Residual Correlation

From the factor loadings matrix V, a modeled correlation matrix can be computed from the matrix product VVt, where Vt is the transpose of V. The difference between the actual correlations (those in the Correlation Matrix folder) and the modeled correlation VV^t is the residual correlation. For a full-rank principal component analysis or factor analysis, the residual correlation will be 0 for all entries (that is, 100% explained variance). For a principal component analysis or factor analysis of less than full rank, the residual correlation shows where the unexplained variance is located.

R_mod = modeled correlation matrix = VV^t

R = correlations computed from extracted parameters

ΔR = R - VV^t