Multivariate non-linear time series modelling of exposure and risk in road safety research

Authors: Bijleveld, Frits1; Commandeur, Jacques1; Koopman, Siem Jan2; Montfort, Kees van2

Source: Journal of the Royal Statistical Society: Series C (Applied Statistics), Volume 59, Number 1, January 2010 , pp. 145-161(17)

Publisher: Wiley-Blackwell

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A multivariate non-linear time series model for road safety data is presented. The model is applied in a case-study into the development of a yearly time series of numbers of fatal accidents (inside and outside urban areas) and numbers of kilometres driven by motor vehicles in the Netherlands between 1961 and 2000. The model accounts for missing entries in the disaggregated numbers of kilometres driven although the aggregated numbers are observed throughout. We consider a multivariate non-linear time series model for the analysis of these data. The model consists of dynamic unobserved factors for exposure and risk that are related in a non-linear way to the number of fatal accidents. The multivariate dimension of the model is due to its inclusion of multiple time series for inside and outside urban areas. Approximate maximum likelihood methods based on the extended Kalman filter are utilized for the estimation of unknown parameters. The latent factors are estimated by extended smoothing methods. It is concluded that the salient features of the observed time series are captured by the model in a satisfactory way.

Keywords: Approximate maximum likelihood; Extended Kalman filter; Missing data; Road casualties; State space model; Unobserved factors

Document Type: Research Article


Affiliations: 1: Institute for Road Safety Research, Leidschendam, The Netherlands 2: Vrije Universiteit Amsterdam, The Netherlands

Publication date: January 1, 2010

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