Understanding Influence In Multivariate Regression

Multivariate regression influence measures contain a dimension of synergistic interaction not present in univariate regression. This is primarily due to the covariance structure among the multiple dependent variables. Even considering only single cases, the influence can be decomposed into a leverage component and a residual component. This residual term can be further decomposed into residual effects due to the individual dependent variates, and an additional component that measures the joint contribution due to the covariance. Such a decomposition is useful to the investigator in attributing the cause and recommending accommodation of influential cases.