Variable selection in multivariate methods using global score estimation

A variable selection method using global score estimation is proposed, which is applicable as a selection criterion in any multivariate method without external variables such as principal component analysis, factor analysis and correspondence analysis. This method selects a subset of variables by which we approximate the original global scores as much as possible in the context of least squares, where the global scores, e.g. principal component scores, factor scores and individual scores, are computed based on the selected variables. Global scores are usually orthogonal. Therefore, the estimated global scores should be restricted to being mutually orthogonal. According to how to satisfy that restriction, we propose three computational steps to estimate the scores. Example data is analyzed to demonstrate the performance and usefulness of the proposed method, in which the proposed algorithm is evaluated and the results obtained using four cost-saving selection procedures are compared. This example shows that combining these steps and procedures yields more accurate results quickly.