Time-specific Safety Performance Functions (SPFs) were proposed to achieve accurate and dynamic crash frequency predictions. This study contributes to the literature by developing time-specific SPFs for freeways that include reversible lanes (RL) and freeways that include High-Occupancy Vehicle lanes (HOV) using Microwave Vehicle Detection System (MVDS) data from Virginia, Arizona and Washington States. Variables that capture the time-specific traffic turbulence were prepared and considered in the developed SPFs. Moreover, two different hierarchical models were proposed to identify factors associated with the different crash types or severity in crash frequency prediction. The results indicated that the variables representing the volume difference between reversible and general-purpose lanes (GPL) were positively associated with crash frequency. Further, the variable that indicated the design of the access point of the reversible lane was positively associated with crash frequency. The models comparison results showed that the hierarchical models outperformed the corresponding Poisson lognormal model with lower AIC and MAE values. This study also tested the proposed hierarchical models on High-Occupancy Vehicle freeway sections and reached the same conclusion on model comparison results. The significant variables representing the logarithm of volume were found to be significant and positive with crash frequency. Moreover, the difference in average speed between the HOV lanes and GPL was also found to be positive and significant with the crash frequency. In general, this study successfully identified the factors associated with the different crash types or severity in crash frequency prediction models.