# A Statistical Approach to Discovering Process Regime Shifts and Their Determinants
## 4 Case Studies
### Case 3: Deaths in Road Accidents and Impact of the Safety Program  
The third case belongs to the road traffic system, which can be classified as a socio-technical system. This system involves several things, including a road network infrastructure, road safety rules, cars and drivers, among others. Several environmental factors may be important, including weather, etc. We are interested in mining the process generating major road accidents leading to deaths for this system. We mined ten years of a log obtained for a major middle eastern region (Figure 14). The main determinants considered are road safety measures implemented during the same periods. These measures include strict seatbelt penalty laws, which came into full effect by January 2015. Following this, cameras for detecting red lights running were introduced in March 2015. Finally, automatic detection cameras with heavy penalties for speeding were installed by 1 March 2017.  
Figure 14: Road accident deaths data for December 2009–December 2019.  
Figure 12: Worldwide Deaths caused by COVID-19 (until 31 December 2021).  
Figure 13: Regime Changes in WTI spot price data (base model with COVID-19 variable).  
The mining objectives are again twofold, i.e., determining whether there are any positive or negative regime changes in deaths in road accidents; and whether the safety measures played any role in enhancing the existing traffic safety situation. For this case, as compared to the first two, we are dealing with count data that may be following Poisson or negative binomial distribution, depending upon mean vs. variance present in the data. Accordingly, we found that the mean = 60.25 deaths/month and that the variance = 406.91, and thus we considered a generalized linear regression model with a negative binomial distribution. Considering both the level and trend, the minimal form of the model turns out to be \(\log(p_{i}^{\prime})=t_{i}\alpha_{i}+\epsilon_{i}\) (as suggested via Equation (2a) and Equation (2b)). The model was tested for regime changes, and the results are shown in Figure 15. The results show two regime changes, where, in the first regime, a sharp rise in deaths is evident, followed by the lowering of the death rate in the second regime. Finally, we clearly see a negative trend in the third regime.  
Since the multiple new safety measures were introduced at varying times, we ranked these measures based on their occurrences and tested them in the same sequence. The results of this incremental procedure are shown in Table 5.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{3}{*}{**Models**} & \multicolumn{6}{c}{**Model Fit Details**} \\ \cline{2-9}  & \multicolumn{4}{c}{**Significance Codes: 0 *** 10.001 *** 10.01 *** 10.05 \(\boldsymbol{\cdot}\)\(\boldsymbol{\cdot}\)\(\boldsymbol{\cdot}\)\(\boldsymbol{\cdot}\)\(\boldsymbol{\cdot}\)\(\boldsymbol{\cdot}\)10.1 \(\boldsymbol{\cdot}\)\(\boldsymbol{\cdot}\)\(\boldsymbol{\cdot}\)\(\boldsymbol{\cdot}\)11**} \\ \cline{2-9}  & **Regime Period** & **Term** & **Estimate** & **Stand. Error** & **z-Value** & **Pr (\textgreater{}\textgreater{The first iteration shows the results for the base model with level and trend only. Both the level and the trend term turn out to be significant in all three segments. When the seatbelt variable was introduced, it did not cause any regime shifts. This determinant seems to have a mild effect only in the second regime segment. A similar outcome is evident in the case of red-light cameras. However, when speed cameras were introduced, the second shift turned out to be undetected, showing that the last segment's negative trend is caused by this measure.