A comprehensive investigation into the mechanisms and causes of traffic crashes holds significant implications for crash prevention and mitigating crash injury severity. Under the influence of unobservable factors, the impact of the same factor on crash injury severity might not only vary spatially but also exhibit temporal instability. Neglecting these characteristics could lead to biased model estimations and confounding effects, potentially resulting in ineffective or even counterproductive traffic safety strategies. Simultaneously considering the spatial heterogeneity and temporal instability of factors that influence crash injury severity, this paper first collects traffic crash data from the Austin metropolitan area in Texas, USA, spanning the years 2017 to 2019, where various independent variables are selected as candidate variables for analyzing crash injury severity, and a latent class logit model is constructed. Subsequently, annual traffic-related statistical exogenous data involving 11 counties are utilized to establish class probability functions within the latent class logit model, thereby accounting for the spatial heterogeneity of crash injury severity. Finally, this study conducts the partially constrained approach for modeling annual basis, simultaneously analyzing the temporal instability of safety factors’ impact on crash injury severity. Notably, this paper not only identifies numerous factors significantly influencing crash injury severity but also discovers that certain factors exhibit significant temporal instability effects on crash injury severity. Several explanatory variables showed temporally instability in terms of their effect on resulting injury severities. Such as, crash locations, lighting conditions, driver age, driver gender, vehicle types, vehicle model year. The findings of this study serve as a valuable reference for delving deeper into the causal mechanisms of crash injury severity as well as formulating effective safety measures.