Algorithms for unweighted least-squares factor analysis

Estimation of the factor model by unweighted least squares (ULS) is distribution free, yields consistent estimates, and is computationally fast if the Minimum Residuals (MinRes) algorithm is employed. MinRes algorithms produce a converging sequence of monotonically decreasing ULS function values. Various suggestions for algorithms of the MinRes type are made for confirmatory as well as for exploratory factor analysis. These suggestions include the implementation of inequality constraints and the prevention of Heywood cases. A simulation study, comparing the bootstrap standard deviations for the parameters with the standard errors from maximum likelihood, indicates that these are virtually equal when the score vectors are sampled from the normal distribution. Two empirical examples demonstrate the usefulness of constrained exploratory and confirmatory factor analysis by ULS used in conjunction with the bootstrap method.