Canonical Causal Analysis Between Multivariate Continuous Treatments and Outcomes

Canonical correlation analysis (CCA) is a powerful technique for assessing the relationship between two sets of variables. However, classical CCA does not distinguish between treatment and outcome variables, and it fails to account for potential confounding effects that may bias the estimated results. This study proposes a novel method called canonical causal analysis (Causal-CCA) that extends CCA to estimate the canonical causal effects between multivariate continuous treatments and outcomes while adjusting for confounding variables. Causal effects are estimated within a framework where treatments and outcomes are prespecified. The proposed approach uses Gram–Schmidt orthogonalization and entropy balancing weights for multivariate treatments (EBMT) to extract unconfounded canonical causal variates and compute the canonical causal effects. Extensive simulations across various scenarios demonstrate that Causal-CCA consistently outperforms classical CCA, weighted CCA with multivariate generalized propensity score weighting (MVGPS) and CCA with EBMT in terms of bias and mean squared error. The proposed method is applied to a real-world dataset to study the causal relationship between psychological factors (self-concept and motivation) and academic achievement (math and science scores), showing a significant positive causal effect of the psychological variables on academic performance.