Truck freight has high importance to the national economy as it handles more cargo than other types of freight transportation. To improve the safety of commercial vehicles, several studies have focused on determining factors leading to crashes. Parametric models have been extensively employed to explain crash causal factors for heavy trucks. Unlike studies in the past, a comprehensive framework was proposed in this study to compare crash underlying factors utilizing several statistical approaches. The structural equation modeling approach was used to assess latent factors affecting the crash severity of large trucks. In addition, ordinary (binary) logistic and random parameter models were employed to assess the direct effect of the observed data, and the heterogeneity in parameter means was also estimated. Three crash categories were investigated: single-truck crashes, multi-vehicle truck crashes, and total truck crashes. A total of five years of crash data from 2015 to 2019 were analyzed. The results showed that multiple observed variables were factored to measure crash severity. Direct and indirect effects were identified, in which challenging roadway conditions had an indirect effect on crash severity for single-truck crashes. Random parameter logit models indicated that roadway geometry and adverse weather conditions were among the significant contributing factors increasing crash severity for trucks. This study recommends that improving the situational awareness of truck drivers, providing more frequent rest stops, updating variable speed limit algorithms, and integrating roadway geometry information into connected vehicle applications in Wyoming could be considered to assist stakeholders in promoting safety on rural interstate corridors.