From Innovation Drivers to Regional Patterns: A Hybrid Econometric and Machine Learning Framework

<title>Abstract</title> <p>This study develops an integrated Explain–Predict–Classify framework to investigate the determinants, territorial heterogeneity, and predictability of regional innovation performance. Using Regional Innovation Scoreboard data for 246 regional units across 31 European countries over 2016–2023, the analysis combines panel-data econometrics, unsupervised clustering, and supervised machine-learning regression. The Summary Innovation Index (SII) is examined alongside indicators capturing scientific collaboration, non-R&amp;D innovation expenditure, SME product and process innovation, collaborative networks, design applications, innovative sales, and environmental conditions. Econometric results show positive and statistically significant associations across all selected innovation dimensions. The Hausman test favors fixed effects over random effects, while the dynamic specification indicates significant persistence in regional innovation performance, although instrument-validity diagnostics require caution. The clustering analysis compares six algorithms using multiple internal validation criteria. K-Means provides the strongest overall solution, with R² = 0.6301, a Calinski–Harabasz index of 370.60, and relatively balanced cluster sizes, revealing ten heterogeneous and partially overlapping regional innovation profiles. The predictive analysis compares seven regression algorithms. K-Nearest Neighbors achieves the strongest test performance (R² = 0.9482; RMSE = 7.90; MAE = 4.793), followed by Random Forest (R² = 0.9289). Permutation importance identifies international scientific co-publications, design applications, and SME collaboration as the most influential KNN predictors. Overall, the findings demonstrate that regional innovation combines common systematic relationships with heterogeneous territorial configurations and nonlinear predictive structures. Integrating econometrics, clustering, and machine learning therefore provides a richer empirical basis for understanding regional innovation and designing differentiated, place-sensitive innovation policies.</p>