Generalized covariance-adjusted canonical correlation analysis with application to psychiatry

The lack of control over covariates in practice motivates the need for their adjustment when measuring the degree of association between two sets of variables, for which canonical correlation is traditionally used. In most studies however, there is also a lack of control over the attributes of responses for the sets of variables of interest. In particular, a portion of the response variable may be continuous and the other discrete. For such settings, the traditional partial canonical correlation approach is restrictive, since a covariate-adjustment for a set of continuous variables is assumed. By ignoring the assumption of continuous variates and proceeding with a partial canonical correlation analysis in the presence of continuous and discrete variates, results in canonical correlation estimates that are not consistent. In this paper we generalize the traditional partial canonical correlation approach to covariate-adjustment by allowing the response variables to contain continuous, as well as discrete, variates. The methodology is illustrated with a psychiatric application for examining which sleep variables relate to which depressive symptoms, as measured by commonly used constructs that presents with both continuous and discrete outcomes.