Practical Minimum Sample Size for Road Crash Time-Series Prediction Models

Abstract

Road crashes are problems facing the transportation sector. Crash data in many countries are available only for the past 10 to 20 years, which makes it difficult to determine whether the data are sufficient to establish reasonable and accurate prediction rates. In this study, the effect of sample size (number of years used to develop a prediction model) on the crash prediction accuracy using Autoregressive integrated moving average (ARIMA) method was investigated using crash data for years 1971–2015. Based on the availability of annual crash records, road crash data for four selected countries (Denmark, Turkey, Germany, and Israel) were used to develop the crash prediction models based on different sample sizes (45, 35, 25, and 15 years). Then, crash data for 2016 and 2017 were used to verify the accuracy of the developed models. Furthermore, crash data for Palestine were used to test the validity of the results. The used data included fatality, injury, and property damage crashes. The results showed similar trends in the models’ prediction accuracy for all four countries when predicting road crashes for year 2016. Decreasing the sample sizes led to less prediction accuracy up to a sample size of 25; then, the accuracy increased for the 15-year sample size. Whereas there was no specific trend in the prediction accuracy for year 2017, a higher range of prediction error was also obtained. It is concluded that the prediction accuracy would vary based on the varying socioeconomic, traffic safety programs and development conditions of the country over the study years. For countries with steady and stable conditions, modeling using larger sample sizes would yield higher accuracy models with higher prediction capabilities. As for countries with less steady and stable conditions, modeling using smaller sample sizes (15 years, for example) would lead to high accuracy models with good prediction capabilities. Therefore, it is recommended that the socioeconomic and traffic safety program status of the country is considered before selecting the practical minimum sample size that would give an acceptable prediction accuracy, therefore saving efforts and time spent in collecting data (more is not always better). Moreover, based on the data analysis results, long-term ARIMA prediction models should be used with caution.