# Measuring Efficiency and Effectiveness of Highway Management in Sustainability
## 3 Data, Methods, and Results
### Measuring Effectiveness: Principal Component Analysis Approach
To estimate the effectiveness indicator, we first estimate factor scores using the principal component analysis (PCA) and then apply a variance value as a weight for each component. Thus, the total value of effectiveness is computed as the summation of each state's product of weights and factor scores:  
\[Effectiveness_{i}=W_{m}\sum_{i=1}^{48}F_{mi},\]  
where \(i\) means each state, \(W\) is a weight, \(m\) indicates each component, and \(F\) means a factor score. To find the effectiveness indicator, we employ road condition (IRI), fatality (the number of people fatally injured), and congestion (the annual average daily traffic: AADT). First, we recode raw data values to establish a consistent direction for each variable's value. IRI has score ranges of \"\(<\)60, 60-94, 95-170, 171-220, and \(>\)220,\" and a higher value of IRI means poorer quality. We divided the ranges into \"good (IRI \(<\) 95),\" \"fair (95 \(\leq\) IRI \(\leq\) 170),\" and \"unacceptable (IRI \(>\) 170)\" according to the literature [38; 39; 40] and coded them as 3, 2, and 1, respectively. Then, we computed the weighted mean of each state highway by using the ratio of the certain quality road miles to the total miles: \([3\times\text{good }(\text{miles})+2\times\text{fair }(\text{miles})+1\times\text{poor }(\text{miles})]/\text{total }(\text{miles})\). Fatality and congestion are calculated as the reciprocal of the number of people fatally injured over lane-mile and the reciprocal of AADT per lane-mile and renamed as safety and mobility respectively. Thus, the recoded factors (road condition, safety, and mobility) indicate that a higher value means a better performance. Table 4 has the detailed data information of each component for measuring effectiveness indicator. Second, running the principal component analysis, we found one main component and its factor score. I employed the component's percentage points of variance as a weight value. Thus, the effectiveness indicator is calculated as the product of the factor score and weights value:  
\[Effectiveness_{t}=53.676\%\times F_{1i}.\] \begin{table}
\begin{tabular}{c c c} \hline \hline
**Variable** & **Description** & **Source** \\ \hline Road condition & \([3\times\text{good }(\text{miles})+2\times\text{fair }(\text{miles})+\) & \\  & \(1\times\text{poor }(\text{miles})]/\text{total }(\text{miles})\) & \\ \hline Mobility & Reciprocal of Annual Average Daily Traffic (AADT)/lane-miles & Highway Statistics \\ \hline Safety & Reciprocal of the number of people fatally injured/lane-miles & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Variable Description and Data Source for Principal Component Analysis (PCA). Table 5 presents states' effectiveness indicators, road conditions, safety, and mobility in 2000, 2005, and 2012. For instance, in 2012, West Virginia was the most effective in highway management, but New Jersey was ranked the lowest. With respect to road conditions, Georgia was the best at highway maintenance, but Rhode Island was the worst. West Virginia was ranked first in safety and mobility, but New Jersey and California were the lowest.