On Asymptotic Covariances of A Few Unrotated Factor Solutions
This work provides incremental improvements in statistical inference for factor analysis, aiding researchers in estimating standard errors for rotated loadings.
The paper derived explicit formulas for the asymptotic covariances of unrotated factor loading and unique variance estimates from various factor analysis methods, and a simulation study confirmed that these formulas yield reasonable results.
In this paper, we provide explicit formulas, in terms of the covariances of sample covariances or sample correlations, for the asymptotic covariances of unrotated factor loading estimates and unique variance estimates. These estimates are extracted from least square, principal, iterative principal component, alpha or image factor analysis. If the sample is taken from a multivariate normal population, these formulas, together with the delta methods, will produce the standard errors for the rotated loading estimates. A simulation study shows that the formulas provide reasonable results.