Extended Redundancy Analysis (ERA) has recently been developed and widely applied to investigate component regression models. In this paper, we propose Copula-based Redundancy Analysis (CRA) to improve the performance of regression-based ERA. Our simulation results indicate that CRA is significantly superior to the regression-based ERA. We also discuss how to modify CRA to accommodate models with discrete, censored, truncated outcome variables, or a combination thereof, where ERA cannot be employed. For applications, we provide two empirical analyses: one on academic achievement and one on drug use and health.
Keywords: Component regression; copula; extended redundancy analysis.