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Single-vehicle run-off-road crashes accounts for approximately 35% of all the traffic fatalities in the U.S during the period of 2019-2021. This paper explores the association between driving speed and injury severity outcomes of single-vehicle run-off-road crashes. The single-vehicle run-off-road crash data from 2019 to 2021 on Interstate freeways in Florida are utilized, and categorized into periods of pre-, during-, and post-COVID-19 pandemic. The partially constrained temporal and temporal unconstrained random parameters logit models are developed considering three injury severity outcomes: no injury, minor injury and serious injury/fatality. Multiple variables in terms of driver, vehicle, roadway, environmental, crash, and temporal attributes are observed to significantly affect the injury severity. Moreover, temporal instability and transferability issues are validated through likelihood ratio test and out-of-sample prediction. In the partially constrained models, numerous variables such as indicators of new vehicle, male driver, and restraint-protected driving consistently yield identical parameter values across all periods, whereas various variables clearly illustrate the distinct differences across the three periods and three speed intervals. The marginal effects in the unconstrained models also display the obvious differences across three periods and three speed intervals. Moreover, the findings corroborate the increased risk outcomes linked to larger speed differences and the COVID-19 pandemic period. These results provide better understanding of the risk mechanisms underlying run-off-road crashes and furnish valuable direction for the formulation of effective safety interventions., Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2024 Elsevier Ltd. All rights reserved.)