Single-vehicle crashes are of (hitting pedestrians, animal and object/tree, self-skidding, and overturn) growing concern across the globe because of the high proportion of fatalities associated with them. Their mechanism differs from multi-vehicle crashes and requires particular countermeasures to mitigate related injuries and deaths. In the present research work, stochastic models were used to study the epidemiology of single-vehicle crashes, identify the patterns in the single-vehicle crash datasets, formulate the single-vehicle crash scenarios with identified contributory factors, and suggest effective countermeasures with identified contributory factors. Moreover, we developed visual hazardous models (spatiotemporal feature selection latent class clustering ordered probit/random parameter ordered probit models) to address the dimensionality and heterogeneity in the datasets. Additionally, marginal effects were computed to understand the impact of the predictor variable on each predicted variable. We used comprehensive single-vehicle crash data collected from the Road Accident Database Management System (RADMS) for modelling. The data comprises a crash, location and time, vehicle, driver, pedestrian, road and environment details. The Results show that the following contributory factors: Novice drivers/riders (18-24 age group), illegal drivers/riders (