A variable selection method in principal canonical correlation analysis

We propose a variable selection procedure for the canonical correlation analysis (CCA) between two sets of principal components. We attempt to create predictive models for selecting such variables by combining principal component analysis (PCA) and CCA, and we refer to them collectively as principal canonical correlation analysis (PCCA). We derive a model selection criterion of one set of principal components, based on the selection of a covariance structure analysis within the framework of the PCCA. Compared to the variable selection procedure used in the CCA, the procedure used in the PCCA return a smaller number of variables. This is because the principal components derived from a PCA descend in order of the amount of information that they contain. The principal components with the smallest variance contributions are disregarded because their information contribution becomes negligible. Herein, we demonstrate the effectiveness of this criterion by using an example. Moreover, we investigate the properties of a variable selection criterion using the bootstrap resampling. The variable selection procedure used with the PCCA is compared to that used for the CCA.