Research on the Nonlinear and Interactive Effects of Multidimensional Influencing Factors on Urban Innovation Cooperation: A Method Based on an Explainable Machine Learning Model

Within globalization, the significance of urban innovation cooperation has become increasingly evident. However, urban innovation cooperation faces challenges due to various factors—social, economic, and spatial—making it difficult for traditional methods to uncover the intricate nonlinear relationships among them. Consequently, this research concentrates on cities within the Yangtze River Delta region, employing an explainable machine learning model that integrates eXtreme Gradient Boosting (XGBoost), SHapley Additive exPlanations (SHAP), and Partial Dependence Plots (PDPs) to investigate the nonlinear and interactive effects of multidimensional factors impacting urban innovation cooperation. The findings indicate that XGBoost outperforms LR, SVR, RF, and GBDT in terms of accuracy and effectiveness. Key results are summarized as follows: (1) Urban innovation cooperation exhibits different phased characteristics. (2) There exist nonlinear and interactive effects between urban innovation cooperation and multidimensional factors, among them, the Scientific and Technological dimension contributes the most (30.59%) and has the most significant positive promoting effect in the later stage after surpassing a certain threshold. In the Social and Economic dimension (23.61%), the number of Internet Users (IU) contributes the most individually. The Physical Space dimension (20.46%) generally exhibits mutation points during the early stages of urban development, with overall relationships predominantly characterized by nonlinear positive trends. (3) Through the application of PDP, it is further determined that IU has a positive synergistic effect with per capita Foreign Direct Investment (FDI), public library collections per capita (LC), and city night light data (NPP), while exhibiting a negative antagonistic effect with Average Annual Wage of Staff (AAS) and number of Enterprises above Designated Size in Industry (EDS). (4) For cities at different developmental stages, tailored development proposals should be formulated based on single-factor contribution and multifactor interaction effects. These insights enhance our understanding of urban innovation cooperation and elucidate the nonlinear and interactive effects of multidimensional influencing factors.