An extended redundancy analysis and its applications to two practical examples

An extension of redundancy analysis is proposed that allows analyzing a variety of directional relationships among multiple sets of variables. The proposed method subsumes an existing redundancy analysis method as a special case. It is also extended further to analyze more complex relationships among variables such as direct effects of observed exogenous variables, higher-order components and multi-sample comparisons. An alternating least-squares algorithm is developed for parameter estimation. A small simulation study is conducted to investigate the performance of the proposed method. Two real examples are given to illustrate the empirical use of the proposed method.