Markov states of MGM(1,4) output values.

We propose a multivariate Grey-Markov model to quantify traffic accident risk from different causality factors in roundabouts that is uniquely suited for the scarce and stochastic traffic crash data from roundabouts. A data sample of traffic crashes occurring in roundabouts in the U.S. State of Michigan from 2016 to 2021 was collected to investigate the capabilities of this modeling methodology. The multivariate grey model (MGM(1,4)) was constructed using grey relational analysis to determine the best dimensions for model optimization. Then, the Markov chain is introduced to address the unfitness of stochastic, fluctuating data in the MGM(1,4) model. Finally, our proposed hybrid MGM(1,4)-Markov model is compared with other models and validated. This study highlights the superior predictive performance of our MGM(1,4)-Markov model in fore-casting roundabout traffic accidents under data-limited conditions, achieving a 3.02% accuracy rate, in contrast to the traditional GM(1,1) model at 8.30% and the MGM(1,4) model at 4.47%. Moreover, incorporating human, vehicle, and environmental risk factors into a multivariate crash system yields more accurate predictions than merely aggregating crash counts.