## 3 Results
### Model Validation  
The developed behavior models were validated in terms of model distance and model performance. Table 8 provides answers to the following questions: given two HMMs, the failure model \(\lambda_{Fail}\) and the success model \(\lambda_{Success}\), what is a reasonable measure of the similarity of the two models? An important key point here is similarity criteria. Even though the two models, \(\lambda_{Fail}\) and \(\lambda_{Success}\), look very different, a statistical equivalent of the model can occur. Distance measures \(D(\lambda_{Fail}\), \(\lambda_{Success})\) or \(D(\lambda_{Success}\), \(\lambda_{Fail})\) between models \(\lambda_{Fail}\) and \(\lambda_{Success}\) have a dissimilarity concept with respect to model distance. Several interpretations of the model distance exist in terms of such as cross entropy, divergence, and discrimination of information [28; 35]. The \(MD_{Success}\) is a measure result of how well the model \(\lambda_{Fail}\) matches observations generated by model \(\lambda_{Success}\), relative to how well model \(\lambda_{Success}\) matches observations generated by itself. Also, \(MD_{Fail}\) is a measure result of how well model \(\lambda_{Success}\) matches observations generated by model \(\lambda_{Fail}\), relative to how well model \(\lambda_{Fail}\) matches observations generated by itself.  
Table 8 shows the validation results by comparing the two models. Note that a larger model distance indicates greater discernibility of the model. Meanwhile, model performance increases as the model distance increases. The log likelihood (\(-1.69\)) of \(MD_{Success}\) was about 1.5 times larger than  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Classification** & **Measurement Variable** & **Mean (SD)** \\ \hline \multirow{2}{*}{Model distance} & \(MD_{Success}=D(\lambda_{Fail}\), \(\lambda_{Success})\) & \(-2.60\) (2.68) \\  & \(MD_{Fail}=D(\lambda_{Success}\), \(\lambda_{Fail})\) & \(-1.69\) (1.54) \\ \hline \multirow{2}{*}{Model performance} & \(CR_{Success}\) & 0.7871 \\  & \(CR_{Fail}\) & 0.9434 \\ \hline \hline \end{tabular}
\end{table}
Table 8: Comparison results of two models in terms of model distance and model performance.  
Figure 9: Percentile (%) of behavior performance levels for successful and failed collision avoidance; (**a**) device control behavior for success; (**b**) device control behavior for failure; (**c**) route control behavior for success; and (**d**) route control behavior for failure.  
the log likelihood (\(-2.60\)) of \(MD_{\text{Fail}}\). Thus, dissimilarity was greater for the failure model than that for the success model. As a result, the failure model shows that the degree of dissimilarity with the success model is larger than the success model, but more closely matches the observations generated by the model itself. This result implies that the failure model has a higher predictive power of behavior observed compared to the success model. The reason why the failure model has higher discriminative power than the success model will be discussed in Section 4.  
As the result of model distance, the percentile of model performance was 78.71% for the success model and 94.34% for the failure model.