## 3 Methods
### Risk Factor Coupling Analysis
#### 3.4.1 N-K Model
Given 0 or 1 mapped to \(h\) and \(v\), and pointing to \(r,w,m\in\{0,1\}\), with \(P_{00***}\),\(P_{01***}\),\(P_{0***}\) and \(P_{11***}\), and \(P_{00***}+P_{10***}+P_{11***}=1\). Furthermore, in \(P_{10***}\), \(h=1\), \(v=0\), and \(r,w,m\in\{0,1\}\), \(P_{10***}\) is the sum of all \(P_{n_{strvum}}\) with \(h=1\) and \(v=0\). This means that it requires calculating the frequency of accident samples where human-related risk is present and vehicle-related risk is absent, independent of the other three risk types. \(P(h)\), \(P(v)\), \(P(r)\), \(P(w)\) and \(P(m)\) represent the probability of a single risk type. Taking \(P(h)\) as an example, it is calculated as follows:  
\[P(h)=\sum_{v}\sum_{w}\sum_{m}P_{n_{strvum}} \tag{8}\]  
Given 0 or 1 mapped to \(h\), and pointing to \(v,r,w,m\in\{0,1\}\), with \(P_{0***}\) and \(P_{1***}\) and \(P_{0***}+P_{1***}=1\). In \(P_{1***}\), \(h=1\), \(v,r,w,m\in\{0,1\}\), and \(P_{1***}\) is the sum of all \(P_{n_{strvum}}\) with \(h=1\). This means that it requires calculating the frequency of accident samples where human-related risk is present, independent of the other four risk types. Similarly, the risk coupling value for the three-factor coupling type was calculated as follows:  
\[\left\{ \begin{array}{l}T_{3,1}(H,V,R)=\sum_{h}\sum_{v}\sum_{r}P(h,v,r)\cdot log _{2}\frac{P(h,v,r)}{P(h)P(v)P(r)}\\ T_{3,2}(H,V,W)=\sum_{h}\sum_{v}\sum_{w}P(h,v,w)\cdot log_{2}\frac{P(h,v,w)}{P( h)P(v)P(w)}\\ T_{3,3}(H,V,M)=\sum_{h}\sum_{v}\sum_{m}P(h,v,m)\cdot log_{2}\frac{P(h,v,m)}{P( h)P(v)P(m)}\\ T_{3,4}(H,R,W)=\sum_{h}\sum_{v}\sum_{w}P(h,r,w)\cdot log_{2}\frac{P(h,v,m)}{P( h)P(v)P(w)}\\ T_{3,5}(H,R,M)=\sum_{h}\sum_{v}\sum_{m}P(h,r,m)\cdot log_{2}\frac{P(h,r,m)}{P( h)P(r)P(m)}\\ T_{3,6}(H,W,M)=\sum_{h}\sum_{v}\sum_{m}P(h,w,m)\cdot log_{2}\frac{P(h,v,m)}{P( h)P(h)P(v)P(m)}\\ T_{3,7}(V,R,W)=\sum_{v}\sum_{w}P(v,r,w)\cdot log_{2}\frac{P(v,w)}{P(v)P(v)P(w)}\\ T_{3,8}(V,R,M)=\sum_{v}\sum_{m}P(v,r,m)\cdot log_{2}\frac{P(v,m)}{P(v)P(v)P(m)} \\ T_{3,9}(V,W,M)=\sum_{v}\sum_{w}\sum_{m}P(v,w,m)\cdot log_{2}\frac{P(v,w,m)}{P( v)P(v)P(m)}\\ T_{3,10}(R,W,M)=\sum_{v}\sum_{w}\sum_{m}P(r,w,m)\cdot log_{2}\frac{P(r,w,m)}{P( r)P(v)P(m)}\end{array} \right. \tag{9}\]  
where \(P(h,v,r)\), \(P(h,v,w)\), \(P(h,v,m)\), \(P(h,r,w)\), \(P(h,r,m)\), \(P(h,w,m)\), \(P(v,r,w)\), \(P(v,r,m)\), \(P(v,w,m)\), and \(P(r,w,m)\) represent the joint probabilities of three-factor risk. Taking \(P(h,v,r)\) as an example, it is calculated as follows:  
\[P(h,v,r)=\sum_{w}\sum_{m}P_{n_{strvum}} \tag{10}\]  
The risk coupling value for the four-factor coupling type was calculated as follows:  
\[\left\{ \begin{array}{l}T_{4,1}(H,V,R,W)=\sum_{h}\sum_{v}\sum_{v}P(h,v,r,w) \cdot log_{2}\frac{P(h,v,r,w)}{P(h)P(v)P(r)P(w)}\\ T_{4,2}(H,V,R,M)=\sum_{h}\sum_{v}\sum_{m}P(h,v,r,m)\cdot log_{2}\frac{P(h,v,m)}{P( h)P(v)P(r)P(m)P(m)}\\ T_{4,3}(H,V,W,M)=\sum_{h}\sum_{v}\sum_{w}\sum_{m}P(h,v,w,m)\cdot log_{2}\frac{P( h,v,m)}{P(h)P(v)P(v)P(m)}\\ T_{4,4}(H,R,W,M)=\sum_{h}\sum_{v}\sum_{m}P(h,r,w,m)\cdot log_{2}\frac{P(h,v,m)}{P( h)P(v)P(w)P(m)}\\ T_{4,5}(V,R,W,M)=\sum_{v}\sum_{v}\sum_{m}P(v,r,w,m)\cdot log_{2}\frac{P(v,w,m)}{P( v)P(v)P(w)P(m)}\\ \end{array} \right. \tag{11}\]where \(P(h,v,r,w)\), \(P(h,v,r,m)\), \(P(h,v,w,m)\), \(P(h,r,w,m)\), and \(P(v,r,w,m)\) represent the joint probabilities of four-factor risk. Taking \(P(h,v,r,w)\) as an example, it is calculated as follows:  
\[P(h,v,r,w)=\sum_{m}P_{hvvwm} \tag{12}\]  
The risk coupling value for the five-factor coupling was calculated as follows:  
\[T_{5}(H,V,R,W,M)=\sum_{h}\sum_{v}\sum_{r}\sum_{w}\sum_{m}P(H,V,R,W,M)\cdot log_ {2}\frac{P(H,V,R,W,M)}{P(H)P(V)P(R)P(W)P(M)} \tag{13}\]