A simulation analysis to explore when using a calibration function is preferred over a scalar factor for calibrating safety performance functions

Abstract The Highway Safety Manual (HSM) recommends calibrating Safety Performance Functions using a scalar calibration factor. Recently, a few studies explored the merits of estimating a calibration function instead of a calibration factor. Although it seems a promising approach, it is not clear when a calibration function should be preferred over a scalar calibration factor. On the one hand estimating a scalar factor is easier than estimating a calibration function; on the other hand, the calibration results may improve using a calibration function. This study performs a simulation study to compare the two calibration strategies for different ranges of data characteristics (i.e.: sample mean and variance) as well as the sample size. A measure of prediction accuracy is used to compare the two methods. The results show that as the sample size increases, or variation of data decreases, the calibration function performs better than the scalar calibration factor. If the analyst can collect a sample of at least 150 locations, calibration function is recommended over the scalar factor. If the HSM recommendation of 30-50 locations is used and the analyst desires a better accuracy, calibration function is recommended only if the coefficient of variation of data is less than 2. Otherwise, calibration factor yields better results.