Abstract
The traditional treatment of estimators in factor analysis as scale free versus not scale free is compared to the results that can be obtained on scale invariance. A theorem is given to the effect that we can obtain scale-invariant estimators of the parameters in any model that prescribes the structure of a correlation matrix, rather than a covariance matrix, by maximum likelihood and by generalized least squares both in the metric of the sample covariance matrix and in the metric of the sample variances. An examination is made of the conditions under which we may properly neglect the scaling parameters connecting the model describing the correlation matrix with the fitted covariance matrix.