On the use of conventional and statistical-learning techniques for the analysis of PISA results in Spain

A simple and general feature extraction procedure is presented which provides robust nonparametric estimates on the statistical relevance of data features, by computing the confidence intervals for the model weights in the case of linear models, and for the change in the error rate when removing each feature in the case of nonlinear models. The method performance is specially scrutinized for the prediction of the 2009 PISA scores of the Spanish students. We compare the ability of logistic regression, Fisher linear discriminant analysis, and Support Vector Machine (SVM, both with linear and with nonlinear kernel), to classify top performers in the mathematics exam. All the methods yield similar accuracy, with linear and nonlinear SVM providing improved feature reduction capabilities, at the expense of computational complexity. The results show relevant relationships of the success rate with regional variables, computer availability, gender, immigration status, learning strategies, and some others. The proposed feature selection procedure for machine learning classification can be readily used in other fields, and it can be improved with further theoretical and probabilistic development.