A method to account for outliers in the development of safety performance functions

Accident data sets can include some unusual data points that are not typical of the rest of the data. The presence of these data points (usually termed outliers) can have a significant impact on the estimates of the parameters of safety performance functions (SPFs). Few studies have considered outliers analysis in the development of SPFs. In these studies, the practice has been to identify and then exclude outliers from further analysis. This paper introduces alternative mixture models based on the multivariate Poisson lognormal (MVPLN) regression. The proposed approach presents outlier resistance modeling techniques that provide robust safety inferences by down-weighting the outlying observations rather than rejecting them. The first proposed model is a scale-mixture model that is obtained by replacing the normal distribution in the Poisson-lognormal hierarchy by the Student t distribution, which has heavier tails. The second model is a two-component mixture (contaminated normal model) where it is assumed that most of the observations come from a basic distribution, whereas the remaining few outliers arise from an alternative distribution that has a larger variance. The results indicate that the estimates of the extra-Poisson variation parameters were considerably smaller under the mixture models leading to higher precision. Also, both mixture models have identified the same set of outliers. In terms of goodness-of-fit, both mixture models have outperformed the MVPLN. The outlier rejecting MVPLN model provided a superior fit in terms of a much smaller DIC and standard deviations for the parameter estimates. However, this approach tends to underestimate uncertainty by producing too small standard deviations for the parameter estimates, which may lead to incorrect conclusions. It is recommended that the proposed outlier resistance modeling techniques be used unless the exclusion of the outlying observations can be justified because of data related reasons (e.g., data collection errors).