Development of a canonical correlation model involving non linearity and asymmetric variables

The classical canonical correlation analysis (CCA) can characterize, but is limited to, symmetric and linear associations. This study formulated a new model which generalized CCA to non linear associations and asymmetric distributions. Special cases of the proposed model were discussed. The behavior of canonical solutions under varying mixtures of skewness and non linearity (NL) was also examined in a simulation study. In addition, these solutions were compared with some commonly used methods of Hotelling, Spearman, and Kendall. Our empirical findings showed, among others, that for a fixed level of NL, the canonical correlation (ρ) increases as skewness increases. By and large, whether by ρ, likelihood, Akaike information criterion and Bayesian information criterion, the proposed method performed better than the other methods in all degrees of skewness and NL considered. This was further confirmed with real-life data application as Hotelling, Spearman, and Kendall overestimated ρ by 2.08%, 37.81%, and 22.15%, respectively, compared to the proposed technique.