Rollover crashes are responsible for a notable number of serious injuries and fatalities; hence, they are of great concern to transportation officials and safety researchers. However, only few published studies have analyzed the factors associated with severity outcomes of rollover crashes. This research has two objectives. The first objective is to investigate the effects of various factors, of which some have been rarely reported in the existing studies, on the injury severities of single-vehicle (SV) rollover crashes based on six-year crash data collected on the Malaysian federal roads. A random-effects generalized ordered probit (REGOP) model is employed in this study to analyze injury severity patterns caused by rollover crashes. The second objective is to examine the performance of the proposed approach, REGOP, for modeling rollover injury severity outcomes. To this end, a mixed logit (MXL) model is also fitted in this study because of its popularity in injury severity modeling. Regarding the effects of the explanatory variables on the injury severity of rollover crashes, the results reveal that factors including dark without supplemental lighting, rainy weather condition, light truck vehicles (e.g., sport utility vehicles, vans), heavy vehicles (e.g., bus, truck), improper overtaking, vehicle age, traffic volume and composition, number of travel lanes, speed limit, undulating terrain, presence of central median, and unsafe roadside conditions are positively associated with more severe SV rollover crashes. On the other hand, unpaved shoulder width, area type, driver occupation, and number of access points are found as the significant variables decreasing the probability of being killed or severely injured (i.e., KSI) in rollover crashes. Land use and side friction are significant and positively associated only with slight injury category. These findings provide valuable insights into the causes and factors affecting the injury severity patterns of rollover crashes, and thus can help develop effective countermeasures to reduce the severity of rollover crashes. The model comparison results show that the REGOP model is found to outperform the MXL model in terms of goodness-of-fit measures, and also is significantly superior to other extensions of ordered probit models, including generalized ordered probit and random-effects ordered probit (REOP) models. As a result, this research introduces REGOP as a promising tool for future research focusing on crash injury severity.