Bridging Theory and Data: Linking Regional Innovation System Dimensions to Patent Outcomes Through CFA-CatBoost Integration

Background: Understanding how Regional Innovation Systems (RISs) drive innovation outputs remains a central question in innovation studies. Most existing empirical research relies on linear or single-indicator models, which fail to capture nonlinear interactions among the key RIS dimensions—Firms, Knowledge, Government, and Economy. Methodology: This study proposes an integrated analytical framework that combines Confirmatory Factor Analysis (CFA), CatBoost machine learning, and SHAP-based explainability to bridge theory-driven modeling with data-driven prediction. Using provincial panel data from China spanning 2011–2023, CFA is first employed to construct and validate four latent RIS dimensions. These latent constructs are then used as inputs in a CatBoost model to predict regional patent outputs, followed by SHAP analysis to quantify the marginal and interactive contributions of each dimension. Results: The CFA results confirm the reliability and validity of the four latent dimensions, establishing a robust structural foundation for the RIS. The CatBoost model achieves high predictive accuracy (log-transformed R 2 = 0.975, RMSE = 0.206), substantially outperforming traditional linear benchmarks. SHAP analysis indicates that the Firm dimension is the primary driver of innovation output, while Knowledge, Government, and Economy dimensions exhibit context-dependent moderating effects characterized by diminishing returns, threshold effects, and nonlinear synergies. Conclusions: By integrating latent-variable modeling with interpretable machine learning, this study develops a “CFA-CatBoost-SHAP” closed-loop paradigm for transparent and high-precision analysis of innovation mechanisms. This approach advances RIS theory by empirically validating its multidimensional structure, enriches the methodological toolkit for innovation research, and provides actionable insights for the design of targeted R&D and innovation policies.