Research on the Construction of a Risk Assessment Indicator System for Transportation Infrastructure Investment under Public–Private Partnership Model

Abstract

This paper is dedicated to developing a risk assessment indicator system applicable to transportation infrastructure investment projects in the public–private partnership (PPP) model. Initially, through practical research, literature reviews, and expert interviews, key risk factors for transportation infrastructure investment projects in the PPP mode were identified. Based on these risk factors, a preliminary risk assessment indicator system was established. Subsequently, the principal component analysis (PCA) was used to reduce the dimensions of the indicators, simplify the structure of the system, and highlight key risk factors. Simultaneously, the CRITIC-EWM method was applied to calculate the weights of the indicators. Furthermore, to validate the effectiveness of the indicator system, a questionnaire survey was conducted, collecting 314 responses. Structural equation modeling was applied to validate the effectiveness of the indicator system and examine its application value in practical risk management processes. The primary contribution of this study lies in proposing a method for constructing a risk assessment indicator system that combines quantitative and qualitative analyses, providing new theoretical and practical guidance for risk management of transportation infrastructure investment projects under the PPP mode.

1. Introduction

In the context of global economic integration and regional economic cooperation, the public–private partnership (PPP) model has emerged as a key mechanism to promote investment and development in transportation infrastructure. During the past decade, countries around the world have shown significant differences in their investment in transport infrastructure [1]. According to the International Transport Forum (ITF), China and Hungary saw a particularly significant growth in investment in transport infrastructure in 2020 [2]. In the past decade, China’s investment in transportation infrastructure has continued to grow. Total investment has increased from about CNY 2.05 trillion in 2011 to CNY 3.85 trillion in 2022, with a cumulative increase of more than 87.8%. The cumulative investment exceeds CNY 32.25 trillion, and the investment in 2022 reached CNY 3.85 trillion, reaching an all-time high. With the rapid development of the economy and the acceleration of the urbanization process, the demand for transportation infrastructure is increasing. The PPP model is widely used in the construction and operation of transportation infrastructure such as bridges, highways, and rails. According to PwC’s Global Infrastructure Outlook: 2024–2025, released in November 2023, global transportation infrastructure investment is expected to grow at an average annual rate of about 5% from 2014 to 2025. The Asia–Pacific region is the largest market for transportation infrastructure, and its investment is expected to increase from USD 557 billion to nearly USD 900 billion [3]. However, transportation infrastructure projects usually involve huge investment, a long construction period, and a complex operating environment, and risk management and evaluation have become the key to ensuring project success and maximizing social and economic benefits. Especially in the PPP mode, due to the cooperation between the government and the private sector, the identification, assessment, and distribution of risks are more complicated, which requires the establishment of a scientific and reasonable risk assessment indicator system to guide investment decision-making and risk management of transportation infrastructure.

In the current risk management practice of transportation infrastructure investment projects, there is a common problem that the risk assessment indicator system is not systematic and comprehensive [4,5]. However, in recent decades, with the rapid development of transportation infrastructure and the wide application of public–private partnerships (PPPs), the emphasis on risk management has increased. Both academic and practical circles have conducted a great deal of research on the identification, assessment, and management of risks in investments in transportation infrastructure projects [6]. However, these studies often focus on specific types of risk such as financial, construction, operational, etc., or focus on a certain stage of the project, lacking complete and comprehensive coverage of the risks of transportation infrastructure investment projects [7,8]. Additionally, existing risk management methods and tools often ignore the appetite for risks and the affordability of different stakeholders, as well as the interaction and complexity between risk factors. Therefore, the current situation of risk management of transportation infrastructure investment projects reflects the urgent need to build a systematic, comprehensive, and adaptable risk assessment indicator system, which should be able to fully cover all stages and various risks of the project, taking into account the needs and characteristics of all parties involved in the project, in order to achieve effective identification, assessment, and management of risks, thereby improving the success rate and investment efficiency of the project. Currently, there are still large research gaps and practical needs in this field. It is urgent that academic and practical circles work together to develop and improve the risk assessment indicator system suitable for transportation infrastructure investment projects.

Based on the shortcomings of current research, this study first starts with the identification of risk factors and systematically identifies the main risk factors for transportation infrastructure investment projects under the PPP model through a literature review, expert interviews, and case studies. Then, this paper proposes an indicator system construction method that combines principal component analysis (PCA) and the CRITIC-EWM method, with the aim of screening and determining risk assessment indicators and their weights in a scientific and systematic way. Finally, the validity of the indicator system is tested using the structural equation model (SEM) method. This paper answers the following two questions:

• How to establish a scientific and systematic risk assessment indicator system?
• Among the many risk factors, what are the key indicators for assessing the risk of investment in transportation infrastructure?

Compared to existing literature, the innovation of this study is mainly reflected in the following aspects:

• This study comprehensively identifies and integrates the key risk factors of transportation infrastructure investment projects under the PPP model through a systematic literature review, expert interviews, and case studies. It constructs a comprehensive risk assessment indicator system covering six dimensions: economic, technical, management, policy, social environment, and market. This system not only comprehensively covers the main risks throughout the project lifecycle but also fills the gap of incomplete risk identification in existing research.
• This study is the first to combine principal component analysis (PCA) and the CRITIC-EWM method to screen and determine risk assessment indicators and their weights. This method not only improves the scientific and systematic nature of the indicator system but also simplifies the indicator structure through dimensionality reduction, highlighting key risk factors and making the risk assessment more accurate and operational.

Through an in-depth study of the construction and application of the transportation infrastructure investment risk assessment indicator system under the PPP model, this article not only enriches theoretical research in the field of transportation infrastructure investment risk management but also provides a powerful tool and strategy for risk management in practice. It has an important theoretical and practical value in guiding the risk management of transportation infrastructure investment projects.

2. Literature Review

Synthesizing the current relevant research, it is found that the existing research mainly focuses on three aspects: the identification of risk factors of transportation infrastructure investment, the construction method of the indicator system, and the dynamic and adaptability of the indicator system.

Risk factor identification is the basis for constructing an effective risk assessment indicator system. Early research is mainly based on a literature review and expert experience to identify risk factors for transportation infrastructure investment projects [9]. These studies have found that risk factors usually include, but are not limited to, market risk, financial risk, policy and legal risk, technical risk, and environmental risk. Recent work by Chen et al. (2022) on risk propagation in multilayer heterogeneous networks of large engineering projects further emphasizes the complexity and interconnectivity of risk factors in infrastructure projects [10]. In recent years, researchers have begun to use quantitative methods, such as fault tree analysis (FTA) and event tree analysis (ETA), to systematically identify risk factors and improve the completeness and precision of the identification process [5,11]. These studies mainly use qualitative analysis methods, such as expert interviews, case studies, etc., to identify risk factors. However, these studies mainly use qualitative analysis methods, such as expert interviews, case studies, etc., to identify risk factors. Additionally, Luo et al. (2022) utilized machine learning to analyze transport infrastructure connectivity and conflict resolution, highlighting the growing use of artificial intelligence in risk factor identification [12].

The construction method is the key to ensuring the effectiveness and practicability of the risk assessment indicator system. Traditionally, researchers have relied on the analytic hierarchy process (AHP) and the Delphi method to determine the weight and importance of risk indicators [13,14]. These methods focus on the integration of expert opinions; however, although effective, they may be affected by subjective bias. To overcome this limitation, recent studies have proposed the application of complex network theory and artificial intelligence techniques, such as machine learning, to construct and optimize indicator systems [15,16]. For instance, Sun et al. (2022) utilized a game-theoretic approach for multipriority data transmission in vehicular networks, demonstrating the potential of advanced methodologies in risk assessment [17]. These modern methods can process large amounts of data, identify hidden risk factors, and improve the scientificity and accuracy of the indicator system. Despite this, existing research often lacks complete consideration of the dynamic changes of projects and the needs of multiple stakeholders when constructing the indicator system.

In practical applications, transportation infrastructure investment projects typically involve long-term, large-scale investments and are influenced by various factors such as policy, technology, market, and social environment. These factors change continuously throughout the project lifecycle, leading to changes in the nature and extent of risks. Consequently, the risks associated with transportation infrastructure investment are dynamic and unpredictable. Therefore, the risk assessment indicator system needs to be dynamic and adaptable to timely reflect and respond to these changes, thereby improving the effectiveness and accuracy of risk management [18,19]. Early studies tend to ignore this requirement of the indicator system [20], while the latest research has begun to focus on how to adapt the indicator system to environmental changes and project development needs [21,22]. By introducing time series analysis and dynamic simulation methods, researchers try to make the indicator system reflect and adapt to changes in risk factors over time, to improve the timeliness and effectiveness of risk management [23,24]. For example, Rong et al. (2022) developed a real-time bus waiting time estimation system based on multi-source data, which illustrated the importance of real-time data integration in dynamic risk management [25]. Although research in this area has improved the flexibility and effectiveness of risk management, current methods and tools still face challenges in practical applications, especially the realization of the automatic update and real-time adjustment of the indicator system has not been widely resolved.

On the basis of a comprehensive analysis of the existing research literature, it can be found that the shortcomings of the current research are mainly reflected in the following aspects:

• Many studies have adopted a static risk assessment framework, ignoring the impact of environmental and condition changes on risk factors in the project life cycle;
• Existing risk assessment methods often focus on specific types of risk but do not consider the interaction between risk factors and fail to form a comprehensive and systematic risk assessment system;
• Most studies rely on a single methodology, such as the analytical hierarchy process (AHP) or fuzzy logic, and fail to make full use of the advantages of multiple methodologies to improve the accuracy and reliability of risk assessment;
• Although some studies have mentioned the dynamic adaptability of risk assessment, specific implementation strategies and tools are still lacking, and it is difficult to cope with the changing risk environment during project implementation.

In summary, many scholars have used evolutionary game methods to study and explore government regulation, low carbon transformation of companies, and quality supervision, which provides a rich research base for the research of this paper. The differences between this paper and related literature include mainly the following points.

• The study constructs a dynamic risk assessment framework, with particular emphasis on changes and updates of risk factors in the project life cycle, to better reflect the actual risk situation.
• Through the comprehensive analysis of the multidimensional risk factors of transportation infrastructure investment, a comprehensive risk assessment indicator system is constructed, which covers the interaction between risk factors and reflects the concept of systematic risk management.
• The combination of principal component analysis (PCA) and CRITIC-EWM is used to improve the scientificity and precision of risk assessment through the complementary advantages of different methods.

The differences between this paper and related literature include mainly the following points:

• This paper constructs a method to construct a dynamic risk assessment indicator system, which can fully reflect the changes and updates of risk factors in the life cycle of investment projects in transportation infrastructure;
• Through the comprehensive analysis of the multidimensional risk factors of transportation infrastructure investment, a comprehensive risk assessment indicator system is constructed, which covers the interaction between risk factors and reflects the concept of systematic risk management;
• The combination of principal component analysis (PCA) and CRITIC-EWM is used to improve the scientificity and precision of risk assessment through the complementary advantages of different methods.

3. Methodology

3.1. Research Framework and Structural Design

3.1.1. Research Framework

Considering the dynamic and complexity of the risk assessment of investment in transportation infrastructure, the logical structure of this paper is systematically revealed by combining qualitative and quantitative methods. First, through a literature review, this study identifies and selects key indicators of risk assessment and establishes the theoretical basis of the research. Subsequently, the principal component analysis (PCA) and CRITIC-EWM methods were used to extract the most representative risk factors from multidimensional data to construct a scientific and reasonable indicator system. On this basis, to further test the effectiveness of the indicator system, the structural equation model (SEM) is used to test the validity and reliability of the evaluation indicator system. The research framework of this paper is shown in Figure 1.

The analysis of the interrelationships between various risk sources is as follows:

Economic risk: economic risk affects cash flow and investment returns, which directly impact technical investment and management resource allocation, thereby increasing technical risk and management risk. Additionally, technical risk involves the feasibility of technical solutions and construction complexity; technical failures or issues can lead to cost overruns and schedule delays, further exacerbating economic risk.

Technical risk: technical risk, by involving the feasibility of technical solutions and construction complexity, directly impacts economic risk through cost overruns and delays if technical issues arise.

Management risk: management risk, through the organization, coordination, and allocation of resources within the project, directly affects the implementation of technical solutions and cost control, thus intertwining with both technical and economic risks.

Policy risk: policy risk, by affecting laws, regulations, and regulatory requirements, changes the financing environment and management framework of the project, thereby closely relating to economic and management risks.

Social–environmental risk: social–environmental risk impacts the social acceptance and environmental effects of the project, increasing policy pressure and market uncertainty, thus interacting with policy and market risks.

Market risk: market risk, through changes in market demand and competitive conditions, directly affects the economic benefits and social recognition of the project, further exacerbating economic risk and social–environmental risk.

3.1.2. Structure of the Indicator System

When designing the risk assessment indicator system for investments in transportation infrastructure, a key step is to divide the risk dimension and design a structured preliminary risk assessment indicator system accordingly. Transportation infrastructure investment projects face multiple sources of risk due to their long-term, capital-intensive, and significant socioeconomic impact [26]. In the division of risk sources, the research of various countries often focuses on the characteristics of localization and classifies the risk of investment in transportation infrastructure. Furthermore, there are differences in understanding and classifying technical risks and management risks [27,28]. Despite such differences, current research jointly emphasizes the importance of building a comprehensive and systematic risk assessment indicator system when studying the risk of investing in transportation infrastructure. The relevant research on the division of the risk dimensions of investment in transportation infrastructure in the United States and abroad is shown in

Table 1. Division of the risk dimension of investment in transportation infrastructure.

Related Research Literature	Risk Dimension Division
Choueiri (2009) [29]	Political Risk, Financial Risk, Technical Risk, Market Risk
Lakshmanan (2011) [30]	Economic Risk, Technical Risk, Market Risk
Labanauskas and Palšaitis (2012) [31]	Economic Risk, Political Risk, Market Risk, Operational Risk
Ang and Marchal (2013) [32]	Environmental Risk, Social Risk, Economic Risk
Sharma (2013) [33]	Legal Risk, Technical Risk, Economic Risk, Construction Risk
Tran and Molenaar (2014) [34]	Construction Risk, Design Risk, Policy Risk
Amiril (2014) [9]	Environmental Risk, Economic Risk, Social Risk, Management Risk
Yucelgazi and Yitmen (2018) [35]	Technical Risk, Financial Risk, Political Risk, Management Risk, Construction Risk, Legal Risk, Natural and Environmental Risk

.

Based on research findings from domestic and foreign scholars and combined with surveys conducted on major enterprises involved in the investment of transportation infrastructure, such as China Railway Construction Corporation Group Limited (CRCC), China Railway Group Limited (CREC), and China Communications Construction Company Limited (CCCC), this study proposes a structured risk assessment indicator system for the investment of transportation infrastructure. This indicator system is designed based on a summary of relevant academic research and practical survey results, covering six dimensions of risk: economic risk, technical risk, management risk, social and environmental risk, policy risk, and market risk. These dimensions comprehensively cover various risks faced by investments in transportation infrastructure and provide support for the subsequent research of this study. Each risk dimension is briefly outlined as follows:

• Economic risk reflects financial stability and cost-effectiveness in the investment implementation process, which is the key to investment success. The core of the risk concern in this dimension is capital liquidity and the economic feasibility of the project. In the context of global economic integration, economic risks cover factors such as return on investment, financing costs, and material price fluctuations that may be encountered in the transportation infrastructure investment process. These factors may lead to the project investment return not being as expected, increasing the project’s financial pressures and affecting the confidence of investors and related parties.
• Technical risk focuses on technical problems and challenges that can be encountered in the design, construction, and operation of investment projects in transportation infrastructure. This includes the feasibility of technical solutions, the uncertainty of technological innovation, the complexity of construction technology, and the reliability of equipment. Transportation infrastructure projects are usually large in scale, have high technical requirements, and involve many engineering and technical problems. Immaturity or improper selection of technology may lead to project delays, cost overruns, and even technical failure.
• Management risk focuses on organizational structure, the decision-making process, and the allocation of resources for transportation infrastructure investment projects. Management risk involves the efficiency and effectiveness of project management, including project planning, organization and coordination, resource allocation, schedule control, etc. Improper project management can lead to waste of resources, schedule delays, quality problems, etc., which in turn affect overall performance and return on investment of the project.
• Social environmental risks include the impact of project construction on the environment, the acceptance of the public, social stability, and other factors. Transportation infrastructure projects often have a significant impact on the local social environment. If the relationship with the local community is not properly handled or the impact on the environment is not effectively assessed and reduced, it may encounter public protests and legal proceedings, resulting in project delays or additional costs.
• Policy risk refers to the risk caused by changes in government policies and uncertainty of laws and regulations. Transportation infrastructure projects often require long-term planning and construction cycles, and policy changes can affect the legitimacy, economy, and sustainability of the project.
• Market risk involves changes in market demand, competitive situation, price fluctuations, and other factors. Investment in transportation infrastructure is huge, and the recovery cycle is long. Market risk is reflected mainly in the uncertainty of user demand and the fluctuation of operating income. Accurate prediction of market demand and in-depth analysis of the competitive environment are crucial to reducing market risks and ensuring project success.

3.1.3. Selection of Sample and Data Sources

To ensure the comprehensiveness and scientificity of the evaluation, this study obtains data on 76 transportation infrastructure investment projects that have been implemented by the government and the Center for Social Capital Cooperation of the Ministry of Finance (CPPPC Project Management Database), the National PPP Project Information Monitoring Service Platform of the National Development and Reform Commission, and other official institutions as research samples. The sample information is shown in

Table 2. Sample information.

No.	Object	Province	Average Investment (CNY Billion)
1–29	Expressway	Shandong Province, Henan Province, Guangdong Province, Anhui Province, Zhejiang Province, Guangxi Province, Shaanxi Province, Guizhou Province, Heilongjiang Province	63.85
30–36	Municipal highways	Beijing Municipality, Chongqing Municipality, Shandong Province, Zhejiang Province	18.96
37–41	Tunnels	Jiangsu Province, Guangdong Province, Hubei Province	39.54
42–50	Rail Transit	Shandong Province, Jilin Province, Xinjiang Uygur Autonomous Region, Shanxi Province, Gansu Province, Chongqing Municipality	69.76
51–55	Railway	Anhui Province, Zhejiang Province, Shanghai Municipality	56.93
56–61	Bridges	Shanxi Province, Guangdong Province, Hebei Province, Shandong Province, Jiangxi Province	19.84
62–64	Ports	Shandong Province, Jiangsu Province, Hainan Province	32.53
65–71	Channel	Shandong Province, Henan Province, Guangxi Province	66.57
72–76	Airports	Shaanxi Province, Sichuan Province, Guangdong Province, Guangxi Province, Hubei Province	28.82

.

To ensure the representativeness of the sample and the validity of the data, this study adopted field research and extensive data collection as the primary data acquisition methods. This approach is supported and validated by numerous scholars. According to De Vaus (2013) [36], sample representativeness is key to ensuring that research results are generally applicable. Additionally, Bernard (2017) noted that extensive data collection enhances the comprehensiveness and accuracy of the data, thereby strengthening the reliability of research conclusions [37]. The selection of research objects has been strictly screened, and transportation infrastructure projects of different regions, different scales, and different types have been selected to ensure the breadth and depth of the research. In the actual investigation, in-depth interviews were conducted with the business personnel of the relevant units in the investigation samples to collect first-hand information from the project and ensure that the data obtained could fully reflect the actual situation. In terms of data collection, this study covers a variety of sources, from project evaluation reports, academic literature, government reports, and industry analysis to data published by professional institutions, ensuring the diversity and richness of information. In addition, relevant data is captured using tools such as Python, from which existing risk factors are extracted as supplementary sources of information. In terms of effectiveness evaluation, the managers of relevant business departments, such as the CRCC, CECC, and CCCC, as well as the scientific research backbones in relevant fields, such as Beijing Jiaotong University and the Academy of Sciences of the Ministry of Transport, are invited to correct and supplement the Risk factors collected in each dimension to form a set of Risk factors for transportation infrastructure investment process.

From the perspective of risk sources, economic risk, technical risk, and management risk can be summarized as internal risks, while social–environment risk, policy risk, and market risk can be regarded as external risks. Based on the structure of the indicator system designed above, a preliminary structured risk assessment indicator system is formed. The structure of the indicator system is shown in Figure 2.

Studies such as Fisher et al. (2001) [38], Shi et al. (2018) [39], and Reznikov (2020) [40] agree that it is generally appropriate to retain 7 to 10 indicators for each risk dimension. Based on research by Mishra et al. (2013) [41] and Ermolaeva et al. (2022) [42], combined with the risk indicators summarized in this article, the Risk Assessment Indicator System for Investment in the Transportation Infrastructure is being constructed preliminarily. There are six risk dimensions and 49 evaluation indicators in this indicator system. The details are shown in

Table 3. Preliminary risk assessment indicators.

Risk Dimensions	Evaluation Indicators	Indicator Attribute
Economic (E)	E11: Return on Investment	Positive
	E12: Fund Flow Fluctuation	Positive
	E13: Inflation	Negative
	E14: Tax Policy	Negative
	E15: Financing Difficulty	Negative
	E16: Land Acquisition Costs	Negative
	E17: Investment Overrun	Negative
	E18: Labor Costs	Negative
	E19: Material Price Fluctuation	Negative
	E10: Cost of Capital Utilization	Negative
Technical (T)	T21: Design Planning Deviation	Negative
	T22: Technical Implementation Difficulty	Negative
	T23: Material Technology Qualification Rate	Positive
	T24: Technical Personnel Experience	Positive
	T25: Equipment Failure Rate	Negative
	T26: Geological Survey Error	Negative
	T27: Technical Environment Adaptability	Positive
	T28: Technical Standard Compliance Rate	Positive
Management (M)	M31: Management Team Experience	Positive
	M32: Decision Delay Rate	Negative
	M33: Contract Default Risk	Negative
	M34: Budget Overrun Rate	Negative
	M35: Key Personnel Attrition Rate	Negative
	M36: Supply Chain Management	Positive
	M37: Quality Management	Positive
	M38: Incomplete Management System	Negative
Policy (P)	P41: Policy Support Level	Positive
	P42: Policy Change Frequency	Negative
	P43: Positive Intensity of Policy Implementation Intensity	Positive
	P44: Policy Uncertainty	Negative
	P45: Regulatory Compliance Risk	Negative
	P46: Regional Policy Differences	Negative
	P47: Policy–Market Disconnect	Negative
	P48: Government Intervention Risk	Negative
Social–environment (S)	S51: Public Opposition Degree	Negative
	S52: Frequency of Social Conflict Events	Negative
	S53: Land Acquisition and Demolition Risk	Negative
	S54: Environmental Pollution Risk	Negative
	S55: Public Safety Incidents	Negative
	S56: Social Opinion Risk	Negative
	S57: Negative Social Responsibility Fulfillment	Negative
	S58: Social-Cultural Conflict	Negative
Market (C)	C61: Market Demand Fluctuation	Negative
	C62: Intensity of Market Competition	Negative
	C63: Price Fluctuation Risk	Negative
	C64: Market Acceptance	Positive
	C65: Market Regulation	Negative
	C66: Brand Image	Positive
	C67: Market Information Asymmetry	Negative

.

3.2. Construction of an Indicator System Based on the PCA and CRITIC-EWM Method

In this study, we applied principal component analysis (PCA) and the CRITIC-EWM method to screen and determine risk assessment indicators and their weights. The PCA method simplifies the data structure through dimensionality reduction, highlighting key risk factors, while the CRITIC-EWM method determines the weights of each indicator by comprehensively considering the correlation and information content among indicators. These methods have been applied and proven effective in multiple studies [43,44]. The specific implementation steps are as follows.

3.2.1. Indicator Data Processing

The Risk Assessment Indicator of Transportation Infrastructure Investment and its quantitative method have been initially established. However, the original indicator data have varying units and dimensions, complicating subsequent calculations. Therefore, it is necessary to standardize the original data, converting each indicator’s data to a value between [0, 1]. This standardization is essential for constructing the risk assessment indicator system model. Depending on the different types of indicators, the standardized processing of the indicator data is as follows.

• Standardization of positive indicator data

Suppose that $x_{ij}$ is the standardized score of the $j$th sample of the $i$th indicator, $s_{ij}$ is the original data of the $j$th sample of the $i$th indicator, and $n$ is the total number of samples. There is a data standardization formula for positive indicators:

$$x_{ij}=\frac{s_{ij}-\underset{1\le j\le n}{\min }\left(s_{ij}\right)}{\underset{1\le j\le n}{\max }\left(s_{ij}\right)-\underset{1\le j\le n}{\min }\left(s_{ij}\right)}, i=1,2,\cdots ,n; j=1,2,\cdots ,n$$

(1)

2.

Standardization of negative indicator data

$$x_{ij}=\frac{\underset{1\le j\le n}{\min }\left(s_{ij}\right)-s_{ij}}{\underset{1\le j\le n}{\max }\left(s_{ij}\right)-\underset{1\le j\le n}{\min }\left(s_{ij}\right)}, i=1,2,\cdots ,n; j=1,2,\cdots ,n$$

(2)

3.

Standardization of interval indicator data

Suppose that $s_{ij}$ is the original data of the $j$th sample of the $i$th indicator, $q_1$ is the right boundary of the optimal interval of the indicator, and $q_2$ is the right boundary of the optimal interval of the indicator. There is a standardized formula for the interval indicator data:

$$x_{ij}=\left\{\begin{array}{c}1-\frac{q_1-s_{ij}}{max\left[q_1-\underset{1\le j\le n}{\min }\left(s_{ij}\right),\underset{1\le j\le n}{\max }\left(s_{ij}\right)-q_2\right]},s_{ij}<q_1\\ 1-\frac{s_{ij}-q_2}{max\left[q_1-\underset{1\le j\le n}{\min }\left(s_{ij}\right),\underset{1\le j\le n}{\max }\left(s_{ij}\right)-q_2\right]},s_{ij}>q_2\\ 1 ,q_2<s_{ij}<q_1\end{array}\right.$$

(3)

3.2.2. Degradation of the Indicator Dimension Based on the PCA Method

The PCA method can effectively reduce the dimension of the data, extract the main information, remove interference factors from the evaluation system, and simplify the complexity of the original feature analysis. Specific implementation steps are as follows:

Step 1. Decentralization Processing of Indicator Data.

The risk assessment indicator system for investment in the transportation infrastructure has been established preliminarily. On this basis, the original evaluation matrix $X={\left[x_{ij}\right]}_{n\times m}$ is established, and the decentralized matrix $S={\left[s_{ij}\right]}_{n\times m}$ is obtained by the Z-score method. The decentralized processing of the indicator data is as follows:

$$s_{ij}=\frac{x_{ij}-\overline{x_i}}{\sqrt{F{c}_j}},i=1,2,\cdots ,n;j=1,2,\cdots ,m$$

(4)

$$\overline{x_i}=\frac{1}{m}{\displaystyle \sum }_{i=1}^n{x}_{ij},i=1,2,\cdots ,n;j=1,2,\cdots ,m$$

(5)

$$F{c}_j=\frac{1}{n-1}{\displaystyle \sum }_{i=1}^n{\left(x_{ij}-\overline{x_i}\right)}^2,i=1,2,\cdots ,n;j=1,2,\cdots ,m$$

(6)

where $F{c}_j$ is the variance of column $j$.

Step 2. Construct the correlation coefficient matrix between indicators.

Calculate the correlation coefficient between each indicator:

$${\xi }_{ij}=\frac{{{\displaystyle \sum }}_{k=1}^n(s_{ki}-\overline{S_i})·(s_{kj}-\overline{S_j})}{\sqrt{{{\displaystyle \sum }}_{k=1}^n{(s_{ki}-\overline{S_i})}^2·{{\displaystyle \sum }}_{k=1}^n{(s_{kj}-\overline{S_j})}^2}},i=1,2,\cdots ,n;j=1,2,\cdots ,m$$

(7)

In the formula, $s_{ki}$ and $\overline{S_i}$ represent the indicator value and the average value after decentralization, respectively. On this basis, the correlation coefficient matrix $Z={\left[{\xi }_{ij}\right]}_{m\times m}$ is constructed.

Step 3. Calculate the eigenvalues and eigenvectors of the correlation coefficient matrix.

$Z={\left[{\xi }_{ij}\right]}_{m\times m}$ is a positive definite matrix, which must be orthogonal to the diagonal matrix, so there are:

$$U^{T}ZU=\left[\begin{array}{ccc}{\lambda }_1& & \\ & \ddots & \\ & & {\lambda }_m\end{array}\right]$$

(8)

${\lambda }_i,U=\left[u_1,u_2,\cdots ,u_m\right]$ A is the characteristic root and the corresponding characteristic vector.

Step 4. Calculate the contribution rate.

The contribution rate is the result of feedback on the importance of the indicator. The calculation method is as follows:

$${\omega }_i=\frac{{\lambda }_i}{{{\displaystyle \sum }}_{j=1}^m{\lambda }_i},j=1,2,\cdots ,m$$

(9)

where ${\omega }_i$ represents the contribution rate of the $i$th principal component.

Step 5. Determine the number of principal components.

The indicators are sorted according to the contribution rate, and the threshold $\alpha$ is determined. If the contribution rate $\beta$ of the first $p$ indicators is greater than the threshold $\alpha$, the number of principal components is $p$. Then there are the following.

$$\beta ={\displaystyle \sum }_{i=1}^p{\omega }_i>\alpha ,i=1,2,\cdots ,p$$

(10)

Step 6. Calculate the load and score of each principal component.

According to the eigenvector $U$ obtained by the correlation coefficient matrix, which is the load matrix of the main component, the standardized evaluation indicator matrix $S={\left[s_{ij}\right]}_{n\times m}$ is brought into the principal component to obtain the score of the main component.

$$\begin{gathered} F=\left[F_1,F_2,\cdots ,F_P\right]={\left[F_{ij}\right]}_{p\times m},i=1,2,\cdots ,p;j=1,2,\cdots ,m \\ \left\{\begin{array}{c}{F}_1=u_{11}{S}_1+u_{12}{S}_2+\cdots +u_{1m}{S}_m\\ F_2=u_{21}{S}_1+u_{22}{S}_2+\cdots +u_{2m}{S}_m\\ ⋮\\ F_p=u_{p1}{S}_1+u_{p2}{S}_2+\cdots +u_{pm}{S}_m\end{array}\right. \end{gathered}$$

(11)

3.2.3. Calculation of the Weight of the Indicator System Based on the CRITIC-EWM Method

In the previous section, the main risk assessment indicators for investment in transportation infrastructure were successfully selected using the PCA method, which laid a solid foundation to build a more concise and effective risk assessment system. However, only identifying the main risk assessment indicators is not enough to complete the construction of the entire assessment system. The next key step is to determine the weight of these indicators to reflect their relative importance throughout the evaluation system. The CRITIC method is an objective weighting method. Determine the weight based on the correlation between indicators, which can effectively avoid subjective interference. It can measure the contrast strength between indicators, but it cannot measure the impact of dispersion. The EWM (entropy weight method) is a method that aims to determine the indicator weight according to the degree of dispersion between the indicators, which can comprehensively and objectively reflect the information content of each indicator. By combining the two methods, a weight determination method can be obtained that can not only reflect the correlation between indicators but also fully consider the amount of information on the indicators. More importantly, the CRITIC-EWM method has good dynamics. With the passage of time and the generation of new data, this method can automatically adjust the weight of each risk assessment indicator so that the evaluation system always maintains the optimal state, which is helpful in constructing a scientific, objective, and dynamic risk assessment indicator system for investments in traffic infrastructure. Therefore, this paper chooses to combine the CRITIC and EWM methods to determine the indicator weight.

• The CRITIC method.

The CRITIC method reflects the differences and internal conflicts between the indicators through the standard deviation and correlation coefficient. In traditional practice, the correlation coefficient can produce negative numbers, leading to wrong results. When the dimension and magnitude of the data are different, there will be distortion in the calculation results. To solve the above problems, this paper introduces the absolute value of the correlation coefficient area, introduces the Gini coefficient to replace the standard deviation to measure the conflict between the indicators, and obtains the optimized CRITIC weight calculation method. The calculation steps are as follows:

Step 1. Calculating the correlation coefficient matrix.

Suppose that $T={\left[t_{ij}\right]}_{p\times m}$ is the evaluation matrix composed of the main evaluation indicators, $Y={\left[y_{ij}\right]}_{p\times m}$ is the calculated correlation coefficient matrix, and $y_{ij}$ is the Pearson correlation coefficient between the $i$th evaluation indicator and the $j$th evaluation indicator. The calculation method is as follows:

$$y_{ij}=\frac{{{\displaystyle \sum }}_{k=1}^p(t_{ki}-\overline{T_i})·(t_{kj}-\overline{T_j})}{\sqrt{{{\displaystyle \sum }}_{k=1}^p{(t_{ki}-\overline{T_i})}^2·{{\displaystyle \sum }}_{k=1}^p{(t_{kj}-\overline{T_j})}^2}},i=1,2,\cdots ,p;j=1,2,\cdots ,m$$

(12)

In the formula, $\overline{T_i}$ and $\overline{T_j}$ represent the mean values of indicator i and indicator j, respectively.

Step 2. Calculate the Gini coefficient.

Suppose that ${\epsilon }_j$ is the Gini coefficient, which is used to measure the distribution of the indicator information. The calculation method is as follows:

$${\epsilon }_j=\frac{{{\displaystyle \sum }}_{i=1}^p{{\displaystyle \sum }}_{k=1}^p\left|s_{ij}-s_{kj}\right|}{2n{{\displaystyle \sum }}_{i=1}^p{s}_{ij}},j=1,2,\cdots ,m$$

(13)

It can be seen from the formula that for ${\epsilon }_j\in \left[0,1\right]$, the closer ${\epsilon }_j$ is to 1, the more unbalanced the distribution of the indicator information and the greater the amount of information contained. The closer ${\epsilon }_j$ is to 0, the more balanced the indicator information distribution is, the smaller the amount of information it contains.

Step 3. Calculate the information coefficient.

Assuming that ${\gamma }_j$ is the information coefficient, there is a positive and a negative correlation between the indicators. To ensure the accuracy of the calculation results, the absolute value of the Pearson coefficient is taken and then included in the calculation of the information coefficient. The calculation method is as follows:

$${\gamma }_j={\displaystyle \sum }_{i=1}^p\left(1-\left|t_{ij}\right|\right),j=1,2,\cdots ,m$$

(14)

Step 4. Calculate the amount of comprehensive information from the indicator.

Suppose ${\eta }_j$ is the comprehensive information quantity of indicator $j$, and the calculation method is

$${\eta }_j={\epsilon }_j·{\gamma }_j,j=1,2,\cdots ,m$$

(15)

Step 5. Calculate the weight of indicator $j$.

$$W_j^1=\frac{{\eta }_j}{{{\displaystyle \sum }}_{j=1}^m{\eta }_j},j=1,2,\cdots ,m$$

(16)

where ${\displaystyle \sum }_{j=1}^m{W}_j^1=1$, $0\le W_j^1\le 1$.

2.

The EWM method.

This method is used to use the degree of dispersion between indicators to calculate the indicator weight. The calculation steps are as follows:

Step 1. Calculate the weight ratio of the evaluation object.

Suppose that the weight proportion is $f_{ij}$, and the calculation method is

$$f_{ij}=\frac{t_{ij}}{{{\displaystyle \sum }}_{i=1}^p{t}_{ij}},i=1,2,\cdots ,p;j=1,2,\cdots ,m$$

(17)

Step 2. Calculate the entropy value.

Assuming that the entropy value is $e_j$, the calculation method is:

$$e_j=-\frac{1}{\ln m}·{\displaystyle \sum }_{t=1}^p{t}_{ij}·\ln t_{ij},i=1,2,\cdots ,p;j=1,2,\cdots ,m$$

(18)

Step 3. Calculation weight.

$$W_j^2=\frac{1-e_j}{{{\displaystyle \sum }}_{i=1}^p\left(1-e_j\right)}=\frac{1-e_j}{m-{{\displaystyle \sum }}_{i=1}^p{e}_j},j=1,2,\cdots ,m$$

(19)

where ${\displaystyle \sum }_{j=1}^m{W}_j^2=1$, $0\le W_j^2\le 1$.

3.

Combination weight

By combining the weight $W_j^1$ and the weight $W_j^2$, the combined weight is obtained:

$$W_j=\frac{W_j^1·W_j^2}{{{\displaystyle \sum }}_{j=1}^m{W}_j^1·W_j^2},j=1,2,\cdots ,m$$

(20)

3.3. Construction Indicator System

3.3.1. Standardization of Indicator Data

Integrate all data collected and processed into a raw data set. The statistical results of the raw data set are shown in

Table 4. Raw data statistics for each risk assessment indicator.

		E11	E12	E13	E14	E15	E16	E17	E18	E19	E10
E	Mean	4.97%	5.02%	5.10%	4.99	5.06	50.4	5.08%	5.05	5.1%	5.10%
	Max	7.51%	8.90%	7.93%	7.59	7.28	86.4	7.96%	7.97	8.0%	7.52%
	Min	1.92%	1.73%	3.04%	1.50	1.98	25.1	2.07%	2.09	2.3%	2.20%
T		T21	T22	T23	T24	T25	T26	T27	T28
	Mean	10.06%	9.92%	9.92%	9.95	9.81%	9.88%	9.94	9.92%
	Max	12.97%	12.3%	11.9%	12.66	12.3%	12.3%	12.19	12.1%
	Min	7.08%	7.56%	7.22%	7.09	7.45%	7.39%	7.06	7.11%
M		M31	M32	M33	M34	M35	M36	M37	M38
	Mean	6.88	6.89%	7.02%	7.0%	6.97%	6.95	6.93	6.95
	Max	9.40	9.29%	9.24%	9.28%	9.39%	9.53	9.16	9.40
	Min	4.65	4.78%	5.19%	4.25%	4.81%	4.31	4.49	4.27
P		P41	P42	P43	P44	P45	P46	P47	P48
	Mean	2.90	3.01%	3.11	3.08	3.07	2.99	3.06	3.16
	Max	5.92	6.37%	5.29	5.30	6.21	5.82	5.65	6.03
	Min	0.23	0.16%	1.01	0.04	0.16	0.76	0.54	0.80
S		S51	S52	S53	S54	S55	S56	S57	S58
	Mean	6.02%	5.83%	5.90%	6.02%	5.88%	6.01%	5.92	6.06
	Max	8.16%	8.26%	8.29%	8.14%	8.30%	8.27%	8.37	8.31
	Min	2.87%	3.64%	3.56%	3.74%	3.26%	3.66%	3.68	3.92
C		C61	C62	C63	C64	C65	C66	C67
	Mean	4.04%	4.00%	4.02%	3.98%	3.94	4.03	3.98
	Max	6.77%	6.61%	6.81%	8.10%	6.92	6.88	7.41
	Min	1.18%	1.69%	1.56%	1.38%	1.42	1.47	1.91

.

3.3.2. Dimensional Reduction of Risk Assessment Indicators

Through the indicator system constructed above, it can be found that the correlation of the evaluation indicators contained in each dimension is not strong. If the evaluation indicators under each risk dimension are extracted by the overall principal component analysis, it may have a cross-impact on the indicators under each dimension and affect the extraction of comprehensive indicators. Therefore, this article extracts the principal components of each risk dimension, screens the key indicators under each risk dimension, and determines the risk assessment indicator system for investment in the transportation infrastructure investment process.

• Correlation test of indicators.

The results of the correlation test of the indicators are shown in

Table 5. Results of the correlation test.

		E	T	M	P	S	C
KMO		0.870	0.853	0.745	0.737	0.631	0.6448
Bartlett Sphericity Test	Chi-Square	826.460	719.18	652.08	620.20	610.20	515.18
	DF	45	43	37	52	38	36
	p-value	0.000	0.002	0.007	0.01	0.02	0.014

.

The closer the KMO value is to 1, the more suitable the original variable is for principal component analysis. It can be seen in Table 5 that the KMO value of the economic risk was 0.970 > 0.5; that is, the evaluation indicators included in the economic risk have a strong correlation, and the next analysis of the principal components can be performed. The p-value of the Bartlett sphericity test was 0.000 < 0.05, indicating that there was a significant correlation between the evaluation indicators, further illustrating the need for a principal component analysis for each evaluation indicator.

2.

Extraction of principal components.

Due to space limitations, this paper only takes economic risk as an example to show the extraction process of principal components. The factor variance contribution is used to measure the relative importance of each factor, which can be explained as the factor’s ability to explain the total variance of the original variable. The more important the factor, the higher the variance contribution rate. The explanation of the variation of the economic risk is shown in

Table 6. The variance explanation of economic risk.

No.	Characteristic Root			Principal Component Extraction
	Characteristic	Variance	Accumulation	Characteristic	Variance	Accumulation
1	4.911	49.11	49.11	4.911	49.11	49.11
2	2.18	21.8	70.91	2.18	21.8	70.91
3	0.935	9.35	80.26	0.935	9.35	80.26
4	0.805	8.05	88.31	0.805	8.05	88.31
5	0.606	6.06	94.37	-	-	-
6	0.368	3.68	98.05	-	-	-
7	0.111	1.11	99.16	-	-	-
8	0.052	0.52	99.68	-	-	-
9	0.029	0.29	99.97	-	-	-
10	0.003	0.03	100	-	-	-

.

This article retained the principal components with a cumulative variance contribution rate of more than 85%, and the cumulative variance contribution rate of a total of four principal components reached 88.31%, which could comprehensively reflect the information of each indicator in the economic risk dimension. Therefore, four principal components were selected for analysis under the economic risk dimension. To facilitate the interpretation of the analysis results, the factor rotation of the component matrix was performed to obtain the rotated component matrix, as shown in

Table 7. Rotated component matrix.

No.	Principal Component
	Component 1	Component 2	Component 3	Component 4
E11	0.018	0.341	0.513	0.272
E12	−0.005	−0.018	0.654	0.245
E13	−0.480	−0.019	−0.043	−0.136
E14	0.209	0.057	−0.288	0.455
E15	−0.606	0.151	0.004	0.303
E16	0.142	0.524	−0.164	0.175
E17	0.184	0.448	0.236	−0.501
E18	0.013	0.529	−0.131	−0.219
E19	0.180	−0.307	0.344	−0.413
E10	0.522	−0.084	−0.085	0.222

.

According to the analysis results of Table 7, the first principal component represents the two indicators of financial difficulty and capital use cost, which can be summarized as financing efficiency (E1); the second principal component represents two indicators of land expropriation cost and labor cost, which can be summarized as uncontrollable investment (E2); the third principal component represents the two indicators of return on investment and capital flow fluctuation, which can be summarized as investment benefit (E3); the fourth principal component represents the investment over budget indicator, which can be summarized as budget overrun rate (E4). In summary, the evaluation indicators under the economic risk dimension can be summarized as four indicators: financing efficiency, uncontrollable investment cost, investment benefit indicator, and budget overrun rate.

According to the above method, the principal components of technical risk, management risk, policy risk, social environment risk, and market risk were extracted, respectively. Among them, the evaluation indicators under the technical risk dimension can be summarized as four indicators: technical reliability (T1), technical implementation complexity (T2), engineering quality compliance rate (T3), and technical compatibility rate (T4); the evaluation indicators under the management risk dimension can be summarized as three indicators: decision execution efficiency (M1), management efficiency (M2), and stability of core team (M3). Evaluation indicators under the dimension of policy risk can be summarized as three indicators: stability of the policy environment (P1), effectiveness of the policy (P2), and adaptability to policies and regulations (P3). Evaluation indicators under the dimension of social–environmental risk can be summarized as three indicators: risk of social stability (S1), social acceptance (S2), and adaptability to environmental pressure (S3). The evaluation indicators under the market risk dimension can be summarized as four indicators: market stability (C1), market responsiveness (C2), return volatility (C3), and intensity of market regulation (C4).

3.

Calculation of weight coefficients

The PCA method can effectively select representative and relevant evaluation indicators, simplifying complex data structures. However, this method mainly solves the problem of which indicators should be included in the evaluation system and does not solve the problem of how much weight these indicators should have in the specific evaluation process. The importance of each indicator in practical application is different. Some have a direct impact on the success of investments in transportation infrastructure, while others are relatively minor. The calculation of the weight coefficient can reflect in more detail the relative importance of each indicator. The introduction of the weight coefficient also increases the flexibility and adaptability of the evaluation system. When the external environment changes, the weight is adjusted to adapt to the new situation. According to the previous calculation method, the weight coefficients are calculated using the CRITIC and EWM methods, respectively, and then the combined weights are determined. The results of the calculation of the weight coefficient for each indicator are shown in

Table 8. Weight coefficient of each indicator.

	Weight Coefficient
	E1	E2	E3	E4	T1	T2	T3	T4	M1	M2	M3
$W_j^1$	0.0543	0.0384	0.0512	0.0501	0.0467	0.0418	0.0550	0.0532	0.0399	0.0628	0.0519
$W_j^2$	0.0603	0.0302	0.0536	0.0514	0.0446	0.0358	0.0619	0.0579	0.0325	0.0807	0.0550
$W_j^{ }$	0.0653	0.0232	0.0547	0.0514	0.0416	0.0299	0.0679	0.0615	0.0259	0.1011	0.0570
	P1	P2	P3	S1	S2	S3	C1	C2	C3	C4
$W_j^1$	0.0418	0.0377	0.0563	0.0572	0.0398	0.0368	0.0546	0.0475	0.0483	0.0348
$W_j^2$	0.0358	0.0290	0.0648	0.0670	0.0323	0.0276	0.0610	0.0461	0.0477	0.0248
$W_j^{ }$	0.0299	0.0218	0.0728	0.0765	0.0257	0.0203	0.0664	0.0437	0.0460	0.0173

.

4.

Establishment of the indicator system

After these calculations, the final evaluation indicator system for the risk of investment in transportation infrastructure constructed in this study is obtained, as shown in

Table 9. Indicator system for investment risk in transportation infrastructure.

Risk Dimensions	Indicator	Weight	Variance Contribution
Economic	E1: Financing Efficiency	0.0653	88.31%
	E2: Uncontrollable Investment Costs	0.0232
	E3: Investment Benefit	0.0547
	E4: Budget Overrun Rate	0.0514
Technological	T1: Technical Reliability	0.0416	89.89%
	T2: Technical Implementation Complexity	0.0299
	T3: Engineering Quality Compliance Rate	0.0679
	T4: Technical Compatibility Rate	0.0615
Management	M1: Decision Execution Efficiency	0.0259	88.33%
	M2: Management Efficiency	0.1011
	M3: Stability of Core Team	0.0570
Political	P1: Policy Environment Stability	0.0299	88.05%
	P2: Policy Effectiveness	0.0218
	P3: Adaptability to Policies and Regulations	0.0728
Social-environmental	S1: Social Stability Risk	0.0765	86.37%
	S2: Social Acceptance	0.0257
	S3: Environmental Pressure Adaptability	0.0203
Market	C1: Market Stability	0.0664	92.37%
	C2: Market Responsiveness	0.0437
	C3: Return Volatility	0.0460
	C4: Market Regulation Intensity	0.0173

.

4. Empirical Study

4.1. Theoretical Model and Research Hypotheses

Structural equation modeling (SEM) is a widely used multivariate statistical analysis technique in fields such as social sciences, behavioral sciences, and management sciences. It can evaluate complex relationships between variables and is suitable for studying latent variables that cannot be observed directly but can be indirectly measured through multiple indicators. Through path analysis, SEM can explore causal relationships between variables. In addition, this method can assess the fit of the entire model as well as the importance and strength of each path. Therefore, SEM is an ideal tool to empirically test the effectiveness of indicator systems. This method not only allows for in-depth analysis of interactions between indicators but also provides a comprehensive perspective on the effectiveness and consistency of the entire risk assessment indicator system, thereby examining the effectiveness of the indicator system. Based on the structure of the Risk Assessment Indicator System constructed in Section 3, economic risk, technical risk, management risk, social–environmental risk, policy risk, and market risk are considered first-order latent variables in the structural equation model, while transportation infrastructure investment risk is considered as a second-order latent variable, and the risk assessment indicators under each risk dimension are considered as measurement variables in the model.

Based on the theoretical model and the measurement model of the risk assessment indicator system for investment in the transportation infrastructure investment discussed above, the research hypotheses for latent variables are set as follows:

H1: 

Economic risk has explanatory power for investment risk in transportation infrastructure.

H2: 

Technical risk has explanatory power over investment risk in transportation infrastructure.

H3: 

Management risk has explanatory power over the risk of investment in transportation infrastructure.

H4: 

Social–environmental risk has explanatory power over the risk of investment in transportation infrastructure.

H5: 

The policy risk has explanatory power over the risk of investment in transportation infrastructure.

H6: 

Market risk has explanatory power over the risk of investment in transportation infrastructure.

4.2. Data Source and Reliability and Validity Test

4.2.1. Data Source

This study takes economic risk, technical risk, management risk, social environment risk, policy risk, and market risk as exogenous potential variables to analyze their impact on the risk of investment in the transportation infrastructure investment process. Since these exogenous potential variables cannot be directly measured, these potential variables must be evaluated by the measurement model corresponding to each risk dimension. Therefore, it is necessary to design the research questionnaire and collect data on the measurement variables. Therefore, it is necessary to design a survey questionnaire and collect data on measurement variables. When designing the survey questionnaire, we first design a preliminary questionnaire based on existing research findings and expert opinions. Then, a small number of samples are selected for pre-survey to assess the reliability and validity of the scales. Finally, the questionnaire is modified further based on any issues identified during the survey process, forming the formal survey questionnaire. The questionnaire is divided into two parts: the first part consists of background information on the respondents to ensure a deep understanding of the industry and the effectiveness of the survey. The second part of the questionnaire is the main part of the survey, which mainly includes the measurement indicators corresponding to economic risk, technical risk, management risk, social–environmental risk, policy risk, and market risk. Likert five-point scale items are used for each measurement variable in the survey. After the initial questionnaire was completed, a pre-survey was conducted from 1 November to 10 December 2023. A total of 30 questionnaires were distributed, and 21 were collected. Modifications were made based on the issues identified during the presurvey and the shortcomings of the research. The formal survey was conducted from 1 December to 30 December 2023. A total of 350 questionnaires were distributed, and 314 valid questionnaires were collected, with an effective rate of 89.7%. Among the valid questionnaires collected, 259 respondents had intermediate or higher professional titles, representing approximately 82.48% of the total sample. In terms of age distribution, the highest proportion falls between 35 and 45 years of age, with 134 respondents representing 42.68% of the total sample. In terms of years of service, most have worked for 6–15 years, with 175 respondents representing 55.73% of the total sample. Detailed information on the survey respondents is shown in

Table 10. Basic information of the questionnaire.

Information	Background	Sample Size	Percentage
Age	Under 25	22	7.01%
	26–34	68	21.66%
	35–45	134	42.68%
	Over 45	90	28.66%
Title	Junior	55	17.52%
	Intermediate	72	22.93%
	Associate senior	104	33.12%
	Senior	83	26.43%
Experience	Under 5	68	21.66%
	6–10	82	26.11%
	11–15	93	29.62%
	Over 15	71	22.61%
Education	Associate	64	20.38%
	Bachelor	139	44.27%
	Master	99	31.53%
	Doctorate	12	3.82%

.

4.2.2. Reliability Test

The reliability testing of the variables refers to the stability and consistency of the results obtained when the same questionnaire is repeatedly administered to measure the variables. Assesses the consistency and reliability of the questionnaire by calculating the internal consistency among various indicators of the measurement tool. The commonly used method to test reliability is Cronbach’s α coefficient method. When the α coefficient value is greater than or equal to the threshold of 0.6, the scale is considered to be highly reliable. In this study, the reliability analysis was performed using SPSS 16.0 software. The results are shown in

Table 11. Results of the reliability test.

Latent Variable	Measured Variable	Cronbach’s α Coefficient
Economic	E1: Financing Efficiency	0.9268	0.8271	0.9311
	E2: Uncontrollable Investment Costs	0.9286
	E3: Investment Benefit	0.9276
	E4: Budget Overrun Rate	0.9269
Technological	T1: Technical Reliability	0.9272	0.8112
	T2: Technical Implementation Complexity	0.9274
	T3: Engineering Quality Compliance Rate	0.9292
	T4: Technical Compatibility Rate	0.9282
Management	M1: Decision Execution Efficiency	0.9272	0.7590
	M2: Management Efficiency	0.9287
	M3: Stability of Core Team	0.9288
Political	P1: Policy Environment Stability	0.9289	0.7738
	P2: Policy Effectiveness	0.9274
	P3: Adaptability to Policies and Regulations	0.9280
Social-environmental	S1: Social Stability Risk	0.9276	0.8174
	S2: Social Acceptance	0.9277
	S3: Environmental Pressure Adaptability	0.9279
Market	C1: Market Stability	0.9281	0.7749
	C2: Market Responsiveness	0.9275
	C3: Return Volatility	0.9279
	C4: Market Regulation Intensity	0.9281

.

From Table 11, it can be observed that Cronbach’s α coefficients for all variables in the sample data were greater than 0.7, with some reliability coefficients exceeding 0.9. This indicates that the scale had good reliability and that the data obtained were highly reliable.

4.2.3. Validity Test

Validity testing refers to the extent to which the results obtained by using a scale or other assessment methods meet the expected goals. There are three types of validity: content validity, criterion validity, and construct validity. In this study, factor analysis was used to analyze the structural validity of the survey questionnaire. Generally, the Kaiser–Meyer–Olkin (KMO) measure should be greater than or equal to 0.5, and the Bartlett test of sphericity should be significant for the sample data. The results of the KMO and Bartlett’s sphericity test are shown in

Table 12. Results of the validity test.

Latent Variable	KMO	Bartlett’s Sphericity Test
		Chi-Square	DF	p
Economic	0.870	1141.45	6	0.000
Technological	0.862	1126.65	6	0.000
Management	0.761	673.72	3	0.001
Political	0.760	687.35	3	0.000
Social–environmental	0.763	699.53	3	0.000
Market	0.848	991.09	6	0.000
Overall	0.955	6596.81	210	0.000

.

From Table 12, the total KMO value of the sample data was 0.955, which was greater than 0.8. The latent variables and the general significance test had significant p-values, indicating that the scale had a good general validity of the construct, and further research can be carried out.

4.3. Model Construction and Hypothesis Testing

4.3.1. Model Construction

On the basis of the research presented earlier, it can be observed that the data collected through surveys have undergone reliability and validity tests, indicating high reliability of the data, which meets the requirements for constructing a structural equation model. Building on the theoretical model and the measurement model constructed earlier, the structural equation model for this study is preliminarily constructed, as shown in Figure 3.

4.3.2. Fitting of the First-Order Structural Equation Model

Building upon the structural equation model constructed earlier, this section will focus on studying the fitting of the first-order structural equation model to verify whether each measurement indicator can effectively explain its corresponding risk dimension. The first-order structural equation model for this study was drawn using AMOS 24.0 software. The data obtained from the questionnaire survey, consisting of 314 sets of data, were imported into the software for model fitting, and the coefficients of each path in the first-order structural equation model were obtained. The fitting results are shown in Figure 4.

Figure 4 shows that the path coefficients between the error variables and the observed variables in the first-order structural equation model were not negative, and the error terms also did not have negative values, indicating compliance with the assumption of proper estimation. The covariance results of the latent variables in the first-order structural equation model are shown in

Table 13. Covariance results of latent variables in the first-order structural equation model.

Path	Estimate	S.E	C.R.	p
Economic ↔ Technical	0.701	0.125	9.135	***
Economic ↔ Management	0.688	0.130	8.966	***
Economic ↔ Policy	0.681	0.125	8.842	***
Economic ↔ Social–Environmental	0.693	0.134	9.054	***
Economic ↔ Market	0.719	0.128	9.195	***
Technical ↔ Management	0.670	0.128	8.856	***
Technical ↔ Policy	0.672	0.124	8.799	***
Technical ↔ Social–Environmental	0.669	0.131	8.887	***
Technical ↔ Market	0.700	0.126	9.086	***
Management ↔ Policy	0.656	0.128	8.604	***
Management ↔ Social–Environmental	0.722	0.141	9.269	***
Management ↔ Market	0.674	0.130	8.817	***
Policy ↔ Social–Environmental	0.687	0.134	8.905	***
Policy ↔ Market	0.730	0.129	9.186	***
Social Environmental ↔ Market	0.734	0.138	9.34	***

***: p < 0.001.

.

In Table 13, it can be observed that the fit results for the standard error (SE) ranged from 0.124 to 0.141. The significance level (p-value) for the standard error was less than 0.001 for all variables. The factor loading coefficients between latent variables ranged from 0.656 to 0.734, indicating that the basic fit of the first-order structural equation model had passed the test. The general results of the fit of the first-order structural equation model are shown in

Table 14. The first-order structural equation model fitness.

Indicator	Reference Range	Fitting Result	Model Fitness
X2/DF	≤3.00	1.311	Fit
GFI	≥0.90	0.938	Fit
RMR	≤0.05	0.047	Fit
RMSEA	≤0.08	0.032	Fit
AGFI	≥0.90	0.918	Fit
NFI	≥0.90	0.966	Fit
CFI	≥0.90	0.992	Fit
IFI	≥0.90	0.992	Fit
RFI	≥0.90	0.959	Fit
TLI	≥0.90	0.990	Fit

.

From Table 14, it can be concluded that all the fit indices of the first-order structural equation model met the requirements, indicating that the first-order structural equation model had passed the test and is the optimal model. Therefore, based on the first-order structural equation model, a second-order structural equation model can be constructed to further investigate the relationship between the first- and second-order latent variables.

4.3.3. Fitting of the Second-Order Structural Equation Model

To examine the relationships between the first-order latent variables and second-order latent variables, the second-order structural equation model was fitted. The results of the fitting of the second order structural equation model are shown in Figure 5.

The parameter estimation results of the second-order structural equation model are presented in

Table 15. Parameter estimation results of the second-order structural equation model.

Path	Estimate	S.E	C.R.	p
Economic ← Transportation Infrastructure Investment	0.837
Technical ← Transportation Infrastructure Investment	0.816	0.072	13.494	***
Market ← Transportation Infrastructure Investment	0.861	0.074	13.98	***
Social-environmental ← Transportation Infrastructure Investment	0.844	0.077	13.95	***
Policy ← Transportation Infrastructure Investment	0.822	0.074	13.2	***
Management ← Transportation Infrastructure Investment	0.815	0.075	13.348	***
E1 ← Economic	0.881
E2 ← Economic	0.899	0.043	23.31	***
E3 ← Economic	0.902	0.042	23.464	***
E4 ← Economic	0.905	0.045	23.671	***
T1 ← Technicalssssssssssss	0.893
T2 ← Technical	0.881	0.044	22.925	***
T3 ← Technical	0.888	0.043	23.347	***
T4 ← Technical	0.913	0.043	24.907	***
M1 ← Management	0.892
M2 ← Management	0.892	0.043	22.49	***
M3 ← Management	0.881	0.046	21.993	***
P1 ← Policy	0.869
P2 ← Policy	0.914	0.047	22.516	***
P3 ← Policy	0.887	0.049	21.391	***
S1 ← Social-environmental	0.900
S2 ← Social-environmental	0.897	0.042	23.497	***
S3 ← Social-environmental	0.883	0.042	22.754	***
C1 ← Market	0.879
C2 ← Market	0.884	0.045	22.046	***
C3 ← Market	0.851	0.046	20.439	***
C4 ← Market	0.882	0.045	21.935	***

***: p < 0.001.

.

From Table 15, it can be observed that all the first-order latent variables had significant positive effects on the second-order latent variable, with path coefficients exceeding 0.8. This indicates that these six risk dimensions had a strong explanatory power for infrastructure investment risk in transportation. The overall fit indices of the second-order model are presented in

Table 16. Results of the second-order structural equation model fitness results.

Indicator	Reference Range	Fitting Result	Model Fitness
X2/DF	≤3.00	1.290	Fit
GFI	≥0.90	0.937	Fit
RMR	≤0.05	0.053	Fit
RMSEA	≤0.08	0.030	Fit
AGFI	≥0.90	0.920	Fit
NFI	≥0.90	0.965	Fit
CFI	≥0.90	0.992	Fit
IFI	≥0.90	0.992	Fit
RFI	≥0.90	0.960	Fit
TLI	≥0.90	0.991	Fit

.

From Table 16, it can be observed that the fit indices of the second-order structural equation model all met the standard criteria, indicating the significance of the model parameters. In general, these fit indices demonstrated a good fit between the model and the data, indicating that this study’s transportation infrastructure investment risk assessment indicator system effectively reflects the actual situation of transportation infrastructure investment risk.

4.3.4. Hypothesis Testing

Based on the above research, it can be inferred that the research hypotheses proposed prior to model construction have been validated. The results of the hypothesis testing are shown in

Table 17. The results of the hypothesis testing.

No.	Hypothesis	Result
H1	Economic risk has explanatory power over the risk of investment in transportation infrastructure investment risk	Pass
H2	Technical risk has explanatory power over the risk of investment in transportation infrastructure	Pass
H3	Management risk has explanatory power over the risk of investment in transportation infrastructure	Pass
H4	Social–environmental risk has explanatory power over the risk of investment in transportation infrastructure	Pass
H5	Policy risk has explanatory power over the risk of investment in transportation infrastructure	Pass
H6	Market risk has explanatory power over the risk of investment in transportation infrastructure	Pass

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5. Conclusions

This study constructs a risk assessment indicator system for investment in the transportation infrastructure investment projects in the public–private partnership (PPP) mode employing principal component analysis (PCA) and the CRITIC-EWM method. Addresses the shortcomings of existing research in terms of dynamism, systematicity, and methodological application. Research findings demonstrate that the comprehensive use of the PCA and CRITIC-EWM methods can effectively reduce the dimensions of risk indicators and calculate the weights of each indicator, providing a scientific and systematic assessment tool for the management of risk of transportation infrastructure projects. Through empirical testing, the effectiveness and reliability of the constructed indicator system are validated, providing new theoretical and practical guidance for the risk assessment of transportation infrastructure investment projects in the PPP mode. The conclusions of this study are as follows:

• This study successfully constructs an assessment indicator system containing multidimensional risk factors that can comprehensively reflect the risk status of transportation infrastructure investment projects in the PPP mode;
• By integrating the PCA and CRITIC-EWM methods, this study proposes a new method to build a risk assessment indicator system, improving the precision and practicality of risk assessment;
• The effectiveness of the constructed indicator system is tested using empirical data, verifying its application value in practical PPP project risk assessment.

Based on the above research results, this study proposes the following practical application recommendations for risk management in transportation infrastructure investment projects:

• The risk assessment indicator system constructed in this study can serve as a reference tool for both government and private sectors in project decision-making and risk management, optimizing resource allocation and risk-sharing strategies;
• Establish a dynamic risk monitoring and assessment mechanism, regularly updating risk assessment indicators and their weights to adapt to changes during the project implementation process and in the external environment;
• Establish effective communication and coordination mechanisms among stakeholders to share risk information and collaboratively manage risks, enhancing project management transparency and synergy, thereby increasing the success rate of PPP projects.

Although this study has made certain achievements in constructing a risk assessment indicator system for transportation infrastructure investment projects under the PPP model, there are still some limitations:

• The empirical analysis in this study primarily relies on historical data from completed projects. The availability and quality of these data may affect the accuracy and generalizability of the research conclusions;
• While the PCA and CRITIC-EWM methods performed well in this study, their applicability may vary across different types of PPP projects, requiring further validation and optimization in the future;
• Although efforts were made to ensure the representativeness of the sample, the sample may still not fully represent all types and regions of transportation infrastructure investment projects due to limitations in data sources.

To further enhance the depth and breadth of the research, future studies can focus on the following areas:

• Future research can further explore the applicability and reliability of the indicator system across different types and regions of the PPP projects.
• Investigate how to integrate other methods (such as Bayesian networks and machine learning) to optimize the risk assessment indicator system, improving the accuracy and flexibility of risk prediction.
• Consider the real-time and dynamic nature of data, further studying how to achieve real-time monitoring and dynamic adjustment of risk assessment through big data and artificial intelligence technologies.