Assessment of Linear Dependencies in Multivariate Data

A procedure to identify the linear dependency structure in multivariate data is presented. The linear dependency analysis (LDA) provides a method for assessing the number of dependencies using the eigenvalues of the sample correlation matrix. The dependency structure is then identified from the right singular vectors from a singular value decomposition of the centered and scaled data matrix. An algorithm to identify competing dependencies is given along with procedures for estimating and testing the dependency coefficients. Example data sets from regression, factor analysis, discriminant analysis, and principal component analysis are analyzed.