The Frequency and Severity of Road Traffic Accidents Investigated on the Basis of State Space Methods
E Hermans, G Wets, F van den Bossche, Transportation Research Institute, Limburg University, BE
The developments in the frequency and severity of road traffic accidents and casualties in Belgium in 1974 - 1999 will be described, explained and forecasted using State Space Methods.
In this study we investigate the developments in the frequency and severity of road traffic accidents and casualties in Belgium in 1974 - 1999. We describe the time series in order to discover the trend, quantify the impact of explanatory variables - laws, weather and economic conditions - and predict the accident data of 2000 and 2001. The methodology used throughout the analysis is State Space Methods. A next objective is the comparison between this study and the results of an earlier research (Van den Bossche, Wets and Brijs, 2004) where a regression model with Auto-Regressive Moving Average (ARMA) errors was used on the same data, in order to evaluate the degree of similarity between these two methodologies.
The increasing interest in a traffic safe world has led to the elaboration of numerous studies on this subject. These studies are very diverse, in terms of problem description as well as data used. An important class of traffic safety models makes use of time series models. Those models are used to describe, explain and forecast road safety. From the broad category of time series models we have preferred to apply State Space Methods here. State Space Models decompose a series in distinct components such as a trend, a seasonal and an irregular part. Moreover, explanatory variables can be added and intervention analysis carried out. Each of those components is modelled separately and has a direct interpretation. Furthermore, the components are allowed to change over time.
The data used in this study are monthly observations from January 1974 till December 1999. In addition to four dependent traffic related variables - the number of accidents with persons killed or seriously injured, the number of accidents with lightly injured persons, the number of persons killed or seriously injured and the number of lightly injured persons - we study the effect of sixteen independent variables.
The overall objective of the State Space analysis is to study the development of the state over time using observed values. More specifically, we want to obtain an adequate description of and to find explanations for this development. Additionally, these models have the ability to predict developments of a series into the future. A State Space Model consists of an observation equation and one or more state equations. The state consists of several components: on the one hand a level, slope and seasonal which give a description of the time series and on the other hand explanatory and intervention variables which give an explanation about the actual development in the series.
For each of the four dependent variables we built 8 descriptive models. Each model consisted of a level, a slope, a seasonal or a combination of those components. Furthermore, the component could be chosen deterministically or stochastically. Whereas the slope hardly contributed to the description of the time series, the seasonal was essential. For each dependent variable the best fit was obtained using a model with stochastic level and deterministic seasonal. The actual traffic data are best described when the level is allowed to vary over time and the recurring seasonal pattern is taken into account.
When apart from the descriptive objective, the explanatory objective is aimed at, the effect of 16 independent variables is tested. Several laws - especially these concerning the mandatory seat belt use in front seats (June 1975), a speed limit of 50 km/h in urban areas (January 1992) and a 0.5? blood alcohol concentration (December 1994) - had a clear positive effect. Apart from those, the weather elements precipitation, sun, frost and thunderstorm were important. Frost was the only weather condition with a favorable effect on traffic safety. On the subject of the economic variables, the number of unemployed and the number of car registrations seemed significant. Furthermore, in order to obtain normally distributed residuals - which imply (more) reliable results - we added correction variables to the model. We corrected for the unusual low registered values in January 1979, January 1984, January 1985 and February 1997.
We use the final model - which contains a stochastic level, a deterministic seasonal and significant explanatory and correction variables - to forecast the values of the out-of-sample dataset for 2000 and 2001 and compare them to the actual observations. The graphs show that the predictions are close to the actual observations. So we are able to capture a great part of the fluctuations in the series. Apart from a visual presentation, we also quantified the forecasting precision. The results of the Failure Chi-squared test and the mean squared error (MSE) confirmed our conclusion of accurate predictions.
From this study we can conclude that there is a lot of similarity between the results of the State Space Method and the regression model with ARMA errors. Both methods labeled to a large extent the same explanatory variables as significant and their influence was at all times in the same (expected) direction and of comparable magnitude. The major difference lies in the significance of the economic variables. The forecasting capacity for 2000 of both methods was tested quantitatively and resulted to be approximately the same.
The models developed in this text show large potential for describing the long term trends in traffic safety. On the one hand, they can isolate the effect of phenomena that cannot be influenced, but certainly act upon traffic safety (for example the weather). Similarly, macro-economic and socio-demographic evolutions could be added to the model. On the other hand, the efficiency of policy decisions (for example laws) can be tested. These are the direct tools for increasing the level of traffic safety. Apart from quantifying the impact of variables, forecasts can be made and the corresponding uncertainty can be estimated.
Elke Hermans, Geert Wets and Filip Van den Bossche
Association for European Transport