Novel approach to choosing principal components number in logistic regression

The confirmed approach to choosing the number of principal components for prediction models includes exploring the contribution of each principal component to the total variance of the target variable. A combination of possible important principal components can be chosen to explain a big part of the variance in the target. Sometimes several combinations of principal components should be explored to achieve the highest accuracy in classification. This research proposes a novel automatic way of deciding how many principal components should be retained to improve classification accuracy. We do that by combining principal components with the ANOVA selection. To improve the accuracy resulting from our automatic approach, we use the bootstrap procedure for model selection. We call this procedure the Bootstrapped-ANOVA PCA selection. Our results suggest that this procedure can automate the principal components selection and improve the accuracy of classification models, in our example, the logistic regression.