Regression analysis on high-dimensional, block diagonal structure data with focus on latent variables

This study aims to improve the prediction accuracy for high-dimensional, small-sample-size data in a regression analysis. When using such data, scholars suggest the use of the cluster representative lasso that combines a cluster analysis and lasso, particularly when the covariance matrix has a block diagonal structure. In this study, we propose a new technique, called the graphical principal component lasso with focus on the block diagonal structure of the covariance matrix and latent variables. From the simulation results, we conclude that the proposed method is superior to the adaptive lasso, cluster representative lasso and principal component regression in terms of prediction accuracy for high-dimensional, small-sample-size data.