## 5 Conclusions
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multicolumn{6}{c}{**1 st Model: FMM Cluster**} & \multicolumn{6}{c}{**2 nd Model: Highway Classification Cluster**} \\ \hline  & \multicolumn{3}{c}{**Parameter Estimates**} & \multicolumn{3}{c}{**95\% BCI of Estimates**} & \multicolumn{3}{c}{**Parameter Estimates**} & \multicolumn{3}{c}{**95\% BCI of Estimates**} \\ \hline  & **Mean** & **SD** & **2.50\%** & **97.50\%** & & **Mean** & **SD** & **2.50\%** & **97.50\%** \\ \hline alpha [1] & 3.572 & 0.077 & 3.423 & 3.727 & alpha [1] & 3.186 & 0.126 & 2.943 & 3.432 \\ alpha [2] & 4.895 & 0.105 & 4.691 & 5.103 & alpha [2] & 3.350 & 0.147 & 3.063 & 3.634 \\ alpha [3] & 0.72 & 0.053 & 0.616 & 0.823 & alpha [3] & - & - & - & - \\ alpha [4] & 3.208 & 0.063 & 2.184 & 2.432 & alpha [4] & - & - & - & - \\ b1 & 0.377 & 0.063 & 0.253 & 0.504 & Restrain condition & 1.428 & 0.123 & 1.191 & 1.675 \\ b2 & \(-\)0.039 & 0.05 & \(-\)0.14 & 0.058 & Gender & \(-\)0.067 & 0.009 & \(-\)0.243 & 0.110 \\ b3 & \(-\)0.075 & 0.047 & \(-\)0.169 & 0.018 & Residency & 0.213 & 0.083 & 0.048 & 0.375 \\ b4 & \(-\)0.292 & 0.045 & \(-\)0.383 & \(-\)0.204 & Weather condition & \(-\)0.782 & 0.080 & \(-\)0.940 & \(-\)0.624 \\ b5 & \(-\)0.071 & 0.047 & \(-\)0.163 & 0.022 & Light condition & \(-\)0.101 & 0.084 & \(-\)0.264 & 0.064 \\ b6 & 0.0001 & 0.02 & 0.00008 & 0.00003 & AADT & 0.0002 & 0.07 & 0.00008 & 0.0003 \\ b7 & 0.00002 & 0.3 & 0.00001 & 0.00004 & Barrier length & 0.00004 & 0.5 & 0.00001 & 0.00006 \\ b8 & 0.202 & 0.043 & 0.118 & 0.286 & Highway classification & - & - & - & - \\ cluster & - & - & - & - & cluster & \(-\)0.553 & 0.034 & \(-\)0.621 & \(-\)0.487 \\ \hline \multicolumn{6}{c}{Variance component} \\ \hline Intercept (\(\phi_{\text{P}}\)): & & & & & & & \\ Between crash & 2.876 & 1.518 & 0.052 & 5.72 &
\begin{tabular}{c} Intercept (\(\phi_{\text{P}}^{2}\): Between crash variance \\ \end{tabular} & 3.274 & 2.464 & 2.195 & 4.398 \\ \(\sigma^{2}\): within crash variance & 7 & & \(\sigma^{2}\): within crash variance & 66 & \\ \hline \multicolumn{6}{c}{PD = 13.4, DIC = 8416, \(p=\) 0.515, r= 3.53, var = 7, ICC = 0.3} & \multicolumn{3}{c}{pD = 11.5, DIC = 10.808, \(p=\) 0.12, r = 0.75, var = 66, ICC = \(<\)0.1} \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Model estimations for two hierarchical models. in terms of DIC, 8416 versus 10,808. Additionally, while the subjective hierarchy resulted in the ICC of less than 0.1, the proposed method resulted in ICC = 0.3. The results of this study had an important implication for crash analyses in future studies. This study highlighted that selecting appropriate clusters could account for a significantly higher amount of the heterogeneity in the dataset. Although several studies have been evaluated with FMM, no study to the best of the knowledge of the authors of this study has implemented the BHFMM technique to account for the data heterogeneity in the context of traffic safety. It is highly recommended that this technique to be utilized in future studies instead of subjective use of hierarchies. K.K. supervision and funding; M.R. methodology. All authors have read and agreed to the published version of the manuscript. The funding is supported by WYDOT. There is no conflict of interest across the authors.