Traffic barrier crashes have been a major concern in many prior studies in traffic safety literature, especially in the crash-prone sections of mountainous regions. However, the effect of factors affecting the injury-severities resulting from crashes involving different types of traffic barriers may be different. This paper provides an empirical assessment of the performance of ordered and unordered discrete outcome models for examining the impact of exogenous factors determining the driver injury-severity of crashes involving two types of traffic barriers in mountainous regions: w-beam barriers and cable barriers. For the ordered framework, the alternative modeling approaches include: the generalized ordered logit (GOL) and the random thresholds random parameters generalized ordered logit model (RTRPGOL). Whereas, for the unordered framework, the alternative modeling approaches include: the multinomial logit (MNL), the random parameters multinormal logit (RPL), and the random parameters multinormal logit model with heterogeneity in the means and variances (RPLHMV). Using injury-severity data from 2016 to 2019 for mountainous regions in Guiyang City, China, three injury-severity categories are determined as outcome variables: severe injury (SI), minor injury (MI), and no injury (NI), while the potential influencing factors including drivers-, vehicles-, road-, and environment-specific characteristics are statistically analyzed. The model estimation results show: (a) that the MNL model statistically outperforms the GOL model in terms of goodness-of-fit measures; (b) the RTRPGOL model is statistically superior to the MNL and RPL models; and (c) the RPLHMV model is statistically superior to the RTRPGOL model, and therefore the preferred option among the model alternatives. To that end, the RPLHMV model is leveraged to quantitatively describe the impact of explanatory variables on the driver injury-severity and explore how these factors change over the years (between 2016–2017 and 2018–2019). The results further show that the factors affecting driver injury severities and the effects of significant factors on injury severity probabilities change across traffic barrier crash models and across years. In addition, the results of the temporal effects analysis show that some variables present relative temporal stability, which is important for formulating long-term strategies to enhance traffic safety on mountainous roads. Most importantly, the effects of the explanatory factors that exhibit relative temporal stability are found to vary across traffic barrier crashes. For example, trucks, daylight, curved section segments, and high-speed limit (greater than 55 mph) are some of the factors that have opposite effects between traffic barrier crash models. The findings from this paper are expected to help policy makers to take necessary measures in reducing traffic barrier crashes in mountainous regions by forming appropriate strategies, and by allocating properly their available resources at the pre-planning phase.@en