Sparse principal component regression with adaptive loading
This incremental improvement addresses the problem of PCR ignoring the response variable during component selection, primarily for statisticians and data analysts in regression modeling.
The authors tackled the limitation of principal component regression (PCR) by proposing a one-stage sparse PCR (SPCR) method that adaptively obtains sparse loadings related to the response variable and selects the number of components simultaneously, demonstrating its effectiveness through simulations and real data analyses.
Principal component regression (PCR) is a two-stage procedure that selects some principal components and then constructs a regression model regarding them as new explanatory variables. Note that the principal components are obtained from only explanatory variables and not considered with the response variable. To address this problem, we propose the sparse principal component regression (SPCR) that is a one-stage procedure for PCR. SPCR enables us to adaptively obtain sparse principal component loadings that are related to the response variable and select the number of principal components simultaneously. SPCR can be obtained by the convex optimization problem for each of parameters with the coordinate descent algorithm. Monte Carlo simulations and real data analyses are performed to illustrate the effectiveness of SPCR.