Abstract Background Determining risk factors of single-vehicle run-off-road (SV-ROR) crashes, as a significant number of all the single-vehicle crashes and all the fatalities, may provide infrastructure for quicker and more effective safety measures to explore the influencing and moderating variables in SV-ROR. Therefore, this paper emphasizes utilizing a hybrid of regularization method and generalized path analysis for studying SV-ROR crashes to identify variables influencing their happening and severity. Methods This cross-sectional study investigated 724 highway SV-ROR crashes from 2015 to 2016. To drive the key variables influencing SV-ROR crashes Ridge, Least Absolute Shrinkage and Selection Operator (Lasso), and Elastic net regularization methods were implemented. The goodness of fit of utilized methods in a testing sample was assessed using the deviance and deviance ratio. A hybrid of Lasso regression (LR) and generalized path analysis (gPath) was used to detect the cause and mediators of SV-ROR crashes. Results Findings indicated that the final modified model fitted the data accurately with $${\mathcal{X}}_{3}^{2}$$ X 3 2 = 16.09, P  < .001, $${\mathcal{X}}^{2}$$ X 2 / degrees of freedom = 5.36 > 5, CFI = .94 > .9, TLI = .71 < .9, RMSEA = 1.00 > .08 (90% CI = (.06 to .15)). Also, the presence of passenger (odds ratio (OR) = 2.31, 95% CI = (1.73 to 3.06)), collision type (OR = 1.21, 95% CI = (1.07 to 1.37)), driver misconduct (OR = 1.54, 95% CI = (1.32 to 1.79)) and vehicle age (OR = 2.08, 95% CI = (1.77 to 2.46)) were significant cause of fatality outcome. The proposed causal model identified collision type and driver misconduct as mediators. Conclusions The proposed HLR-gPath model can be considered a useful theoretical structure to describe how the presence of passenger, collision type, driver misconduct, and vehicle age can both predict and mediate fatality among SV-ROR crashes. While notable progress has been made in implementing road safety measures, it is essential to emphasize that operative preventative measures still remain the most effective approach for reducing the burden of crashes, considering the critical components identified in this study.