (ZINB) and SI GAMLSS were developed and compared using two highly dispersed crash datasets. The first dataset contains the crash data collected on 338 rural interstate road sections in Indiana. The second dataset consists of vehicle crash data that occurred on undivided 4-lane rural roadway segments in Texas. Several goodness-of-fit metrics were used to assess the statistical fit of the models. The results show that the Sichel GAMLSS can always have a better fitting performance than the NB and ZINB for the crash datasets examined in this study. Thus, the SI GAMLSS may offer a viable alternative to the traditionally used NB GLMs for analyzing highly dispersed crash datasets.

[1]  Srinivas Reddy Geedipally,et al.  The negative binomial-Lindley distribution as a tool for analyzing crash data characterized by a large amount of zeros. , 2011, Accident; analysis and prevention.

[2]  S. Miaou.  The relationship between truck accidents and geometric design of road sections: Poisson versus negative binomial regressions. , 1994, Accident; analysis and prevention.

[3]  Nalini Ravishanker,et al.  Selecting exposure measures in crash rate prediction for two-lane highway segments. , 2004, Accident; analysis and prevention.

[4]  B. G. Heydecker,et al.  Identification of sites for road accident remedial work by Bayesian statistical methods: an example of uncertain inference , 2001 .

[5]  Fred L Mannering,et al.  A note on modeling vehicle accident frequencies with random-parameters count models. , 2009, Accident; analysis and prevention.

[6]  Dominique Lord,et al.  Application of finite mixture models for vehicle crash data analysis. , 2009, Accident; analysis and prevention.

[7]  Srinivas Reddy Geedipally,et al.  Application of the Conway-Maxwell-Poisson generalized linear model for analyzing motor vehicle crashes. , 2008, Accident; analysis and prevention.

[8]  Srinivas Reddy Geedipally,et al.  Analyzing Different Parameterizations of the Varying Dispersion Parameter as a Function of Segment Length , 2009 .

[9]  Srinivas Reddy Geedipally,et al.  Examining the Poisson-Weibull Generalized Linear Model for Analyzing Crash Data , 2012 .

[10]  Paul H C Eilers,et al.  New Dutch reference curves for birthweight by gestational age. , 2009, Early human development.

[11]  H. S. Sichel,et al.  A bibliometric distribution which really works , 1985, J. Am. Soc. Inf. Sci..

[12]  Harry Joe,et al.  Modelling heavy-tailed count data using a generalised Poisson-inverse Gaussian family , 2009 .

[13]  Fred L. Mannering,et al.  The statistical analysis of crash-frequency data: A review and assessment of methodological alternatives , 2010 .

[14]  R. A. Rigby,et al.  Article in Press Computational Statistics and Data Analysis a Framework for Modelling Overdispersed Count Data, including the Poisson-shifted Generalized Inverse Gaussian Distribution , 2022 .

[15]  Fred L. Mannering,et al.  Negative binomial analysis of intersection accident frequencies , 1996 .

[16]  H. S. Sichel,et al.  Repeat‐Buying and the Generalized Inverse Gaussian–Poisson Distribution , 1982 .

[17]  Dominique Lord,et al.  Poisson, Poisson-gamma and zero-inflated regression models of motor vehicle crashes: balancing statistical fit and theory. , 2005, Accident; analysis and prevention.

[18]  Walter Zucchini,et al.  Parameter Estimation for the Sichel Distribution and its Multivariate Extension , 1987 .

[19]  R. Rigby,et al.  Generalized Additive Models for Location Scale and Shape (GAMLSS) in R , 2007 .

[20]  R. Rigby,et al.  Generalized additive models for location, scale and shape , 2005 .

[21]  K. El-Basyouny,et al.  Comparison of Two Negative Binomial Regression Techniques in Developing Accident Prediction Models , 2006 .

[22]  Nataliya V Malyshkina,et al.  Zero-state Markov switching count-data models: an empirical assessment. , 2008, Accident; analysis and prevention.

[23]  S. Washington,et al.  Statistical and Econometric Methods for Transportation Data Analysis , 2010 .

[24]  Yunlong Zhang,et al.  Crash Frequency Analysis with Generalized Additive Models , 2008 .

[25]  Dominique Lord,et al.  Further notes on the application of zero-inflated models in highway safety. , 2007, Accident; analysis and prevention.

[26]  Andrew P Tarko,et al.  Tobit analysis of vehicle accident rates on interstate highways. , 2008, Accident; analysis and prevention.

[27]  Srinivas Reddy Geedipally,et al.  The negative binomial-Lindley generalized linear model: characteristics and application using crash data. , 2012, Accident; analysis and prevention.