Variable Selection Using Principal Component and Procrustes Analyses and its Application in Educational Data

Principal component analysis (PCA) is a dimension-reducing technique that replaces variables in a multivariate data set by a smaller number of derived variables. Dimension reduction is often undertaken to help in describing the data set, but as each principal component usually involves all the original variables, interpretation of a PCA result can still be difficult. One way to overcome this difficulty is to select a subset of the original variables and use this subset to approximate the data. On the other hand, procrustes analysis (PA) as a measure of similarity can also be used to assess the efficiency of the variable selection methods in extracting representative variables. In this paper we evaluate the efficiency of four different methods, namely B2, B4, PCA-PA, and PA methods. We apply the methods in assessing the academic records of first year students which include fourteen subjects.