To investigate the factors influencing the severity of injuries resulting from risk-taking behaviors, comprehensive crash data from Rawalpindi City spanning 2017-2021 was meticulously analyzed. This study concentrated on three potential injury severity outcomes: property damage only, injury, and fatality. It examined a comprehensive range of variables encompassing driver, vehicle, roadway, environmental, temporal, and crash characteristics. Random parameter logit models with heterogeneity in means and variances were employed to effectively address the unobserved heterogeneity, exploring potential relationships between variables and random parameters. The presence of temporal instability was confirmed through likelihood ratio tests and out-of-sample predictions, and marginal effects were calculated to further elucidate this issue. Moreover, the partially constrained temporal modeling approaches were also developed and compared to the temporally unconstrained approaches. These findings not only contribute to the understanding of the nexus between risk-taking behaviors and injury outcomes but also shed light on the impact of the COVID-19 pandemic on traffic safety.