# Comprehensive Evaluation of a Sparse Dataset, Assessment and Selection of Competing Models
## 5 Results
### Model Comparisons
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Distributions**} & \multicolumn{2}{c}{**GLM**} & \multicolumn{2}{c}{**Zero Augmented**} \\ \cline{2-6}  & **Poisson** & **Quasi-Poisson** & **Negative Binomial** & **Hurdle** & **Zero Inflated** \\ \hline \multirow{2}{*}{Intercept} & \(4\times 10^{-1}\) & \(3.736\times 10^{-1}\) & \(-2.138\) & \(-1.3\times 10\) & \(1.683\) \\  & (\(<\)0.005) & (0.722) & (\(<\)0.005) & (0.9704) & (0.006) \\ \hline \multirow{2}{*}{Shoulder width} & \(-1.455\) & \(-1.455\) & \(1.158\) & \(-2.40\) & \(-1.479\) \\  & (\(<\)0.005) & (0.243) & (0.111) & (0.0833) & (0.047) \\ \hline \multirow{2}{*}{Barrier height} & \(3.6\times 10^{-2}\) & \(3.603\times 10^{-2}\) & \(1.136\times 10^{-1}\) & \(-6.61\times 10^{-2}\) & \(-1.6\times 10^{-2}\) \\  & (\(<\)0.005) & (0.301) & (\(<\)0.005) & (0.0982) & (0.427) \\ \hline \multirow{2}{*}{Barrier length} & \(2.6\times 10^{-4}\) & \(2.235\times 10^{-4}\) & \(2.224\times 10^{-4}\) & \(3.93\times 10^{-4}\) & \(2.926\times 10^{-4}\) \\  & (\(<\)0.005) & (\(<\)0.005) & (\(<\)0.005) & (\(<\)0.005) & (\(<\)0.005) \\ \hline \multirow{2}{*}{Cable barrier} & \(-2.491\) & \(-2.491\) & \(-1.432\) & \(7.51\times 10^{-2}\) & \(-4.82\times 10^{-1}\) \\  & (\(<\)0.005) & (0.092) & (\(<\)0.005) & (0.943) & (0.363) \\ \hline \multirow{2}{*}{Concrete barrier} & \(1.9\times 10^{-1}\) & \(1.991\times 10^{-1}\) & \(-3.539\times 10^{-1}\) & \(4.05\times 10^{-1}\) & \(1.302\times 10^{-1}\) \\  & (\(<\)0.005) & (0.617) & (0.074) & (0.3006) & (0.545) \\ \hline \multirow{2}{*}{W beam barrier} & \(1.6\times 10^{-1}\) & \(1.571\times 10^{-1}\) & \(-3.283\times 10^{-1}\) & \(-2.23\times 10^{-1}\) & \(-2.50\times 10^{-1}\) \\  & (\(<\)0.005) & (0.541) & (0.006) & (0.3514) & (0.043) \\ \hline \multirow{2}{*}{Restraint condition} & \(1.425\) & \(1.425\) & \(2.892\) & \(5.64\) & \(2.842\) \\  & (\(<\)0.005) & (\(<\)0.005) & (\(<\)0.005) & (\(<\)0.005) & (\(<\)0.005) \\ \hline \multirow{2}{*}{Speed compliance} & \(3.7\times 10^{-1}\) & \(3.754\times 10^{-1}\) & \(1.218\) & \(9.51\times 10^{-1}\) & \(8.690\times 10^{-1}\) \\  & (\(<\)0.005) & (0.331) & (\(<\)0.005) & (0.063) & (\(<\)0.005) \\ \hline \multirow{2}{*}{Shoulder width \(\times\) barrier height} & \(5.6\times 10^{-2}\) & \(5.620\times 10^{-2}\) & \(-2.913\times 10^{-2}\) & \(9.18\times 10^{-2}\) & \(5.895\times 10^{-2}\) \\  & (\(<\)0.005) & (0.159) & (0.232) & (0.045) & (0.017) \\ \hline \multirow{2}{*}{Intercept} & \(-\) & \(-\) & \(-\) & \(-1.351\) & \(20.516\) \\  & & & & (\(<\)0.005) & (0.336) \\ \hline \multirow{2}{*}{Shoulder width} & \(-\) & \(-\) & \(-\) & \(1.04\) & \(-6.300\) \\  & & & & (\(<\)0.005) & (0.006) \\ \hline \multirow{2}{*}{Barrier height} & \(-\) & \(-\) & \(-\) & \(5.239\) & \(-3.289\) \\  & & & & (\(<\)0.005) & (\(<\)0.005) \\ \hline \multirow{2}{*}{Traffic (AADT)} & \(-\) & \(-\) & \(-\) & \(2.37\) & \(-0.0002\) \\  & & & & (\(<\)0.005) & (0.005) \\ \hline \multirow{2}{*}{Barrier length} & \(-\) & \(-\) & \(-\) & \(1.44\) & \(-0.001\) \\  & & & & (\(<\)0.005) & (0.011) \\ \hline \multirow{2}{*}{Cable barrier} & \(-\) & \(-\) & \(-\) & \(-6.849\) & \(84.698\) \\  & & & & (\(<\)0.005) & (\(<\)0.005) \\ \hline \multirow{2}{*}{Concrete barrier} & \(-\) & \(-\) & \(-\) & \(-2.496\) & \(18.452\) \\  & & & & (\(0.636\)) & (0.507) \\ \hline \multirow{2}{*}{W beam barrier} & \(-\) & \(-\) & \(-\) & \(-1.101\) & \(48.66\) \\  & & & & (\(<\)0.005) & (\(<\)0.005) \\ \hline \multirow{2}{*}{Shoulder width \(\times\) barrier height} & \(-\) & \(-\) & \(-\) & \(-1.351\) & \(0.223\) \\  & & & & (\(<\)0.005) & (0.012) \\ \hline \multirow{2}{*}{Degree of freedom} & \(10\) & \(10\) & \(11\) & \(20\) & \(19\) \\ \hline \multirow{2}{*}{Log likelihood} & \(-14.805\) & \(-\) & \(-3466\) & \(-3138\) & \(-3425\) \\ \hline \multirow{2}{*}{AIC} & \(29.630\) & \(-\) & \(6955\) & \(6315\) & \(6890\) \\ \hline \end{tabular} – Indicates estimates were not available for those measures.  
\end{table} 
Table 2: Summary of various fitted count models, \(p\)-value in parentheses.