Evaluating the Negative Binomial and Poisson with Linear Correction Models for Crash Prediction in terms of Precision and Accuracy

In recent years considerable studies have been carried out to investigate the relationships between crashes and related factors. In modelling the count data such as crash frequency, Poisson family as a part of Generalized Linear Models (GLMs) has shown to be reasonable. However; the requirement of such model is that the variance equals the mean. When dealing with crash count data, such assumption is mostly violated since the variance is much greater than mean; a phenomenon known as over-dispersion. Negative Binomial model has proved successful in dealing with such problem, however; such model cannot hold the consistency of the sum of the observed and predicted values for dependent variable. Using ۳-year crash data from ۲۰۱۷-۲۰۱۹ and its relating factors, this study aims to develop Poisson with linear correction model In Mashhad, Iran and compare the results with common GLMs with Poisson and Negative Binomial distribution. The models were compared in terms of precession and accuracy and theresults indicated that NB is more precise due to the lower AIC and BIC and higher log likelihood values and the Poisson with linear correction is more accurate owing to thelower Mean Square Error, Mean Absolute Deviance and higher coefficient of determination and therefore can be employed in safety analysis to develop the accurate models with high prediction power due to the consistency between sum of the predicted and input values.

Keywords:

Safety , Negative Binomial , Poisson with linear correction , crash , urban areas