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Journal ArticleDOI: 10.1080/19439962.2019.1638475

Comparison of confidence and prediction intervals for different mixed-Poisson regression models

04 Mar 2021-Journal of Transportation Safety & Security (Informa - Taylor and Francis Group)-Vol. 13, Iss: 3, pp 357-379
Abstract: A major focus for transportation safety analysts is the development of crash prediction models, a task for which an extremely wide selection of model types is available. Perhaps the most common cra...

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Topics: Poisson regression (54%), Prediction interval (54%), Poison control (50%)
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10 results found


Open accessPosted Content
04 Jul 2020-arXiv: Methodology
Abstract: Motivated by the current Coronavirus Disease (COVID-19) pandemic, which is due to the SARS-CoV-2 virus, and the important problem of forecasting daily deaths and cumulative deaths, this paper examines the construction of prediction regions or intervals under the Poisson regression model and for an over-dispersed Poisson regression model. For the Poisson regression model, several prediction regions are developed and their performance are compared through simulation studies. The methods are applied to the problem of forecasting daily and cumulative deaths in the United States (US) due to COVID-19. To examine their performance relative to what actually happened, daily deaths data until May 15th were used to forecast cumulative deaths by June 1st. It was observed that there is over-dispersion in the observed data relative to the Poisson regression model. An over-dispersed Poisson regression model is therefore proposed. This new model builds on frailty ideas in Survival Analysis and over-dispersion is quantified through an additional parameter. The Poisson regression model is a hidden model in this over-dispersed Poisson regression model and obtains as a limiting case when the over-dispersion parameter increases to infinity. A prediction region for the cumulative number of US deaths due to COVID-19 by July 16th, given the data until July 2nd, is presented. Finally, the paper discusses limitations of proposed procedures and mentions open research problems, as well as the dangers and pitfalls when forecasting on a long horizon, with focus on this pandemic where events, both foreseen and unforeseen, could have huge impacts on point predictions and prediction regions.

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7 Citations


Open access
01 Jan 2013-
Abstract: Reliable predictive accident models (PAMs) have a variety of important uses in traffic safety research and practice They are used to help identify sites in need of remedial treatment, in the design of transport schemes to assess safety implications, and to estimate the effectiveness of remedial treatments The PAMs currently in use in the UK are now quite old; the data used in their development was gathered up to 30 years ago Many changes have occurred over that period in road and vehicle design, in road safety campaigns and legislation, and the national accident rate has fallen substantially It seems unlikely that these aging models can be relied upon to provide accurate and reliable predictions of accident frequencies on the roads today This paper addresses a number of methodological issues that arise in seeking practical and efficient ways to update PAMs Models for accidents on rural single carriageway roads have been chosen to illustrate these issues, including the choice of distributional assumption for overdispersion, the choice of goodness of fit measures, questions of independence between observations in different years, and between links on the same scheme, the estimation of trends in the models, the uncertainty of predictions, as well as considerations about the most efficient and convenient ways to fit the required models, given the considerable advances that have been seen in statistical computing software in recent years

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Topics: Carriageway (51%)

3 Citations


Journal ArticleDOI: 10.1016/J.AAP.2020.105833
Jinjun Tang1, Fan Gao1, Fang Liu2, Chunyang Han1  +1 moreInstitutions (2)
Abstract: In recent years, globally quantile-based model (e.g. quantile regression) and spatially conditional mean models (e.g. geographically weighted regression) have been widely and commonly employed in macro-level safety analysis. The former ones assume that the model coefficients are fixed over space, while the latter ones only represent the entire distribution of variable effects by a single concentrated trend. However, the influence of crash related factors on the distribution of crash frequency is observed to vary over space and across different quantiles. Therefore, a geographically weighted Poisson quantile regression (GWPQR) model is employed to investigate the spatial heterogeneity of variable effects crossing different quantiles. Five categories, including exposure, socio-economic, transportation, network and land use were selected to estimate the spatial effects on crash frequency. In the case study, vehicle related crashes collected in New York City were used to validate the predicted performance of the proposed models. The results show that the GWPQR outperforms the NB, QR and GWNBR for modeling the skewed distribution, reconstructing the crash distribution and capturing the unobserved spatial heterogeneity. Additionally, the significant coefficients are further used to classify all 21 variables into key, important and general parts. Then we discuss how these factors affects the regional crashes over space and distribution of crash frequency. This study confirms that the influencing factors have varying effects on different quantiles of distribution and on different regions, which could be helpful to provide support for making safety countermeasures and policies at urban regional level.

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Topics: Quantile regression (62%), Quantile (61%), Poisson distribution (55%)

3 Citations


Open access
Graham Wood1Institutions (1)
01 Jan 2004-
Abstract: Generalised linear models, with "log" link and either Poisson or negative binomial errors, are commonly used for relating accident rates to explanatory variables. This paper adds to the toolkit for such models. It describes how confidence intervals (for example, for the true accident rate at given flows) and prediction intervals (for example, for the number of accidents at a new site with given flows) can be produced using spreadsheet technology.

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Topics: Negative binomial distribution (57%), Poisson distribution (55%), Confidence interval (54%) ... show more

3 Citations



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46 results found


Journal ArticleDOI: 10.1023/A:1008929526011
Abstract: WinBUGS is a fully extensible modular framework for constructing and analysing Bayesian full probability models. Models may be specified either textually via the BUGS language or pictorially using a graphical interface called DoodleBUGS. WinBUGS processes the model specification and constructs an object-oriented representation of the model. The software offers a user-interface, based on dialogue boxes and menu commands, through which the model may then be analysed using Markov chain Monte Carlo techniques. In this paper we discuss how and why various modern computing concepts, such as object-orientation and run-time linking, feature in the software's design. We also discuss how the framework may be extended. It is possible to write specific applications that form an apparently seamless interface with WinBUGS for users with specialized requirements. It is also possible to interface with WinBUGS at a lower level by incorporating new object types that may be used by WinBUGS without knowledge of the modules in which they are implemented. Neither of these types of extension require access to, or even recompilation of, the WinBUGS source-code.

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Topics: Interface (Java) (51%)

5,367 Citations


Open accessJournal ArticleDOI: 10.1111/J.1467-9876.2005.00510.X
Abstract: Summary. A general class of statistical models for a univariate response variable is presented which we call the generalized additive model for location, scale and shape (GAMLSS). The model assumes independent observations of the response variable y given the parameters, the explanatory variables and the values of the random effects. The distribution for the response variable in the GAMLSS can be selected from a very general family of distributions including highly skew or kurtotic continuous and discrete distributions. The systematic part of the model is expanded to allow modelling not only of the mean (or location) but also of the other parameters of the distribution of y, as parametric and/or additive nonparametric (smooth) functions of explanatory variables and/or random-effects terms. Maximum (penalized) likelihood estimation is used to fit the (non)parametric models. A Newton–Raphson or Fisher scoring algorithm is used to maximize the (penalized) likelihood. The additive terms in the model are fitted by using a backfitting algorithm. Censored data are easily incorporated into the framework. Five data sets from different fields of application are analysed to emphasize the generality of the GAMLSS class of models.

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1,941 Citations


Journal ArticleDOI: 10.1016/J.TRA.2010.02.001
Dominique Lord1, Fred L. Mannering2Institutions (2)
Abstract: Gaining a better understanding of the factors that affect the likelihood of a vehicle crash has been an area of research focus for many decades. However, in the absence of detailed driving data that would help improve the identification of cause and effect relationships with individual vehicle crashes, most researchers have addressed this problem by framing it in terms of understanding the factors that affect the frequency of crashes - the number of crashes occurring in some geographical space (usually a roadway segment or intersection) over some specified time period. This paper provides a detailed review of the key issues associated with crash-frequency data as well as the strengths and weaknesses of the various methodological approaches that researchers have used to address these problems. While the steady march of methodological innovation (including recent applications of random parameter and finite mixture models) has substantially improved our understanding of the factors that affect crash-frequencies, it is the prospect of combining evolving methodologies with far more detailed vehicle crash data that holds the greatest promise for the future.

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Topics: Poison control (51%)

1,281 Citations


Journal ArticleDOI: 10.2307/3314912
Jerald F. Lawless1Institutions (1)
Abstract: A number of methods have been proposed for dealing with extra-Poisson variation when doing regression analysis of count data. This paper studies negative-binomial regression models and examines efficiency and robustness properties of inference procedures based on them. The methods are compared with quasilikelihood methods. Plusieurs methodes ont ete proposees en vue de traiter le probleme de la variation extra-poissonnienne dans une analyse de regression pour donnees de denombrement. Cet article a pour objet l'etude de modeles de regression binomiale negative et se penche sur les proprietes d'efficacite et de robustesse des methodes inferentielles decoulant des modeles. Ces dernieres sont comparees aux methodes de quasi-vraisemblancce.

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998 Citations


Open accessBook
01 Feb 1997-
Abstract: Enables road safety researchers and professionals to interpret correctly the results of one of the main sources of knowledge about the effect of road safety engineering measures, the "observational Before-After study". This three part monograph includes: the essentials; adaptations of conventional approaches; and elements of a new approach.

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744 Citations


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