Partially temporally constrained modeling of speeding crash-injury severities on freeways and non-freeways before, during, and after the stay-at-home order

•Impacts of the stay-at-home order on speeding crashes on freeways and non-freeways are investigated.•Temporal stabilities and instabilities among factors are determined by partially constrained models.•Contributing factors and in-depth heterogeneity across observations are identified.•Hysteretic effects of the order on crash frequency and severity are observed.•Shifts in speeding behaviors and crash outcomes suggest a worse condition after the order. Speeding crashes remain high injury severities after the stay-at-home order in California, highlighting a need for further investigation into the fundamental cause of this increment. To systematically explore the temporal impacts of the stay-at-home order on speeding behaviors and the corresponding crash-injury outcomes, this study utilizes California-reported single-vehicle speeding crashes on freeways (access-controlled) and non-freeways (non-access-controlled) before, during, and after the order. Significant injury factors and in-depth heterogeneity across observations are identified by random parameter logit models with heterogeneity in means and variances. Without segmenting the data by periods, the partially temporally constrained approach is employed to statistically determine varying and stabilized parameters over time through the whole dataset. Different likelihood ratio tests reveal significant temporal instabilities and stabilities of factors between two roadways and three periods. The potential impacts of observation selection issues on the marginal effect calculations of the partially constrained models are also systematically investigated. Significant variations in the probability of severe injury rate per week after the order are also found based on the Mann-Whitney U tests. The hysteretic effects of the order on the crash frequency and severity are observed on both freeways and non-freeways. Overall, seven variables are found to have stable effects, while fifteen variables exhibit unstable effects over time. Significant temporal variations in driver behaviors, including driving under the influence, cell phone usage, hit-and-run, failure to use seat belt, entering or leaving the ramp, and reaction to previous collisions, are observed before, during, or after the order. Specific countermeasures and effects of heterogeneity in means and variances are also discussed. These findings provide insights into understanding the temporal impacts of the stay-at-home order on injury severities, which are va