Suppose that data on (X, Y) are collected from C independent but closely related populations and one is interested in measuring the amount of relationship between sets of variables Y and X within each population. Goria and Flury (1996) argued that in these situations it is more meaningful to construct common canonical variates that are identical across populations, while the canonical correlations themselves may vary across populations. Their method of constructing common canonical variates is based on classical normal theory and is more suitable for measuring only linear relationships. This article constructs common information canonical variates using a recently developed method of Yin (2004) based on Kullback-Leibler information. Furthermore, a sequential permutation test is developed to determine the necessary number of common information canonical variates in practice. The proposed method does not require specific distributional assumptions and is useful in measuring true relations, whether linear or nonlinear. Through simulations and real dataset examples we illustrate our method and contrast our findings, in some instances, with those of Goria and Flury (1996).
Common Canonical variates for Independent Groups Using Information Theory