2.1. Construct risk index system

Based on theoretical research and a literature review, a risk index system for the full life cycle of PPP projects under comprehensive environmental governance is constructed. The full life cycle of a PPP project with comprehensive environmental governance includes the identification stage, the implementation stage, the franchise stage, and the non-franchise stage (Zhang YT, Cai ZH, & Yao Y, 2020). In the PPP project for comprehensive environmental governance, some risks span the entire project, and this study separately sets such risks as the first-level index. Therefore, there are five first-level indicators: whole-cycle stage risk, identification stage risk, implementation stage risk, franchise stage risk, and non-franchise stage risk. The five first-level indicators contain 18 second-level indicators, and the second-level indicators are divided into 43 third-level indicators (Table 1).

2.2. Construction of principal component model

Principal component analysis (PCA) is undertaken to recombine a series of correlated data with uncorrelated data through dimensionality reduction and replace the original data with these data to reflect the original indicators (Pan XN, Wang L, 2012). Through SPSS software dimensionality reduction, it is concluded that the variance in the linear combination is the largest, which means that the more information F1 contains, the more F1 is considered the first principal component. If the first principal component cannot reflect the information from all of the original indicators, the second principal component must be selected to continue to reflect the original data information. The second principal component is represented by F2. In order to ensure that the original information is not missing, if it still cannot fully reflect the original data information, the third, fourth,…, and P-th principal components will be extracted (Zhu GH, 2015).

First, the data is reduced in dimensionality through the SPSS24.0 software, and then the linear equation of the principal components is obtained as follows:

…

The formula, a1i, a2i, …, api(i = 1,……,m) contains the eigenvectors corresponding to the eigenvalues of the covariance matrix of X, and X1, X2,…, Xp are the original variables.

Second, the ratio of the feature value corresponding to each principal component to the sum of the total feature value of the extracted principal components is used as the weight by which to calculate the principal component synthesis model:

2.3. Questionnaire design and descriptive statistics

The questionnaire was designed according to the 43 risk indicators in Table 1, and the Likert scale was used for assignment. The “lowest risk”, “low risk”, “medium risk”, “high risk” and “highest risk” are assigned points 1, 2, 3, 4, and 5 respectively (Zainudin A, Asyraf A & Mustafa M, 2016). The questionnaire was sent to PPP project companies, governments, consulting companies, and major teaching and scientific research units that have participated in PPP projects through electronic questionnaires, using the “snowball” method to expand upon the interview. The survey began in October 2021, and after three months, the questionnaire survey had been widely implemented.

A total of 110 questionnaires were returned, of which one questionnaire was eliminated due to inconsistencies in the questionnaire responses. A total of 109 valid questionnaires were obtained, with a response rate of 99%. Respondents in the sample have worked for an average of 8.2 years and have participated in a number of PPP projects involving 19 industries, for a total of 168 frequent participations. Among the participating industries, municipal engineering participated the most frequently, with a frequency rate of 17.86%, followed by the transportation industry. At the other end of the spectrum, only one person participated in forestry. It can be seen that the interviewees have rich experience in PPP projects, thereby ensuring the reliability of the data (Table 2).

According to the reliability analysis of Cronbach’s Alpha, the overall value of Cronbach’s α is 0.934, which is greater than 0.9. Cronbach’s α of “full cycle stage risk evaluation,” “identification stage risk evaluation,” “implementation stage risk assessment,” “franchise stage risk assessment,” and “non-franchise stage risk assessment” are all between 0.772 and 0.895, reaching a critical value of 0.7, which indicates strong reliability (Akinyi, OP, Rambo, CM, & Ndiritu, A. 2019). The combined reliability CR value of the four variables is between 0.703 and 0.8016, exceeding the critical value of 0.7 and indicating good reliability. The average extracted variance (AVE) value of the four variables is between 0.604 and 0.728, exceeding the critical value of 0.5, which indicated that the convergence validity of the four variables is stronger. In summary, the survey data is very reliable (Table 3).

The reliability and validity of the questionnaire were tested using SPSS 24.0. The independent variables are “Risk Evaluation in the Whole Cycle Stage,” “Risk Evaluation in the Identification Stage,” “Risk Evaluation in the Implementation Stage,” “Risk Evaluation in the Franchise Stage,” and “Risk Evaluation in the Non-franchise stage.” In terms of the KMO and Bartlett tests, the KMO value is 0.891, and the significance test sig value is 0.000, indicating that the validity of the questionnaire is very high and factor analysis is suitable (Akintayo O., Godwin O.J. 2017). In the questionnaire with secondary indicators, the minimum KMO value is between 0.725 and 0.859, which exceeds the standard of 0.7, indicating that the questionnaire is valid (Table 4).

3.1 Analysis of the full-cycle risk assessment of PPP project of comprehensive environmental management

The political risk, legal risk, environmental risk, and force majeure risk in the comprehensive environmental management PPP project are risks that are present throughout the entire project cycle. Thus, they have a greater impact on the entire project. Therefore, a separate risk assessment is carried out. Using SPSS24.0 software, the dimension of the data is reduced, and a total of nine components are obtained in all indicators, which can represent the value of the original data. Component values observed features and extracted four eigenvalues of the component greater than one. The cumulative contribution rate was also derived. The cumulative contribution rate reached 83.025%, and the contribution rate was greater than 80%. This represents a high degree of reliability, indicating that these four components can reflect the information in the data. Therefore, the first four components can be used as principal components to evaluate the risk of the entire cycle (Table 5). The four principal components were extracted as F1, F2, F3, and F4, and their characteristic values were 3.676, 2.548, 1.906, and 1.003. The contribution rates were 33.422%, 23.161%, 17.327%, and 9.115%, respectively, and the total contribution rate reached 83.025%. Principal component analysis can be performed (Table 6).

The data is subjected to principal component loading matrix analysis (Table 7, “Principal component loading number”). X2, X3, X4, X5, X6, X7, and X11 in F1 have extremely significant relationships, and the correlation is very strong, indicating these risks overlap in terms of information. At the same time, the load numbers of these indicators are very high, indicating that the first principal component basically reflects the information from these indicators. In the same way, X8 and X9 in F2 can reflect indicator information. Both X10 in F3 and X1 in F4 can also reflect indicator information.

There are three steps to calculating the weight of risk factors. The first step is to calculate the combination coefficient of the principal component and divide the load number of the corresponding risk index by the square root of the characteristic value of the principal component, which can be seen in Table 7, “Combination coefficient of principal components.” We then establish a principal component mathematical model based on the combination coefficient.

The second step is to calculate the comprehensive score for each risk factor. In the formula, ${\upsilon }_n$M10 \documentclass[10pt]{article} \usepackage{wasysym} \usepackage[substack]{amsmath} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage[mathscr]{eucal} \usepackage{mathrsfs} \usepackage{pmc} \usepackage[Euler]{upgreek} \pagestyle{empty} \oddsidemargin -1.0in \begin{document} \[ {\upsilon _n} \] \end{document} (n = 1,2,3…) represents the variance contribution rate of the extracted principal components. In this model, four principal components are extracted: namely, n = 4. The risk variables are separately calculated to obtain the comprehensive score of each indicator. Taking “X1” as an example, the comprehensive score = 33.422/83.025*0.167+23.161/83.025*(-0.310)+17.327/83.025*0.105+9.115/83.025*0.669=0.103. By analogy, a comprehensive score of all risk factors is obtained.

The third step is to normalize the weights of the comprehensive scores of all risk factors to obtain their respective weights. According to the data, the environmental pollution risk (X9) has the highest weight. Because China’s requirements for environmental protection are becoming stricter, it is also necessary to pay attention to environmental protection when implementing PPP projects for comprehensive environmental management. The second is the risk caused by natural disasters (X10), because once the risk of natural disasters is realized, the resulting damage is unimaginable. The government corruption risk (X4) has the lowest weight, indicating that China’s anti-corruption work has truly been implemented. When implementing the PPP comprehensive environmental governance project, there is no need to worry too much about the risks of government officials’ corruption.

3.2. Risk assessment analysis of PPP project identification stage of comprehensive environmental management

According to the risk analysis method of the entire cycle stage, to analyze the risk in the identification stage, the SPSS24.0 software obtains three components with characteristic values greater than one, which become the principal components. The three principal components were extracted as F1, F2, and F3, and their characteristic values were 3.414, 2.143, and 1.779. The contribution rates were 37.934, 23.900, and 19.673, respectively. The total contribution rate reached 81.507%, and the cumulative contribution rate exceeded 80%. The components can reflect the information from the indicators, and principal component analysis can be performed (Table 8).

According to the weight analysis method for the entire cycle, the risk weight of the identification stage is obtained (Table 9). In the identification stage of a comprehensive environmental management PPP project, there are three main types of risk: land acquisition, project approval delays, and financing. The highest risk weight is the difficulty of project approval (X14). Because the approval process is very complicated and involves a wide range of areas, this risk has the highest weight. The second is work efficiency risk (X16). If work efficiency is low, it will inevitably increase the risk of approval delays. The risk of expected investment return (X17) has the lowest weight. The comprehensive environmental governance PPP project has conducted a significant research and investigation, including the calculation of investment income in the early stages, with all factors that affect investment income taken into account, so such risks have the lowest impact.

3.3. Analysis of Risk Assessment in the Implementation Phase of PPP Project of Comprehensive Environmental Treatment

According to the principal component analysis method, to analyze the risks in the implementation stage, SPSS24.0 software obtains three components with characteristic values greater than one, which become the principal components. The three principal components were extracted as F1, F2, and F3, and their characteristic values were 5.451, 2.670, and 2.002. The contribution rates were 45.421, 22.247, and 16.680, respectively. The total contribution rate reached 84.348%, and the cumulative contribution rate exceeded 80%. These principal components can reflect the information in the index, and principal component analysis can be performed (Table 10).

According to the principal component analysis method, the risk weights at the implementation stage are obtained (Table 11). In the implementation phase of the PPP project for comprehensive environmental management, there are primarily four types of risk: financing, construction, supply, and technology. The highest risk weight is the completion risk (X22). Due to the long construction period and significant variables, this risk has the highest weight. The second is engineering quality risk (X21). The design unit’s qualification risk (X27) has the lowest weight, and the PPP comprehensive environmental management project generally selects design units with certain performance and experience measures in design. Therefore, such risks have the lowest impact.

3.4. Risk Assessment Analysis of PPP Project Concession Management Stage of Comprehensive Environmental Treatment

According to the principal component analysis method to analyze the risk in the franchise stage, the SPSS24.0 software obtains three components with characteristic values greater than 1, which become the principal components. The three principal components were extracted as F1, F2, and F3, and their characteristic values were 5.862, 2.280, and 2.087. The contribution rates were 48.849, 18.996, and 17.392, respectively. The total contribution rate reached 85.237%, and the cumulative contribution rate exceeded 80%. These principal components can reflect the information in the index, and principal component analysis can be performed (Table 12).

According to the principal component analysis method, the risk weight of the franchise stage is obtained (Table 13). In the concession stage of the PPP project for comprehensive environmental management, there are primarily five types of risk: demand, operations, finance, interest rates, and inflation. The highest risk weight is the risk of interest rate fluctuations (X38). Due to the long operating period, generally a 30-year franchise period, the fluctuation of interest rates is relatively large, and the resulting benefits will also fluctuate. Therefore, interest rate fluctuation risk has the highest weight, and the second highest is financial market stability risk (X39). This category is also regulated by the state. It cannot be changed and can only be dealt with. All of the risks are also relatively large. Operational and maintenance cost risk (X33) has the lowest weight. The companies selected for the comprehensive environmental management PPP project have a very complete operating system, so the impact of such risks is the lowest.

3.5. Risk Assessment and Analysis of the Non-concession Operation Phase of the PPP Project of Comprehensive Environmental Treatment

According to the principal component analysis method, to analyze the risk in the franchise stage, the SPSS24.0 software obtains two components with characteristic values greater than one, which become the principal components. The two principal components extracted were F1 and F2, and their characteristic values were 3.418 and 1.540. The contribution rates were 56.960 and 25.665, respectively. The total contribution rate reached 82.625%, and the cumulative contribution rate exceeded 80%. These principal components can reflect the information from the indicators, and principal component analysis can be performed (Table 14).

According to the principal component analysis method, the risk weight of the franchise stage is obtained (Table 15). In the non-concession stage of the comprehensive environmental management PPP project, there are primarily two types of risk: operational and residual value. The highest risk weight is the franchise signing period risk (X41). Due to the long operating period, it is generally a 30-year franchise that will be transferred after 30 years. Great changes have taken place in the policy environment and the economic environment in the past 30 years. No experts or scholars can predict the future economic environment. Therefore, this risk has the highest weight, followed by the risk of operational management experience capability (X42). The risk of expected operating returns has the lowest weight. The comprehensive environmental management PPP project has considered a long-term benefit when designing the benefit, so this kind of risk has the lowest impact.