## 3 Methods and Materials
### Fuzzy-Set Qualitative Comparative Analysis (fsQCA)  
A Fuzzy-Set Qualitative Comparative Analysis (fsQCA) is not limited to handling purely categorical issues but also deals with partial membership problems, where membership degrees range from 0 to 1. This method transforms fuzzy-set data into truth tables, maintaining the advantages of truth tables in handling qualitative data and demonstrating benefits in constructing \"simplified configurational\" pathways. Thus, fsQCA integrates the dual advantages of qualitative and quantitative analysis [48] by applying fsQCA to explore the sufficient or necessary subset relationships between configurations composed of different elements and specific outcomes [49]. The main analysis steps are as follows:  
(1) Selecting explanatory variables. A configurational analysis focuses on exploring how combinations of variables work together at the configurational level. When using the QCA method to analyze \"configurational effects\", it is first necessary to identify the explanatory variables, typically through induction. This involves reviewing the relevant literature and cases to identify and construct key explanatory variables related to the research configuration. Different explanatory variables will form different configurations, and as the number of explanatory variables increases, the number of configurations will grow exponentially. Therefore, maintaining a reasonable ratio between the sample size and the number of explanatory variables is crucial to reducing sample diversity and issues with individual case explanations.  
(2) Data calibration. The calibration process involves converting the raw data of the selected explanatory variables into set memberships. The aim is to impart \"meaning\" to the variables and incorporate them within the framework of set membership concepts. This requires identifying three key thresholds: \"full membership\", \"full non-membership\", and the \"crossover point\" that distinguishes between full membership and non-membership. Following [PERSON]'s direct calibration method, this paper converts the data into predetermined thresholds: \"full membership\" (0.95), \"crossover point\" (0.5), and \"full non-membership\" (0.05).  
(3) The construction of truth tables. Set-theoretic research primarily explores the causal links between explanatory and outcome variables by analyzing the relationships between \"sets and subsets\", identifying all combinations of explanatory variables that can trigger changes in the outcome variables, known as \"truth tables\". Based on this, fsQCA software generates a truth table that includes all the potential configurations. It then automatically filters out those explanatory paths with sufficient explanatory power, based on the consistency thresholds and case frequencies set by the researcher.  
(4) Sufficiency and necessity analyses. The aim of a sufficiency and necessity analysis is to assess the impact strength of a specific combination of explanatory variables on the outcome variable, as well as the degree to which this combination constitutes the sufficient and necessary conditions for the occurrence of the outcome variable. This allows for the identification of multiple pathways that lead to changes in the outcome variable. In Qualitative Comparative Analysis (QCA), the reliability of the results is evaluated based on two metrics: consistency and coverage, both of which range from 0 to 1.  
(5) Robustness test. The robustness test is a critical analytical step in the fsQCA method, covering aspects such as parameter setting and model construction. The robustness test is implemented by adjusting calibration thresholds, modifying case frequencies, and altering consistency thresholds.