Comparison of prediction- and correlation-based methods to select the best subset of principal components for principal component regression and detect outlying objects

In the present work the use of prediction and correlation criteria for the best subset selection of principal components for principal component regression is compared. Results for both methodologies are similar, and always equal to or better than those obtained by using top-down principal component regression, In this comparison, the prediction criterion is based on the use of leverage-corrected residuals. In addition, the plot of leave-one-out cross-validated residuals vs, leverage-corrected residuals for the selected model is also proposed as a new graphic tool to detect possible outliers, In a test of the different methodologies, three different data sets have been studied.