 Orthogonal factor model

The latent factor vector has mean zero and covariance $I_q$, the specific errors have mean zero and diagonal covariance $\Psi$, and the two are uncorrelated. Thus the off-diagonal covariance is explained by shared factors. Normality additionally gives a likelihood model, but the covariance identity needs only these second-moment assumptions. Positive diagonal entries of $\Psi$ describe variation not explained by the factors. Unlike principal component analysis, the model separates shared and specific variation rather than only maximizing total projected variance.