## 2 Materials and Methods
### Construction of Indicator System
The adaptive LASSO algorithm has become an ideal choice because of its breakthroughs in high-dimensional data dimensionality reduction, variable importance differentiation, and \"oracle nature\" at the theoretical level. This method assigns weights inversely proportional to the initial estimate to the regression coefficient, imposes a small penalty on important variables to retain their influence, and increases the penalty on minor variables to make their coefficients approach 0. This method can not only solve the problem of misdeletion of important variables caused by the equal penalty of all variables in the traditional LASSO but also achieve consistency in variable selection and asymptotic normality of coefficient estimation in high-dimensional scenarios. Adaptive LASSO has achieved theoretical breakthroughs in variable selection and coefficient estimation by differentiating penalty weights, which is particularly suitable for scenarios with high-dimensional data, severe multicollinearity, and significant differences in importance between variables. In this study of the competitiveness of French-speaking African countries, this method can not only screen out the core driving factors but also quantify the contribution of each factor, providing an accurate basis for policymaking. The adaptive LASSO algorithm has been widely used in many fields, such as economics, biomedicine, and environmental science, due to its advantages in variable selection and coefficient estimation [52; 53; 54]. Assume that the comprehensive competitiveness index of African French-speaking countries is N, and the above 30 indicators are used as independent variables X1-X30 to construct a linear regression model:  
\[\mathrm{N}=\alpha+\sum_{\mathrm{j}=1}^{30}\beta_{\mathrm{j}}X_{\mathrm{j}}+\varepsilon\]  
Among them, \(\alpha\) is the intercept term, \(\beta_{\mathrm{j}}\) is the regression coefficient corresponding to the independent variable, and \(\varepsilon\) is the random error term. When applying the adaptive LASSO algorithm, variable selection is achieved by adding different weights to each regression coefficient. The weight is calculated as (usually 1), where the coefficient estimate is obtained by some initial estimation method (such as ordinary least squares). In the actual calculation process, the adaptive LASSO algorithm is implemented using the glmnet package in the R language or the sklearn_linear_model module in Python 3.12.6. First, the data are sorted and input according to the above model format, and then the model is trained and fitted by setting a series of penalty parameter values. As it gradually increases, the algorithm will adjust the regression coefficient according to the importance of the variable so that the coefficients of some variables that have less impact on competitiveness gradually approach 0, thereby achieving the purpose of variable screening. The choice of regularization parameters is the core issue of balancing the model's fitting ability and generalization ability. Through the principle of bias-variance trade-off, find the \(\lambda\) that minimizes the test error, that is, the point where the sum of the bias and the variance is the smallest. The implementation steps are to use the cross-validation method to divide the data set into a training set and a validation set and evaluate the generalization ability of different \(\lambda\)s through the validation set error, that is, randomly divide the 26 African French-speaking countries into 10 subsets, each time using 9 subsets for training and 1 subset for validation. In this process, the Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC) are used for calculation. The smaller the AIC/BIC value, the better the model, so as to find the \(\lambda\) corresponding to the minimum value. The adaptive LASSO algorithm is used to screen variables in the above model. In the algorithm, more accurate variable selection is achieved by adding different weights to each regression coefficient.