The article proposes a two-staged modelling approach to identify the association between one vehicle's attributes, as well as roadway engineering, environmental and crash characteristics, and the injury severity of occupants in the partnering vehicle in two-vehicle crashes. The modelling approach uses a bivariate binary probit model, and crash data for Toronto, to first determine the probability of injury and no injury occurring, followed by the use of a bivariate ordered probit model to investigate the conditional probability of the specific severity level. Vehicles in two-vehicle crashes are categorized as “not-at-fault” (NAF) or “at-fault” (AF) and their occupants also categorized as such. The findings demonstrate that the modelling approach used in this study can reveal meaningful insights by improving understanding of how the same attribute could behave differently for NAF and AF vehicles. For example, factors found to be associated with increased probability of more severe injuries of NAF vehicle occupants are inattentive driving, left-turn movement, heavy vehicle type of the AF vehicle, and angle and rear-end impact type; conversely, for AF vehicles, their probability of more severe injury is positively associated with inattentive driving and heavy vehicle type of the NAF vehicle, and angle and approaching impact type. [ABSTRACT FROM AUTHOR]