## 3 Materials and Methods
### Data Analysis
#### 3.4.2 The Use of Machine Learning Instruments to Assess Drivers of GAI Use  
We begin by establishing the direction of the relationship between USE and the explanatory variables using Spearman correlations, and by estimating the model presented in Figure 1 using linear regression. These analyses allow us to empirically verify whether the direction and significance of the relationships proposed in Section 2 are supported. Additionally, linear regression serves as a benchmark for assessing the ability of ML methods to fit the proposed model.  
Subsequently, to address RO1, we fit a DTR and its generalizations, RF and XGBoost, using the full sample. Model fit was assessed using the coefficient of determination (R\({}^{2}\)), root mean squared error (RMSE), and mean absolute error (MAE). Although RF [24] and XGBoost [25] are expected to yield substantially higher R\({}^{2}\) values, DTR provides a clear visual representation of how threshold values for explanatory variables direct observations toward lower-level nodes. For instance, if a node splits under the condition X < Xa, leading to nodes associated with lower usage, the relationship between USE and X is interpreted as increasing. Conversely, if the condition is X > Xa, USE is considered to decrease with X. Surrogate splits will also be of interest, as they help infer the sign of the relationship for explanatory variables that are not primary split criteria, but may act as substitutes. In this step, we also conducted a preliminary analysis of the predictive performance of the machine learning methods and linear regression using a holdout validation test. Evaluating predictive power is essential for theory development and validation as well as for selecting models to support decision-making in management and policy [76]. The evaluation was based on three performance metrics: Stone-Geisser's Q\({}^{2}\), root mean squared error (RMSE), and mean absolute error (MAE), and randomly splitting the sample into 80% training and 20% testing sets. This approach provides an initial comparison of the out-of-sample predictive capabilities of each method.  
Third, to develop RO2, we first conduct a deeper comparison than in RO1 of the predictive capacities of the three tree-based methods by using Monte Carlo cross-validation. The performance of methods was again assessed using Stone-Geisser's Q\({}^{2}\), RMSE, and MAE. To test the significance of the differences among the methods, an ANOVA was conducted to examine the homogeneity of the RMSE and MAE across the three models. For pairwise comparisons, paired-sample Student's \(t\)-tests were applied with [PERSON]'s adjustment for \(p\)-values. A total of 500 simulations were conducted by randomly splitting the sample into 80% training and 20% testing sets. Finally, we determined the explanatory importance of each variable using the SHAP method [31], applied to the ML method with the highest predictive performance.  
All analyses were conducted in R 4.5.0 using various libraries. The _rpart_ and _rpart.plot_ packages were used to fit and visualize the decision tree. The _randomForest_ library was used for RF and _xgboost_ for the XGBoost model. Monte Carlo cross-validation was implemented using the _caret_, _dplyr_, and _tibble_ packages. Finally, SHAP analysis was performed using the _iml_ package.