Factor Analysis of Partial Covariance Matrices

Partial covariance matrices C_y.x are sometimes employed in factor analytic studies. The relation between the factor pattern C_yy and C_y.x is derived, where x and y are any two sets of variables. It is shown that the factor pattern is invariant, and the factor intercorrelation matrix P becomes P_f.x , where the latter is the variance covariance matrix of the factors f.x, i.e., f from which x is partialed out. The factor pattern of the two solutions can be rotated to proportional profiles in orthogonal space.