Predictive Framework for Regional Patent Output Using Digital Economic Indicators: A Stacked Machine Learning and Geospatial Ensemble to Address R&D Disparities

Abstract

As digital transformation becomes an increasingly central focus of national and regional policy agendas, parallel efforts are intensifying to stimulate innovation as a critical driver of firm competitiveness and high-quality economic growth. However, regional disparities in innovation capacity persist. This study proposes an integrated framework in which regionally tracked digital economy indicators are leveraged to predict firm-level innovation performance, measured through patent activity, across China. Drawing on a comprehensive dataset covering 13 digital economic indicators from 2013 to 2022, this study spans core, broad, and narrow dimensions of digital development. Spatial dependencies among these indicators are assessed using global and local spatial autocorrelation measures, including Moran’s I and Geary’s C, to provide actionable insights for constructing innovation-conducive environments. To model the predictive relationship between digital metrics and innovation output, this study employs a suite of supervised machine learning techniques—Random Forest, Extreme Learning Machine (ELM), Support Vector Machine (SVM), XGBoost, and stacked ensemble approaches. Our findings demonstrate the potential of digital infrastructure metrics to serve as early indicators of regional innovation capacity, offering a data-driven foundation for targeted policymaking, strategic resource allocation, and the design of adaptive digital innovation ecosystems.

1. Introduction

Over the past decade, China has made notable progress in enhancing its innovation capacity under the framework of its innovation-driven development strategy. According to the Global Innovation Index 2021, China’s ranking in the National Innovation Index rose from 38th in 2000 to 12th in 2020—surpassing the OECD average and making it the only middle-income country among the global top 30. This ascent has largely been fueled by sustained increases in R&D (research and development) investment, often captured through patent applications and grants. However, the input-driven nature of this growth raises concerns about its long-term sustainability [1].

The digital economy has emerged as a transformative force, reshaping industry value chains [2,3] and playing a critical role in driving economic growth and improving energy efficiency [4]. By 2021, the digital economy of China further expanded to CNY 45.5 trillion, representing 39.8% of its GDP and growing by 16.2% year on year [5]. By 2024, the added value generated by the core industries of the digital economy accounted for approximately 10% of the GDP, while total data production reached 41.06 zettabytes—reflecting a strong year-on-year growth rate of 25%, according to the Digital China Development Report 2024 issued by the National Data Administration [6]. This remarkable growth underscores the increasing importance of digitalization in driving economic advancement and efficiency, as evidenced by its expanding contribution to China’s GDP [7,8].

The digital economy promotes high-quality development by enhancing resource allocation efficiency, boosting total factor productivity, and stimulating entrepreneurial activity [9]. Furthermore, it accelerates the integration of digital technologies with R&D systems, profoundly influencing innovation dynamics and the formation of innovation networks [10]. This integration occurs both directly—by improving labor productivity [11] and manufacturing productivity [12]—and indirectly—through the optimization of service sectors [13]. As a result, the digital economy fosters open innovation, enhances human capital, and promotes corporate innovation through improved organizational management and increased demand-driven technological advancement [14]. In summary, the digital economy catalyzes corporate innovations by reducing costs, fostering innovation-driven ecosystems, and enabling organizational transformation [15]. These innovations, often measured by metrics such as patent filings, demonstrate how the digital economy translates into tangible R&D outcomes.

However, sustaining the momentum of innovation requires substantial investment—often exceeding a firm’s internal financing capabilities [16]. In the rapidly evolving digital landscape, firms must secure additional funding to overcome information asymmetries and financing constraints—needs increasingly met by financial technology (FinTech) [17,18]. Digital finance, by enhancing financial flexibility, has been shown to boost R&D investment, particularly among technology-based SMEs [19]. In China, FinTech policies have supported sustainable innovation and enhanced business performance without increasing risk [20]. Meanwhile, advances in information and communication technologies underpin a digital economy that fosters growth and productivity, streamlines operations, and broadens access to finance through platforms such as e-commerce [12,21]. The synergy between the digital economy and FinTech creates a virtuous cycle: improved credit asset quality enables financial institutions to assume greater FinTech-related risks, fostering non-traditional credit-scoring models and expanding SME credit access [22,23]. In turn, FinTech drives financial inclusion, reduces transaction costs, and accelerates technological progress, reinforcing economic growth and innovation. These dynamics highlight that unlocking the digital economy’s full innovation potential also depends on financing mechanisms to yield measurable innovation outcomes.

China’s regional innovation landscape remains uneven, making research and development (R&D) a critical focus for growth. Compared to some developed nations, Chinese firms still have considerable room to enhance their innovation capacity and increase R&D intensity [24]. Moreover, while prior studies document the impacts of the digital economy on aggregate innovation, little is known about how regional digital indicators predict firm-level R&D intensity and patent outcomes. To capture both the inputs and outputs of innovation activity, this study uses patent counts as a proxy for R&D output—the tangible result of inventive processes [25,26,27]. The goals of this article are (1) to examine a comprehensive framework of the mechanisms by which the digital economy drives corporate R&D investment and innovation, through which the relationship between a firm’s innovative output and the surrounding digital economy is closely integrated; (2) to evaluate the spatial correlations of these digital economy indicators, which are essential for constructing an informed innovation environment; and (3) to identify and utilize key regionally monitored digital economy indicators to effectively approximate and predict firm-level innovation outcomes.

This study leverages several widely used machine learning (ML) methods, including Random Forest (RF), Support Vector Machine (SVM), XGBoost, Extreme Learning Machine (ELM), and stacking ensembles. While well established, these techniques are applied to a novel context of modeling the predictive relationship between digital infrastructure metrics and firm-level innovation performance across regions in China—a previously unexplored linkage in prior ML-based studies. The novel contributions of this study are threefold:

(1)

This study introduces a novel hybrid framework that evaluates spatial autocorrelation measures in parallel with ML modeling and uses the resulting spatial insights to guide the potential embedding of spatial features into the ML algorithms. This dual-track approach serves two distinct purposes: first, spatial insights provide explicit regional decision-making guidance that complements and runs alongside ML results, helping to contextualize predictions within broader spatial patterns; and second, they enhance the robustness and accuracy of the ML models themselves by informing the modeling process and allowing for more realistic predictions that account for the regional interdependencies and spatial dynamics of innovation activity.

(2)

By conducting spatial analysis separately but in close dialogue with ML modeling, this study presents an innovative and replicable framework for applying machine learning to geospatial data. This framework not only improves predictive accuracy and robustness but also produces richer, spatially informed policy insights that can be integrated with the machine learning results. It holds significant promise for adaptation to other domains where geographic context is critical, thereby advancing the frontier of machine learning applications for spatially structured data in decision making, especially in the context of regional development and policy design.

(3)

Finally, this section situates this study within the context of emerging research from 2023 to 2024 on innovation and development. Unlike much of the current literature that relies on spatial analysis and traditional statistical methods, this work makes a distinctive contribution by explicitly integrating spatial thinking with ensemble machine learning techniques. The resulting framework offers more direct, actionable, and monitorable insights that can effectively support targeted regional innovation policies and inform strategies for high-quality regional development through spatially aware predictive monitoring.

2. Literature Review

2.1. The Role of the Digital Economy in Enhancing Corporate R&D

The digital economy, initially conceptualized by Tapscott (1996) [28], represents an economic paradigm underpinned by advances in information and communication technologies (ICTs). According to the Chinese government’s 2020 White Paper on the Development of China’s Digital Economy, it is characterized by digital knowledge and information as core production factors, digital technologies as drivers of economic activity, and modern information networks as foundational infrastructure [29]. Empirical evidence indicates that the digital economy enhances total factor productivity [30] and contributes substantially to national economic growth [2].

The digital economy exerts its influence on corporate R&D investment through several key mechanisms (Figure 1). First, digital transformation lowers operational costs and improves efficiency, thereby facilitating innovation. Digital technologies streamline production and distribution processes while minimizing energy use, transaction costs, and other operational expenditures [31]. By lowering search, transportation, and validation costs, firms increase profitability and gain a greater capacity for R&D investment [32]. Furthermore, digital platforms enhance industrial and supply chain coordination, which, in turn, supports sustainable economic development and technological innovation [33]. Applications such as the Internet and smart terminals enable real-time, cost-effective information exchange, particularly across geographic boundaries, thereby enhancing processing efficiency. The process of informatization has been linked to productivity gains across multiple sectors, including agriculture [34], manufacturing [12], and services such as retail [35].

Second, the digital economy fosters the development of innovation ecosystems, which are further strengthened by the unique properties of data as a production factor—its virtual nature, non-rivalrous characteristics, and varying degrees of excludability [36]. Strong network externalities enhance information accessibility and reduce barriers to innovation [37]. These attributes facilitate collaborative innovation by enabling multiple entities to derive value from shared datasets. Furthermore, the digital economy supports the formation of industrial clusters through Internet-based platforms, improving economic efficiency through scale effects and technological externalities [38]. Digital transmission enables real-time information sharing across regions [39], overcoming geographic constraints and amplifying knowledge spillovers. Prioritizing data openness maximizes these benefits, broadening access to information and fostering knowledge creation.

Third, the digital economy drives transformation in organizational and sectoral structures. In addition to its technological advantages, it promotes organizational change, facilitates open innovation, and enhances human capital [40,41]. Corporate innovation is propelled through mechanisms such as open innovation, human capital development, and shifts in organizational management. The role of data in the innovation ecosystem becomes especially transformative when combined with the backward forcing mechanism, where consumer demand and downstream feedback push firms to enhance technological capabilities and accelerate innovation [42]. Resource-dependent industries benefit notably, as the digital economy enables a shift from heavy industries to service-oriented, technology-driven sectors, creating new opportunities for research and development [43]. The integration of the real and digital economies further facilitates the substitution of market capital with social capital, emphasizing interaction and engagement. This fusion amplifies the Pareto-improving effects of digital technology in production, strengthens the synergy between physical and digital R&D, and drives “creative destruction” in traditional industries and market structures [44,45]. Additionally, open innovation initiatives support the commercialization of emerging technologies, thereby maximizing their economic potential [46].

In summary, the digital economy catalyzes corporate innovations by reducing costs, fostering innovation-driven ecosystems, and enabling organizational transformation. These mechanisms highlight its transformative role in advancing technological progress and stimulating corporate innovation. This study uses patent filings as a proxy for R&D outcomes, assessing how the digital economy influences both the scale of R&D investment and its tangible results.

2.2. The Role of FinTech in Advancing R&D Investment

Firm-level R&D is significantly supported by the development of financial technology (FinTech), as innovation activities often require substantial external funding beyond the capacity of internal resources [16]. Firms engaged in intensive R&D typically face high levels of information asymmetry and lack sufficient tangible collateral, leading to credit constraints in traditional financial markets [46]. These constraints are especially pronounced among SMEs, which often lack the “hard” information preferred by conventional lenders—frequently resulting in the abandonment of innovation projects [47,48].

FinTech addresses these challenges by expanding credit access through alternative data sources, including social media activity and big data analytics [49]. Technologies such as big data, cloud computing, and artificial intelligence enable the creation of alternative credit scoring models, thereby improving credit availability for SMEs lacking comprehensive financial records [22,23]. In addition, FinTech reduces transaction and regulatory costs, increases market liquidity, and enhances financial transparency—alleviating financing constraints for innovation-driven firms [50]. Platforms such as peer-to-peer (P2P) lending and crowdfunding further facilitate direct financing for firms unable to access traditional funding channels [51,52].

By aggregating financial data, expert opinions, and crowdsourced insights, FinTech also reduces information asymmetry and agency problems, fostering both R&D investment and the realization of innovation outcomes, often measured through proxies such as patent filings [53,54]. Moreover, FinTech enhances corporate risk-taking capacity by supporting data-driven decision making [55,56]. Automated financial algorithms reduce transaction costs and broaden funding possibilities—particularly for larger or more opaque firms—supporting the translation of R&D investments into tangible innovation outputs [57,58]. In China, supportive FinTech policies have stimulated sustainable innovation and business performance, with the number of FinTech firms increasing by 28.08% in 2021—a testament to the growing role of digital finance in fostering R&D investment [59].

2.3. Synergies Between Digital Economy and FinTech in Advancing R&D

FinTech, as a technology-driven financial innovation, remains fundamentally tied to finance and cannot eliminate systemic risks inherent in the traditional financial sector [60]. Compared to financial innovations such as asset securitization, FinTech represents a deeper financial transformation, carrying a broader range of risks—including network, operational, strategic, and compliance risks [61].

Improving the quality of credit assets benefits FinTech development, a concept explored within the framework proposed by Chen, Yan, and Chen (2023) [62], which underscores the role of credit asset quality in driving FinTech innovation in the digital economy. China’s bank-led financial system makes technological innovation within banks a pivotal factor for advancing the country’s FinTech sector. Banks, as primary drivers of FinTech innovation, extend credit while managing risk within defined limits, creating a trade-off between FinTech risk and credit risk: lower credit risk and higher credit asset quality allow for greater tolerance of FinTech risk. Thus, enhancing the quality of credit assets enables banks to engage in more FinTech innovation, advancing development while mitigating associated risks.

The digital economy plays a key role in improving credit asset quality through multiple channels. One major mechanism is fostering economic growth. By enhancing resource allocation efficiency, increasing entrepreneurial activity, and raising total factor productivity, the digital economy drives high-quality economic development [63,64]. This growth environment improves enterprise profitability and solvency, reducing the non-performing loan (NPL) ratio and elevating credit asset quality. As a result, banks are encouraged to allocate resources toward FinTech innovation, ensuring financial stability while minimizing risk.

Additionally, digital technologies, such as ICT, significantly enhance operational efficiency across industries by boosting productivity and reducing costs [12,21]. In the financial sector, these advancements lower transaction costs, facilitate integration between traditional banks and FinTech firms, and eliminate spatial constraints on financial services. This enhances commercial bank efficiency, reduces NPL rates, and streamlines credit delivery, creating an environment conducive to sustained FinTech innovation.

Digital infrastructure, a key component of the digital economy, is also crucial in reducing information asymmetry [65]. By leveraging platforms such as e-commerce, the digital economy bridges the information gap between borrowing enterprises and financial institutions. The collaboration between e-commerce platforms and banks introduces an innovative credit model that effectively utilizes SMEs’ credit information, minimizing asymmetry between SMEs and banks [66]. This leads to more accurate credit assessments, enhancing financial institutions’ ability to implement FinTech solutions efficiently.

As a result, FinTech and the digital economy create a feedback loop that drives R&D investment by firms. Improved credit asset quality supports FinTech advancements in two key ways. First, reduced NPL ratios free up resources for banks to implement innovative technologies, such as alternative credit scoring and automated lending platforms [22]. Second, enhanced credit quality enables financial institutions to tolerate higher levels of FinTech-related risks, spurring the development and integration of FinTech solutions into traditional financial systems. As FinTech expands, it promotes innovation in the digital economy by improving financial inclusion and reducing transaction costs, reinforcing the cycle of economic growth and technological progress. This synergistic relationship demonstrates the digital economy’s pivotal role in driving financial and technological advancements, establishing a feedback loop in which improved access to finance fuels R&D investment and drives greater innovation, as evidenced by increased patent activity.

This study proposes that digital economic indices can predict regional patent output, serving as a proxy for R&D outcomes, and may be extrapolated to forecast innovation trends across Chinese provinces. The objectives are (1) to develop machine learning models for predicting regional patent output based on digital economic indicators; (2) to assess regional associations between key predictors of patent output and their impact on model accuracy and applicability; (3) to compare the predictive performance of four machine learning models—Random Forest (RF), Support Vector Machine (SVM), Extreme Learning Machine (ELM), and XGBoost—evaluating their accuracy and other relevant metrics to identify the most suitable approach; and (4) to offer actionable insights for policymakers and businesses to optimize regional innovation strategies using measurable digital economy indicators. These insights will support data-driven development, foster innovation, and guide strategic decision making at the regional level.

3. Materials and Methods

3.1. Variables Selection and Data Processing

Bukht and Heeks (2017) [67] defined the digital economy as consisting of three interconnected layers: core, narrow, and broad layers. The core layer includes digital industrial sectors such as IT consulting, software development, telecommunications, and information services. The narrow layer encompasses digital services and the platform economy, while the broad layer extends to areas such as e-commerce, the algorithmic economy, mechanized agriculture, and emerging industries [68]. This study specifically utilized these layers as a foundation for analysis, placing greater emphasis on core layers to ensure that they accurately represent the overall digital economy. The selected variables were chosen based on their measurability across regions and their relevance in capturing the digital economic landscape in relation to corporate innovation levels, thereby enhancing the predictive accuracy of the model (

Table 1. Digital economy variables and classification by layers.

Layer	Variable	Variable Abbreviation	Reason for Classification
Core Layer	IPv4 Address Count	ipv4_count	IPv4 addresses are fundamental to Internet infrastructure, aligning with IT consulting and telecommunications.
	Internet Domain Count	domain_count	Internet domains are essential for online services and software-driven activities.
	Broadband Internet Users	broadband_users	Broadband access is critical infrastructure for IT services, telecommunications, and digital operations.
	Internet Access Ports	access_ports	Internet access ports support foundational IT infrastructure and digital industrial content.
	Long-Distance Fiber Optic Cable Length per Unit Area	fiber_cable_density	Fiber optic cables are the backbone of telecommunications and digital industrial services.
	Mobile Base Station Density	mobile_base_density	Mobile base stations are critical infrastructure for telecommunications and IT services.
	IT Service Revenue as Percentage of GDP	it_service_gdp	IT services, including software development and consulting, are central to the core digital economy.
	Telecom Services Revenue as Percentage of GDP	telecom_gdp	Telecom services form a foundational part of the digital industrial content in the core layer.
Broad Layer	E-commerce Revenue as Percentage of GDP	ecommerce_gdp	E-commerce aligns with the broad layer as a key component of digital trade and algorithmic economic activities.
	Express Delivery Volume	delivery_volume	Express delivery supports the e-commerce ecosystem, which is part of the broad layer.
	Proportion of Enterprises Engaged in E-commerce	enterprise_ecommerce	E-commerce enterprise participation is part of the broad layer, supporting the digital trade economy.
Narrow Layer	R&D Funding	rd_funding	R&D funding drives digital services, platform innovations, and advancements in the digital economy.
	Number of Computers Used per 100 Employees	computer_usage	Computer usage supports the platform economy and digital services by enabling productivity tools and platforms.

). Patents, measured by the number of patent applications of industrial enterprises, served as proxies for innovative output, capturing the tangible effects of R&D investments. The variables were sourced from the China Statistical Yearbook and the National Bureau of Statistics.

While R&D represents the input side of innovation, patents capture applied outcomes and formalized knowledge production. Although innovation is a multidimensional concept—including tangible and intangible aspects such as product design, process improvements, and organizational change—patents remain one of the most widely accepted and standardized indicators of formal innovation output, especially in large-scale, panel-based studies due to their availability, comparability, and quantifiability across regions and time [69]. They are particularly robust proxies for technological and product innovation [70], with numerous studies confirming a strong association between patent activity and innovation performance, especially in R&D-intensive sectors such as ICT [25], pharmaceuticals [27], and machinery [26]. Moreover, patent applications also capture early-stage innovation dynamics, reflecting not only R&D success but also firms’ intentions to commercialize novel technologies [71].

The final set of digital economic variables included 14 independent variables representing the core (8 indicators), narrow (2 indicators), and broad (3 indicators) digital economy layers from 2013 to 2020. To further ensure relevance and minimize redundancy in addition to the comprehensive representation of digital economic landscape, the variables selected also complied with the following three criteria: (i) prior empirical evidence linking three broader domains to regional innovation outcomes include digital infrastructure [72] (e.g., broadband penetration and fiber cable density), digital services and platforms [73] (e.g., e-commerce turnover and software industry revenue), and innovation-enabling environments [74] (e.g., R&D expenditure and digital technologies); (ii) the availability and consistency of data across provinces and years; and (iii) their ability to complement rather than duplicate other indicators in the set. Variables with conceptual overlap, poor data quality, or high multicollinearity were excluded to improve model performance and interpretability, thus balancing theoretical relevance and empirical diversity.

Principal component analysis was conducted, and Varimax rotation was not applied, as the principal components already explained the majority of the variance shown by principal component analysis, and applying such a transformation would not have significantly enhanced the variance structure or the interpretability of the components, or predictive power for this study’s objectives. The suitability test resulted in a Kaiser–Meyer–Olkin (KMO) value of 0.788, exceeding the minimum acceptable value of 0.5 suggested by Kaiser (1974) for factor analysis [75]. The KMO value indicates the proportion of variance in the variables that may be attributed to underlying factors, with higher values suggesting that factor analysis is more appropriate for the data. The result of Bartlett’s test of sphericity indicates a chi-square value of 2486.671, with a p-value of 0, suggesting that the correlation matrix significantly differs from an identity matrix and the indicators are suitable for subsequent analysis.

Missing or potentially invalid values (represented as zeros) were removed from all variables prior to model training to ensure consistency across models. Winsorization was planned as a precautionary measure to limit the influence of potential extreme values, and no significant outliers were detected using the interquartile range (IQR) method.

Furthermore, the input variables were normalized to a [0, 1] range to prepare data for deep learning models. This was performed for variables with no negative values and ensured that all variables were appropriately scaled for model training and validation, improving model performance and stability.

3.2. Spatial Relationship of Variables

To uncover spatial relationships in our data, we evaluated spatial autocorrelation for each predictor variable (X) using Moran’s I and Geary’s C. These measures assess the degree of clustering or dispersion across regions, providing insights into the spatial structure of our data. Moran’s I captures the global patterns of spatial dependence across all regions, while Geary’s C captures local spatial relationships, showing how each region’s value is related to the values of neighboring regions.

Moran’s I is calculated as follows:

$$I={\displaystyle \frac{N{\sum }_i {\sum }_j w_{ij}(X_i-\underset{\_}{X})(X_j-\underset{\_}{X})}{{\sum }_i (X_i-\underset{\_}{X}{)}^2{\sum }_i {\sum }_j w_{ij}}}$$

(1)

where $N$ denotes the number of observations; $X_i$ and $X_j$ denote the values of the variable $X$ at locations $i$ and $j$; $\underset{\_}{X}$ denotes the mean of $X$; and $w_{ij}$ denotes the spatial weight between locations $i$ and $j$, defined as 1 if regions $i$ and $j$ are neighbors, and 0 otherwise. The denominator normalizes the index by the total variance and the sum of spatial weights. Moran’s I values range from −1 to +1, where positive values near +1 indicate strong positive global spatial autocorrelation, negative values near −1 suggest strong negative autocorrelation, and values around 0 imply spatial randomness.

$$C={\displaystyle \frac{(N-1){\sum }_i {\sum }_j w_{ij}(X_i-X_j{)}^2}{2{\sum }_i (X_i-\underset{\_}{X}{)}^2{\sum }_i {\sum }_j w_{ij}}}$$

(2)

In this formula, the emphasis shifts to the squared differences between neighboring values, making Geary’s C more sensitive to local spatial variation. As with Moran’s I, $w_{ij}$ indicates spatial proximity. Geary’s C ranges from 0 to 2, with values closer to 0 indicating strong positive local spatial autocorrelation, values near 2 reflecting strong negative local autocorrelation, and values around 1 indicating spatial randomness.

To test the global spatial patterns of CO₂ emissions across Chinese provinces, we applied both Moran’s I and Geary’s C, using an adjacency matrix based on direct neighboring provinces. This matrix, which assigns a value of 1 to adjacent regions and 0 to non-adjacent regions, allowed for the analysis of overall spatial autocorrelation, with Moran’s I providing an overall measure of clustering or dispersion, and Geary’s C highlighting local variations in spatial relationships.

If significant spatial autocorrelation (p < 0.05) is detected, it prompts further testing on model residuals to ensure that spatial effects are adequately captured. If spatial dependencies remain unaddressed, spatial modeling approaches incorporating geographic features are employed. These methods allow for the explicit modeling of spatial dependencies, thereby improving the accuracy and interpretability of the findings.

This study employed two complementary spatial weighting schemes—binary and row-standardized matrices. Binary weighting assigns equal influence to all neighboring regions, capturing uniform spatial effects, while row-standardization normalizes weights by the number of neighbors, accounting for such variation in spatial structures. These methods ensure a balanced and accurate assessment of spatial dependencies, guiding necessary model adjustments.

3.3. Machine Learning Models for R&D Prediction

This study employs four machine learning models—Support Vector Machine (SVM), Extreme Learning Machine (ELM), Random Forest (RF), and Extreme Gradient Boosting (XGBoost)—to predict ESG scores in a stacked ensemble configuration. Each model was chosen for its distinct strengths in capturing complex, nonlinear relationships within the data.

SVM is effective in high-dimensional spaces, utilizing kernel functions to map data into higher dimensions [76], while ELM offers computational efficiency by randomly assigning input weights and solving output weights analytically, making it fast with minimal tuning [77]. RF builds multiple decision trees to capture interactions between features, preventing overfitting and improving generalization [78,79]. XGBoost is included for its advanced gradient boosting capabilities, using both gradient and Hessian information for faster, more accurate updates [80].

By combining these models, the ensemble leverages their individual strengths, enhancing overall prediction performance for ESG scores. Below, we provide an overview of each model and its integration into the stacking framework.

3.3.1. Support Vector Machine (SVM)

Support Vector Machine (SVM), a supervised learning algorithm, was introduced by Cortes and Vapnik [76]. The core idea behind SVM is to find a decision boundary that maximizes the margin between two classes in a high-dimensional feature space. This margin maximization allows for the separation of classes with optimal generalization. For nonlinear problems, SVM utilizes kernel functions, which implicitly map input data into higher-dimensional spaces to handle complex patterns. The decision function is given as follows:

$$f\left(x\right)=sign\left({\sum }_{i=1,j=1}^n {\alpha }_i{y}_{i}K(x_i,y_j)+b\right)$$

(3)

where $n$ denotes the number of training samples, ${\alpha }_i$ represents the learned Lagrange multipliers, $y_i$ ∈ {−1,1} represents the class labels, $K(x_i,y_j)$ denotes the kernel function measuring similarity between training sample $x_i$ and input $y_j$, and $b$ denotes the bias term.

In this study, we employ the Radial Basis Function (RBF) kernel, defined as follows:

$$K(x_i,y_j)=exp\left({\displaystyle \frac{\parallel x_i-x_j{\parallel }^2}{2{\sigma }^2}}\right)$$

(4)

where ${\displaystyle \frac{\parallel x_i-x_j{\parallel }^2}{2{\sigma }^2}}$ represents the squared Euclidean distance between samples $x_i$ and $x_j$, and $\sigma$ represents the kernel width parameter controlling the smoothness of the decision boundary.

The RBF kernel is chosen for its ability to capture complex nonlinear relationships, making it particularly useful when the relationship between input variables and the target is not strictly linear. SVM optimizes the classification boundary by minimizing the hinge loss function while enforcing margin maximization:

$$\underset{w,b}{min} {\displaystyle \frac{1}{2}}\parallel w{\parallel }^2+C{\sum }_{i=1}^n \left(\mathrm{0,1}-y_{i}f\left(x_i\right)\right)$$

(5)

where $w$ denotes the weight vector that defines the orientation of the decision boundary, $b$ denotes the bias term that shifts the boundary, $C$ > 0 denotes the regularization parameter that controls the trade-off between maximizing the margin and minimizing classification errors, and $y_{i}f\left(x_i\right)$ represents the margin for sample $i$. This ensures that the model generalizes unseen data well while maintaining robustness to noise and outliers.

The main parameters of SVM include the regularization parameter ($C$), the kernel type (RBF), and the kernel-specific parameter ($\sigma$), all of which influence the model’s flexibility, smoothness, and ability to generalize.

The hyperparameters of SVM were optimized through grid search combined with 5-fold cross-validation to enhance predictive performance and avoid overfitting. The details of the model training, tuning, and validation process are provided in Section 3.5.

3.3.2. Extreme Learning Machine (ELM)

Extreme Learning Machine (ELM), proposed by Guang-Bin Huang, is a single-layer feedforward neural network (SLFN) that differs from traditional neural networks such as backpropagation networks (BPNs) [77]. Unlike BPNs, which require iterative weight updates, ELM randomly assigns input weights and biases; then, it analytically determines the output weights, significantly reducing computational cost and training time.

In this study, we employ an SLFN architecture with the following output function:

$$f_L={\sum }_{i=1}^l{\beta }_i{h}_i\left(x\right)=h\left(x\right)\beta$$

(6)

where $h\left(x\right)$ denotes the activation function that maps inputs to the hidden layer’s feature space, and $\beta$ represents the output weight matrix. We utilize the sigmoid activation function, which is expressed as follows:

$$G(a_i,b_i,x)={\displaystyle \frac{1}{1+exp(a\cdot x+b)}}$$

(7)

where $a$ and $b$ represent the randomly assigned input weights and biases, respectively.

The key parameters of ELM include the number of hidden neurons (L), the type of activation function ($G$, sigmoid in our case), and the randomly initialized input weights ($a$) and biases ($b$). These are not tuned through iterative optimization but are instead fixed upon initialization, with only the output weights ($\beta$) learned analytically through the Moore–Penrose pseudoinverse. This simplicity eliminates the need for learning rates or backpropagation-related settings, making ELM computationally efficient.

ELM’s fast learning speed and minimal parameter tuning make it an efficient choice for our stacking ensemble framework, allowing it to capture complex relationships in the data with reduced computational overhead.

3.3.3. Random Forest (RF)

Random Forest (RF), introduced by Breiman [78,79], is an ensemble learning method that constructs multiple decision trees to reduce overfitting and enhance prediction accuracy. RF creates an ensemble of trees, where each tree is built using a subset of the training data and features. During the construction of individual decision trees, splits are determined using criteria such as the Gini index or entropy, which measure the impurity or uncertainty within a node. The Gini index for a given split is calculated as follows:

$$Gini=1-{\sum }_{i=1}^C p_i^2$$

(8)

where $p_i$ denotes the proportion of class $i$ within the node. A lower Gini index indicates that the node is more homogeneous, meaning the classes within that node are purer, which leads to better splits. After constructing individual trees, the margin function for classification in RF is used to assess the confidence of the predictions made by these trees. The margin function is defined as follows:

$$mg(X,Y)=\alpha v_{k}I\left(h_k\right(X)=Y)-\underset{j\ne Y}{max} \alpha v_{k}I\left(h_k\right(X)=j)$$

(9)

where $k$ represents the total number of trees; $\alpha v_k$ represents the weight assigned to the $k$-th tree; $I\left(h_k\left(X\right)=Y\right)$ represents the indicator function denoting whether the $k$-th tree correctly classifies the input, $X$; $h_k\left(X\right)$ represents the prediction of the $k$-th tree; and ${max}_{j\ne Y}$ represents the maximum weight of misclassifications from other classes. A larger margin value indicates better classification accuracy, reflecting higher confidence in the prediction.

The generalization error is given by the following:

$$P{E}^{*}=P_{X,Y}\left(mg\right(X,Y)<0)$$

(10)

Thus, while the Gini index influences the creation of each tree by selecting optimal splits based on node purity, the margin function aggregates the predictions of all trees in the forest, contributing to improved classification performance.

To ensure robust predictions, RF optimizes classification accuracy by utilizing majority voting in classification tasks and minimizes the Mean Squared Error (MSE) in regression tasks:

$$MSE={\displaystyle \frac{1}{n}}{\sum }_{i=1}^n (y_i-{\widehat{y}}_i{)}^2$$

(11)

where $y_i$ denotes the true value, and ${\widehat{y}}_i$ demotes the predicted output. The main parameters of RF include the number of decision trees in the ensemble (n_estimators), the maximum depth of each tree (max_depth), the minimum number of samples required to split a node (min_samples_split), the number of features considered at each split (max_features), and the criterion used for split quality (e.g., Gini index or entropy). These parameters directly influence the model’s ability to balance bias and variance. By averaging the predictions across multiple trees, RF reduces variance and improves model stability.

In this stacked ensemble, RF excels in modeling complex interactions and capturing nonlinear patterns through its diverse set of trees.

3.3.4. XGBoost

XGBoost, proposed by Chen and Guestrin [80], is a gradient boosting algorithm that builds decision trees sequentially, with each new tree being fitted to correct the errors made by the previous trees. The objective function in XGBoost combines a training loss function and a regularization term to balance model accuracy and complexity. For a given sample, $x_i$, the predicted output, ${\widehat{y}}_i$, is computed as follows:

$${\widehat{y}}_i={\sum }_{k=1}^k f_k\left(x_i\right),f_k\in F$$

(12)

where $F$ represents the set of decision trees, and $f_k\in$ represents the $k$-th tree. The objective function to be minimized at each boosting iteration is given by the following:

$$J\left(f_t\right)={\sum }_{i=1}^n L\left(y_i,{\widehat{y}}_i^{t-1}+f_t\left(x_i\right)\right)+\Omega \left(f_t\right)$$

(13)

where $L$ denotes the loss function (often squared error for regression), ${\widehat{y}}_i^{t-1}$ denotes the prediction from the previous iteration, and $\Omega \left(f_t\right)$ denotes the regularization term that controls the complexity of the trees to prevent overfitting:

$$\Omega \left(f\right)=\alpha \parallel w{\parallel }_1+{\displaystyle \frac{1}{2}} \lambda \parallel w{\parallel }_2^2$$

(14)

where $\alpha$ represents the L1 regularization coefficient, $\lambda$ represents the L2 regularization coefficient, and $w$ represents the tree weights or leaf scores.

To efficiently minimize this objective, XGBoost performs a second-order optimization using both the gradient and Hessian of the loss function. Specifically, the gradient, $g_i$, and Hessian, $h_i$, are computed as follows:

Gradient:

$$g_i={\displaystyle \frac{\partial L(y_i,{\widehat{y}}_i)}{\partial {\widehat{y}}_i}}$$

(15)

Hessian:

$$h_i={\displaystyle \frac{{\partial }^{2}L\left(y_i,{\widehat{y}}_i\right)}{\partial {\widehat{y}}_i}}$$

(16)

where $g_i$ and $h_i$ represent the first and second derivatives of the loss function with respect to the predicted output, ${\widehat{y}}_i$, respectively. These are used in the update step of the boosting algorithm to adjust the tree’s weights and minimize the objective function more efficiently. By incorporating both first- and second-order derivatives, XGBoost can make faster and more accurate updates to the trees, enhancing model performance.

The key hyperparameters of XGBoost include the learning rate (η), the maximum depth of trees, the number of estimators (trees), the subsample ratio of the training instances, the column subsample ratio per tree, the L1 ($\alpha$) and L2 ($\lambda$) regularization terms, and the minimum child weight.

XGBoost’s ability to fine-tune the construction of its trees through gradient-based optimization and regularization makes it an essential component of the stacked ensemble model.

3.4. Stacking Ensemble

To enhance the predictive power of individual models, we employ a stacked ensemble approach, combining the outputs of SVM, ELM, RF, and XGBoost. The predictions from each model are used as input features for a meta-model, which makes the final prediction. This meta-model leverages the strengths of each base learner, thereby improving the overall performance in ESG score prediction. The equation for the stacking ensemble approach can be represented as follows:

$${\widehat{y}}_i=g\left(f_1\left(x_i\right),f_2\left(x_i\right),\dots ,f_m\left(x_i\right)\right)$$

(17)

where ${\widehat{y}}_i$ denotes the final prediction made by the stacking ensemble for the $i$-th instance. The terms $\left(f_1\left(x_i\right),f_2\left(x_i\right),\dots ,f_m(x_i\right)$ represent the predictions made by the $m$ base models, which, in this case, are SVM, ELM, RF, and XGBoost. If the meta-model combines the outputs linearly, the equation can be further specified as ${\widehat{y}}_i={\sum }_{j=1}^m w_j{f}_j\left(x_i\right)$, where $w_j$ represents the weight assigned to the prediction of the $j$-th base model. The function $g$ is the meta-model that takes the outputs of these base models as input features and generates the final prediction. This formulation effectively leverages the strengths of individual base models while improving overall predictive performance through the meta-model.

The main parameters of the stacking ensemble include the choice of base models (e.g., SVM, ELM, RF, and XGBoost), the type of meta-model (e.g., linear regression, Random Forest, or neural network), and the method of combining predictions (e.g., weighted average or learned weights, $w_j$). These parameters influence the ensemble’s ability to balance bias, variance, and model complementarity.

Stacking helps reduce bias and variance, thereby improving predictive accuracy by leveraging the complementary strengths of models. By combining diverse models—such as bagging in Random Forest, which reduces variance via bootstrap aggregation, and boosting in XGBoost, which addresses bias through sequential learning—this architecture mitigates model-specific overfitting and enhances generalization by capturing complementary inductive biases across learners.

3.5. Model Training and Validation

All models were trained on a training dataset spanning from 2011 to 2020 in Python 3.10. For each model analyzed, the same methodological steps were applied and customized for the specific features of the model. Initially, the dataset was filtered to exclude rows with zero values for CO₂ emissions and any rows where independent variables contained zero values. This preprocessing step ensured that only valid data were used for model training. Next, the data were split into training (70%) and testing (30%) sets using a random partition, ensuring an appropriate representation of the data in both sets for final model evaluation.

Hyperparameter optimization was performed using a 5-fold cross-validation approach. In this method, the training dataset was divided into five subsets, and the model was trained and validated five times. Each fold served as a validation set once, with the remaining four folds used as the training set. This cross-validation process allowed for a robust evaluation of model performance across different subsets of the data. To fine-tune each individual model, GridSearchCV was employed, which tested multiple combinations of hyperparameters. The grid was searched through different values for key parameters, such as the learning rate, maximum tree depth, number of estimators, subsample rate, and column sample by tree, to identify the best configuration for optimizing predictive accuracy.

In addition to the tuned models, this study included non-tuned models with default hyperparameters as a baseline for comparison. This approach allowed us to assess whether hyperparameter optimization led to significant improvements in predictive accuracy, or if the default settings were sufficient. The comparison also highlights the trade-off between the computational cost of tuning and the potential gains in model performance.

Once the individual models were optimized, model stacking was implemented to further improve predictive performance. The stacking approach involved training multiple base models, each fine-tuned through the aforementioned hyperparameter search, and combining their predictions using a meta-model. The base models tested in this study include Random Forest, Gradient Boosting, Support Vector Machines (SVMs), and Extreme Learning Machines (ELMs), each contributing unique learning strengths. The meta-model was trained on the predictions made by the base models, including linear models, tree-based models (e.g., Random Forest and Gradient Boosting) for flexibility in capturing nonlinear relationships, and neural networks for complex pattern recognition. This study identifies the most accurate configuration. The stacked model thus leverages the strengths of each individual model while mitigating their weaknesses.

The final model, trained with the best hyperparameters found through GridSearchCV and stacking, was then evaluated using various performance metrics, including the RMSE, MAE, MAPE, SMAPE, MdAPE, and R², on both the training and testing datasets. Additionally, statistical significance was assessed through a one-sample t-test to compare the predicted values with the actual values and to determine whether there were any systematic biases. These metrics and statistical tests provided insights into the model’s accuracy, robustness, and generalization ability, ultimately identifying the most suitable configuration for predicting the target variable.

Overall, this methodology ensured a thorough examination of the model’s ability to predict CO₂ emissions across various data splits and provided insights into its stability and generalization capacity.

3.6. Testing and Performance Evaluation

After training and validation, each model was evaluated on the testing set from 2022 to assess its generalization ability. The models’ predictions were compared with actual R&D outcomes for the year 2022. To quantify model performance, several evaluation metrics were computed, including Mean Error (ME), RMSE, and R². Additionally, cross-validation diagrams were generated to visualize the consistency and accuracy of each model. These metrics helped in understanding how well each model generalized to unseen data.

The performance of the stacked model is evaluated using three error metrics: Root Mean Squared Error (RMSE) [81], Mean Absolute Error (MAE) [82], and Median Absolute Percentage Error (MdAPE) [83].

Significance tests using p-value are utilized to assess whether the predicted values generated by the machine learning models significantly differ from the actual observed target values. The null hypothesis (H₀) assumes there is no significant difference between the predicted and actual values, while the alternative hypothesis (H₁) suggests that such a difference is significant. To test this, we used a 95% confidence level (α = 0.05), where the null hypothesis would be rejected if the p-value is less than 0.05.

The trained models, including the stacked model, were then applied to predict future R&D outcomes for the estimating sub-dataset covering the period from 2023 to 2024. Predictions were made for each of the regions based on the historical data and the optimized model configurations. The forecasting ability of each model was evaluated using the same performance metrics as in the testing phase. The predicted future R&D outcomes were then compared to the actual outcomes to assess the accuracy and reliability of the models’ forecasts.

In summary, this section outlines the ML techniques frequently employed in predictive analytics. The core novelty and contribution of this study lie in their innovative application to a rarely explored linkage between regional digital economy indicators and firm-level innovation performance, as captured by patent data. Spatial dependencies are not only acknowledged but systematically evaluated as a complementary factor that informs and guides the incorporation of spatial considerations into the ML modeling workflow. This approach enhances prediction robustness by explicitly evaluating geographic interconnections and spatial clustering effects that may be fundamental to regional innovation processes.

By combining spatial analysis with ensemble machine learning, this study provides deeper, more contextually grounded insights for policymakers aiming to foster innovation in spatially interconnected regions. This uniquely conceptualized and practically implemented integration represents a significant methodological advancement and opens new avenues for applying ML to geospatial innovation and regional development challenges.

4. Results

4.1. Spatial Correlation Analysis

Spatial autocorrelation in key variables was assessed using Geary’s C and Moran’s I indices, with results for both binary and row-standardized results displayed in Appendix A (

Table A1. Moran’s I and Geary’s for patents and digital economic predictors over 2011–2020. “Proportion Significant” represents the fraction of years in which the variable showed significant spatial autocorrelation (p < 0.05). It is calculated as (significant years/total years).

Variable	Weight Type	Moran’s Mean	Moran’s p-Value	Moran’s Significant Years	Moran’s Total Years	Moran’s Proportion Significant	Geary’s Mean	Geary’s p-Value	Geary’s Significant Years	Geary’s Total Years	Geary’s Proportion Significant
access_ports	Binary	0.211909	2.70 × 10−2	8	8	1	0.792435	0.103647	1	8	0.125
access_ports	Row-standardized	0.095211	1.73 × 10−1	0	8	0	0.943141	0.348676	0	8	0
broadband_users	Binary	0.226952	2.26 × 10−2	8	8	1	0.778581	0.093397	1	8	0.125
broadband_users	Row-standardized	0.106632	1.57 × 10−1	0	8	0	0.934157	0.330132	0	8	0
computer_usage	Binary	0.127828	7.62 × 10−2	0	8	0	0.566018	0.028701	8	8	1
computer_usage	Row-standardized	0.141443	7.30 × 10−2	1	8	0.125	0.695284	0.028113	8	8	1
delivery_volume	Binary	0.105563	1.09 × 10−1	0	8	0	0.752825	0.157597	0	8	0
delivery_volume	Row-standardized	0.072743	1.93 × 10−1	0	8	0	1.016883	0.537215	0	8	0
domain_count	Binary	0.017021	3.54 × 10−1	0	8	0	0.788724	0.213897	1	8	0.125
domain_count	Row-standardized	−0.03557	5.12 × 10−1	0	8	0	0.975974	0.446764	0	8	0
ecommerce_gdp	Binary	0.064524	2.05 × 10−1	1	8	0.125	0.590345	0.048219	5	8	0.625
ecommerce_gdp	Row-standardized	0.079589	1.93 × 10−1	1	8	0.125	0.755151	0.078031	2	8	0.25
enterprise_ecommerce	Binary	0.227441	4.68 × 10−2	5	8	0.625	0.564358	0.020763	6	8	0.75
enterprise_ecommerce	Row-standardized	0.264951	4.86 × 10−2	5	8	0.625	0.640183	0.027061	6	8	0.75
fiber_cable_density	Binary	0.315709	1.11 × 10−5	8	8	1	0.339695	0.019099	8	8	1
fiber_cable_density	Row-standardized	0.385109	5.96 × 10−7	8	8	1	0.435242	0.00133	8	8	1
ipv4_count	Binary	0.085914	1.93 × 10−1	2	8	0.25	0.635364	0.095414	2	8	0.25
ipv4_count	Row-standardized	0.043446	3.34 × 10−1	2	8	0.25	0.885228	0.260824	0	8	0
it_service_gdp	Binary	0.096039	1.50 × 10−1	3	8	0.375	0.619787	0.066267	3	8	0.375
it_service_gdp	Row-standardized	0.141866	1.23 × 10−1	3	8	0.375	0.722599	0.072284	4	8	0.5
mobile_base_density	Binary	0.222615	4.16 × 10−3	8	8	1	0.41174	0.017976	8	8	1
mobile_base_density	Row-standardized	0.280395	1.11 × 10−3	8	8	1	0.532612	0.003765	8	8	1
patents	Binary	0.217555	2.51 × 10−2	7	8	0.875	0.736945	0.136887	1	8	0.125
patents	Row-standardized	0.141918	1.06 × 10−1	3	8	0.375	0.974252	0.445514	0	8	0
rd_funding	Binary	0.27263	5.11 × 10−3	8	8	1	0.744202	0.104182	0	8	0
rd_funding	Row-standardized	0.199609	3.31 × 10−2	8	8	1	0.869696	0.196437	0	8	0
telecom_gdp	Binary	0.412085	9.78 × 10−4	8	8	1	0.512501	0.002287	8	8	1
telecom_gdp	Row-standardized	0.417459	1.41 × 10−3	8	8	1	0.532877	0.00165	8	8	1

). The small mean Geary’s C values suggest weak local spatial autocorrelation for the variables, indicating that the spatial relationships are more globally distributed or less pronounced at local scales, as compared to the Moran’s I index, which captures more generalized spatial patterns.

Meanwhile, three of the digital economy indicators showed significant spatial autocorrelation Moran’s I indices, which reflect broader spatial trends in economic and demographic factors, with proportions significant across all years and consistent patterns across time and correlation indicated at both the binary and row-standardized levels. Based on row standard weight types, Digi_Econ and Tele_Bus show moderate positive spatial autocorrelation (Moran’s I = 0.3851 and 0.4175, respectively), population shows moderate positive spatial autocorrelation (Moran’s I = 0.2804), and R_D_Fund only shows a mild tendency for neighboring locations to have similar values (Moran’s I = 0.19960922).

Figure 2 illustrates the significance, degree of Moran’s I, and its temporal trends for each variable over the years, with higher values indicating stronger positive spatial autocorrelation. Over time, Moran’s I values revealed a general decline in the spatial autocorrelation of patents, suggesting a growing negative spatial autocorrelation. This indicates that regions with high values are increasingly located near regions with low values, reflecting a reduction in global spatial dependence. Conversely, an increasing trend in global spatial clustering was observed for fiber_cable_density, while it_service_gdp showed a consistent upward trend, with Moran’s I becoming significant around 2018. Telecom_gdp demonstrated a sharp increase in spatial autocorrelation from 2017, indicating stronger regional clustering since that time. In contrast, rd_funding and mobile_base_density remained relatively stable, with little change in their spatial patterns. This shift in Moran’s I values highlights the evolving spatial dynamics of technological and economic indicators over the years, suggesting a changing landscape of regional interdependence and spatial distribution.

Given that only four out of the fourteen variables exhibit statistically significant but weak-to-moderate spatial dependencies, incorporating spatial features into the machine learning model is deemed unnecessary. The limited presence and strength of spatial autocorrelation suggest that spatial relationships are not pervasive enough across the dataset to meaningfully improve predictive performance. Including spatial variables with weak or noisy signals can therefore increase model complexity or reduce predictive accuracy, particularly if the spatial patterns are not strongly associated with the target outcome. This is particularly relevant for models such as SVM, which are sensitive to weak or irrelevant features in high-dimensional settings; ELM, which is prone to overfitting when exposed to noisy inputs; and even tree-based methods such as XGBoost and RF, where excessive weak spatial variables can unnecessarily increase model complexity.

Therefore, after evaluating spatial correlations, this study omits spatial dimensions in the modeling process to maintain simplicity and robustness without compromising predictive accuracy, while using spatial insights in parallel with model outputs to inform decision making.

4.2. Machine Learning Outcomes

4.2.1. Model Parameters

The full hyperparameter configurations are provided in

Table A2. Machine learning model parameters.

Model	Tuning Applied	Base Models	Meta-Learner	Hyperparameters (Tuned/Applied)
XGBoost	Default	N/A	N/A	n_estimators = 100, max_depth = 6, learning_rate = 0.1, subsample = 1, colsample_bytree = 1, objective = ‘reg:squarederror’
Random Forest	Default	N/A	N/A	n_estimators = 100, max_depth = 6, random_state = 42
SVM	Tuned	N/A	N/A	Kernel = ‘rbf’; GridSearchCV tuning for C, gamma
Meta-Model (XGBoost)	Tuned	N/A	N/A	GridSearchCV tuning for learning_rate, n_estimators, max_depth, subsample, colsample_bytree
Stacked Model (Full Ensemble)	N/A	XGBoost, RF, SVM, ELM	XGBoost	XGBoost: objective = ‘reg:squarederror’, n_estimators = 100, max_depth = 6RF: n_estimators = 100, max_depth = 6, random_state = 42SVM: kernel = ‘rbf’ELM: n_hidden = 1000
Stacked Model (RF + XGBoost)	N/A	XGBoost, RF	Linear Regression	XGBoost: booster = ‘gbtree’, learning_rate = 0.2, n_estimators = 300, max_depth = 6, subsample = 0.8, colsample_bytree = 1.0, objective = ‘reg:squarederror’RF: n_estimators = 300, max_depth = 6, min_samples_split = 2, min_samples_leaf = 1, random_state = 42

in Appendix A. The ELM model, a single-hidden-layer neural network, was configured with 30 hidden nodes—determined through trial and error—and used the sigmoid function as the feature mapping function. Other parameters remained at default values. RF was implemented with 20 trees, and the model was set to perform regression with feature split points selected based on curvature. The SVM model utilized a linear kernel, and default settings were applied to remaining parameters. XGBoost was implemented using the gbtree booster, with core parameters including a learning rate of 0.1 and 500 boosting iterations, and parallel tree construction was set to 1 to control convergence behavior.

Two ensemble architectures were tested. The first ensemble, stacked model (full ensemble), combined predictions from XGBoost, RF, SVM, and ELM using XGBoost as the meta-learner. XGBoost was chosen given its ability to model complex interactions by capturing nonlinear relationships, handling multicollinearity through its gradient boosting framework, and weighting heterogeneous base learner outputs, thus outperforming simpler meta-learners, such as linear regression and shallow neural networks. The second ensemble, stacked model (RF + XGBoost), used RF and XGBoost predictions combined via a linear regression meta-learner to assess whether a simpler meta-learner could provide competitive accuracy.

4.2.2. Empirical Prediction Results

Based on

Table 2. Performance metrics of base and stacked models.

Model	Sample Size	RMSE	MAE	MdAPE (%)	R2	t-Value	p-Value
Random Forest—Training	136	0.0194	0.01	10.28	0.9838	0.3392	0.735
Random Forest—Testing	59	0.0449	0.0212	18.9	0.9309	0.1251	0.9008
XGBoost—Training	136	0.0006	0.0004	0.56	1	0	1
XGBoost—Testing	59	0.0253	0.0136	16.84	0.978	0.6143	0.5414
SVM—Training	136	0.0088	0.0076	12.3	0.9966	0.0574	0.9543
SVM—Testing	59	0.0381	0.0223	36.01	0.9501	0.1805	0.8574
ELM—Training	136	0.0249	0.0194	33.42	0.9683	−0.0002	0.9999
ELM—Testing	59	0.0304	0.0214	39.56	0.973	−0.2136	0.8316
XGBoost—Training (CV)	136	0.0005	0.0004	0.64	1	−0.0008	0.9994
XGBoost—Testing (CV)	59	0.0297	0.0151	17.65	0.9698	−0.1971	0.8444
XGBoost-RF Stacked Model—Training	136	0.0127	0.0067	5.41	0.993	0.4404	0.6603
XGBoost-RF Stacked Model—Testing	59	0.0247	0.0137	17.62	0.9791	0.0171	0.9864
4-Model Stacked—Training	136	0.0007	0.0005	0.6538	1	0	1
4-Model Stacked—Testing	59	0.0299	0.0146	18.7018	0.9694	1.5252	0.1327

, all four machine learning models achieved high predictive performance on the testing set, with R² values exceeding 0.93. While the RMSE, MAE, and MdAPE values varied across models, they consistently remained low, indicating robust accuracy and generalization capability. Statistical significance was assessed using t-tests to determine whether the predicted values significantly differed from the actual observed target values. For all models tested, the p-values were greater than the 0.05 significance threshold, suggesting that the null hypothesis (no significant difference between predicted and actual values) could not be rejected, indicating no systematic bias in the predictions.

Among the evaluated models, the stacked ensemble combining XGBoost and Random Forest demonstrated the best overall predictive performance on the testing dataset. This model achieved the lowest RMSE (0.0247) and MAE (0.0137), alongside a high R² value of 0.9791, indicating strong predictive accuracy and a close fit to the observed values. It also maintained a relatively low MdAPE of 17.62%, highlighting the stability of its predictions.

While the standalone XGBoost model also performed well, with an RMSE of 0.0253, MAE of 0.0136, R² of 0.978, and MdAPE of 16.84%, the stacked XGBoost-RF ensemble slightly outperformed it across most metrics. This improvement aligns with the theoretical advantage of stacking, which integrates complementary models to reduce bias and variance and thereby generalization error through the aggregation of diverse inductive biases using a meta-learning framework. In contrast, models such as SVM and ELM, despite achieving high R² values (0.9501 and 0.973, respectively), exhibited higher error magnitudes, particularly in MdAPE, suggesting lower consistency in prediction accuracy.

The fully stacked model incorporating all base learners (XGBoost, Random Forest, SVM, and ELM) also showed reasonably good performance (RMSE = 0.0299, MAE = 0.0146, R² = 0.9694, and MdAPE = 18.70%), but it did not surpass the more targeted XGBoost-RF ensemble.

These results are further illustrated in Figure 3, which provides a normalized visual comparison across models based on R² (inverted), RMSE, MAE, and MdAPE. For consistency in interpretation, all metrics were scaled to a [0, 1] range using min–max normalization, where lower values indicate better performance. Since higher R² values represent a better fit, the normalized R² values were inverted (1 − normalized R²) to align directionally with the error metrics. The XGBoost-RF stacked model achieved the lowest average normalized score across all metrics, reinforcing its selection as the most suitable model for predictive modeling in this study due to its optimal balance of accuracy and generalization for unseen data.

The line charts (Figure 4) display the actual values and predicted values of ELM, RF, SVM, and XGBoost models for both the training and testing datasets over the entire period of 2013 to 2021.

5. Discussion

For regional governments, the ability to predict patent outputs based on digital economy indicators is an essential tool for informed decision making. This study aimed to investigate the intricate relationships between regional digital economy indicators and the innovation performance of firms, as measured by patent output, within the context of China’s evolving innovation landscape. A novel hybrid approach—combining spatial autocorrelation analysis alongside machine learning modeling—enhances the robustness and contextual relevance of these predictions. This study’s models—backed by strong predictive accuracy—allow policymakers to forecast innovation trends and identify regions where digital economy investments, such as expanding broadband networks or FinTech infrastructure, are likely to produce the greatest impact. These models can inform targeted policies that foster R&D, attract talent, and boost collaboration among firms in emerging innovation clusters.

The robust performance of the models across China’s provinces demonstrates their strong potential for broad applicability in forecasting regional innovation trends. Importantly, the framework’s flexibility allows for tailored adaptation to provinces with the varying levels of digital infrastructure and innovation development. By incorporating region-specific digital economy indicators or fine-tuning model parameters, the models not only offer a generalizable forecasting tool but also support customized policy design across diverse regional contexts. This tailored transferability is critical for ensuring that even provinces with lower baseline digital development can benefit from data-driven insights, enabling targeted strategies to foster digital infrastructure growth and innovation capacity.

The spatial correlation analysis provides valuable insights into the regional dynamics of digital economy and innovation outcomes, particularly with respect to patent production. Only 4 out of the 14 key variables (Digi_Econ, Tele_Bus, Population, and R_D_Fund) exhibited significant spatial autocorrelation, and even these relationships were relatively weak to moderate. This indicates that the majority of digital economy and innovation indicators do not show strong spatial clustering, reducing the necessity for spatial modeling.

The Moran’s I index for patents showed a general decline over time, suggesting increasing spatial heterogeneity in innovation output. High-performing regions are less likely to be geographically clustered with other high performers, pointing to the decentralization of innovation activity. For policymakers, this decentralization highlights the importance of fostering innovation beyond the well-established hubs. Localized initiatives and policies that promote regional innovation can help ensure that even geographically distant areas can compete in the innovation landscape.

While the overall spatial autocorrelation for digital economy indicators remained weak, certain variables, such as telecom infrastructure (fiber cable density) and IT service GDP, exhibited stronger spatial clustering trends. This indicates emerging spatial clustering trends in technological infrastructure and services, possibly reflecting regional specialization or targeted investments. These regions may attract investments in infrastructure, fostering innovation ecosystems that encourage knowledge spillovers and collaboration. For regional governments, these emerging clusters offer an opportunity to target investments and policies that support local technological development. By identifying regions with growing tech infrastructures, policymakers can facilitate the development of specialized digital ecosystems that are likely to drive regional patent output and innovation.

Traditional R&D inputs, such as R&D funding and mobile base station density, showed stable spatial patterns over time, indicating that these factors are less influenced by geographical proximity and more shaped by institutional or policy-driven decisions. This finding suggests that, while R&D investment might not be directly dependent on regional clustering, it is still crucial to maintain a stable flow of funding and infrastructure development across regions. Policymakers can use this insight to ensure that the regions with established R&D frameworks continue to receive the necessary support, fostering sustained growth in innovation and maintaining regional competitive advantage. In this context, this study’s predictive models can help assess areas where investment in traditional R&D is necessary to maintain innovation momentum.

Given that the spatial relationships between innovation outputs and the digital economy indicators are not strongly spatially dependent across most regions, regional governments can still rely on the general predictive power of the digital economy indices—such as ICT infrastructure, FinTech development, and R&D investment—to forecast regional patent outcomes. The absence of significant spatial autocorrelation suggests that machine learning models, such as those developed in this study, can be applied across various regions without the need for complex spatial modeling. These models can predict patent activity based on digital economy metrics, offering regional policymakers a tool to assess and monitor innovation potential in their areas.

Furthermore, this study integrates insights from the FinTech sector, which has become a key enabler of innovation financing. The literature emphasized that FinTech reduces financing barriers by addressing information asymmetry and improving access to capital, particularly for SMEs. The empirical results validate this by showing that the synergy between the digital economy and FinTech plays a pivotal role in driving R&D investment and, ultimately, innovation output. Our models demonstrate that digital economy metrics, such as ICT infrastructure and FinTech development, can effectively predict patent activity, which has traditionally been a measure of R&D output and technological progress.

In terms of model performance, this study’s results align with and extend the existing work on machine learning applications in innovation forecasting. While all four models (RF, SVM, ELM, and XGBoost) showed high predictive accuracy, the ensemble model combining XGBoost and Random Forest exhibited the best performance. This finding echoes the growing recognition in the literature that hybrid models, which combine the strengths of different machine learning algorithms, are particularly well suited for forecasting in complex, multidimensional domains such as regional innovation. The ensemble approach, by leveraging the complementary strengths of both XGBoost and Random Forest, yielded the most stable and accurate predictions, supporting the growing consensus in the literature that hybrid models are particularly effective in forecasting complex, multidimensional phenomena such as regional innovation.

The success of the stacked XGBoost-RF ensemble also has important implications for the broader understanding of the dynamics between digital economy, FinTech, and innovation. As the literature suggests, the digital economy fosters innovation ecosystems by reducing barriers to collaboration and enabling real-time data sharing, thus facilitating knowledge spillovers and collaborative innovation [2,35,65]. Our findings suggest that these digital transformations are measurable and predictable, thus allowing for a more precise identification of regions where R&D efforts are likely to thrive. Consequently, policymakers can use digital economy indicators to strategically direct resources and interventions aimed at boosting innovation and enhancing competitive advantage. Moreover, the results demonstrate that the predictive models can be generalized across China’s provinces, with high R² values indicating the robustness of the approach. This aligns with the objective of this study, which was to develop a methodology for forecasting regional innovation trends using digital economy indices. The models can be an essential tool for regional policymakers aiming to enhance the digital economic environment. By leveraging these models, policymakers can identify regions with emerging digital economy potential or areas where digital infrastructure and R&D investments may be lagging. The models provide insights into where digital economy indicators—such as ICT infrastructure, FinTech development, and innovation activities—are most likely to boost regional innovation [65]. This allows regional authorities to tailor policies that foster digital ecosystem growth, attract investment in R&D, and improve the overall competitiveness of local industries, ensuring that digital transformation is maximized for sustainable economic growth.

In conclusion, this study confirms the critical role of the digital economy in enhancing corporate R&D and innovation, and it introduces a novel and effective predictive framework that integrates machine learning with regional digital economic indicators. These findings contribute to a deeper understanding of the synergies between digitalization, financial technology, and innovation, offering a roadmap for future research and practical policy implementation. By leveraging digital economy indices to predict patent output, this study provides a powerful tool for fostering innovation in China and potentially other emerging economies navigating the complexities of digital transformation and innovation policy.