The negative binomial-Lindley generalized linear model: Characteristics and application using crash data

Geedipally, Srinivas Reddy; Lord, Dominique; Dhavala, Soma S.

doi:10.1016/j.aap.2011.07.012

Cited by 123 publications

(49 citation statements)

References 24 publications

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“…In other words, just as NB model, little computation effort is needed to apply the PIG models. Comparatively, recent introduced models such as NB-L model which relies on MCMC chain for parameter estimation may require a few hours simulation before converging (Lord et al, 2008b, Geedipally et al, 2012. Actually, at the end of the paper written by Zou et al (2012b), the potential of applying PIG rather than SI was also addressed mainly for its simplicity.…”

Section: Discussionmentioning

confidence: 99%

“…So far, very few studies have examined this issue. A Negative Binomial-Lindley model (NB-L) was introduced by Geedipally et al (2012) to model crash data characterized by large number of zeros. The NB-L model was demonstrated to provide better statistical performance than the Zero Inflated Negative Binomial model (ZINB) and is more theoretically sound (Lord et al, 2005).…”

Section: Introductionmentioning

confidence: 99%

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The Poisson inverse Gaussian (PIG) generalized linear regression model for analyzing motor vehicle crash data

Zha

Lord

Zou

2014

Journal of Transportation Safety & Security

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This paper documents the application of the Poisson Inverse Gaussian (PIG) regression model for modeling motor vehicle crash data. The PIG distribution, which mixes the Poisson distribution and Inverse Gaussian distribution, has the potential for modeling highly dispersed count data due to the flexibility of Inverse Gaussian distribution. The objectives of this paper were to evaluate the application of PIG regression model for analyzing motor vehicle crash data and compare the results with Negative binomial (NB) model, especially when varying dispersion parameter is introduced. To accomplish the objectives, both NB and PIG models were developed with fixed and varying dispersion parameters and compared using two datasets. The Texas undivided rural highway segments dataset includes five years of crash data, while the divided highway segments Washington dataset includes four years. The results of this study show that PIG models perform better than the NB models in terms of goodness-of-fit (GOF) statistics. Moreover, PIG models can perform similarly well in capturing the variance of crash to the NB models. Lastly, PIG models demonstrate almost the same prediction performance compared to NB models. Considering the simple form of PIG model and its easiness of applications, PIG model could be used as a potential alternative to the NB model for analyzing crash data. Zha et al.2

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The Poisson inverse Gaussian (PIG) generalized linear regression model for analyzing motor vehicle crash data

Zha

Lord

Zou

2014

Journal of Transportation Safety & Security

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“…Leaving out important explanatory variables can result in biased parameter estimates and incorrect inferences, especially if the omitted variable is correlated with variables included in the model, which is often the case [43] [44] [45] [46].…”

Section: Common Problems With Crash Datamentioning

confidence: 99%

Road Traffic Crash Data: An Overview on Sources, Problems, and Collection Methods

Abdulhafedh¹

2017

JTTs

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Road traffic crash data are useful tools to support the development, implementation, and assessment of highway safety programs that tend to reduce road traffic crashes. Collecting road traffic crash data aims at gaining a better understanding of road traffic operational problems, locating hazardous road sections, identifying risk factors, developing accurate diagnosis and remedial measures, and evaluating the effectiveness of road safety programs. Furthermore, they can be used by many agencies and businesses such as: law enforcements to identify persons at fault in road traffic crashes; insurers seeking facts about traffic crash claims; road safety researchers to access traffic crash reliable database; decision makers to develop long-term, statewide strategic plans for traffic and highway safety; and highway safety administrators to help educate the public. Given the practical importance of vehicle crash data, this paper presents an overview of the sources, trends and problems associated with road traffic crash data.

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“…For data exhibiting long tails or over or under dispersion, alternative models such as the negative binomial (NB), the generalized Poisson, Famoye et al (2004), the double Poisson and several other distributions, such as, the NB-generalized exponential, Aryuyuen & Bodhisuwan (2013) have been proposed. Other distributions that have received considerable attention in the literature are the Poisson Inverse Gaussian, the NB-Lindley Zamani & Ismail (2010); Lord et al (2011);Geedipally et. (2012) and many others.…”

Section: Introductionmentioning

confidence: 99%

Correcting for Non-Sum to 1 Estimated Probabilities in Applications of Discrete Probability Models to Count Data

Lawal¹

2017

IJSP

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In this paper, we examine some often ignored or assumed problems relating with fitting probability models to count data either exhibiting over, equi, or under dispersion. Of particular concern are last category truncated data, where most often, expected values in this last category are collapsed together so that the sum of the expected values sum to the sample size in the data. That is, so that k ∑ i=0m i = n, the sample size. We shall for illustrative purposes in this paper, consider the following distributions: the negative binomial (NB), the Inverse trinomial (IT), the hyper-Poisson (HP), the Quasinegative binomial (QNBD), the extended com-Poisson distribution (ECOMP) as well as the negative binomial-exponential distribution (NBGE).Though, we have restricted our discussion to these six distributions, other distributions may also be employed but the patterns are always the same, that is, the sum of the estimated probabilities does not equal 1.00 and consequently, the sum of the expected values is always less or equal (Poisson case only) the sample size in the observed data. We propose a common procedure to rectify this problem for both right truncated or non-truncated frequency count data exhibiting either excess zeros or regular frequency data.

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The negative binomial-Lindley generalized linear model: Characteristics and application using crash data

Cited by 123 publications

References 24 publications

The Poisson inverse Gaussian (PIG) generalized linear regression model for analyzing motor vehicle crash data

The Poisson inverse Gaussian (PIG) generalized linear regression model for analyzing motor vehicle crash data

Road Traffic Crash Data: An Overview on Sources, Problems, and Collection Methods

Correcting for Non-Sum to 1 Estimated Probabilities in Applications of Discrete Probability Models to Count Data

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