Abstract
This paper presents a condition that estimators in a covariance structure model are consistent weakly (strongly), which is equivalent to Shapiro's condition. The condition is composed of three parts, each of which is simpler and is checked more easily. This result is applied to a proof of consistency of estimators in a factor analysis model. The population value of a factor analysis model is given which does not admit any consistent estimator. This fact suggests that the proofs of consistency by the previous authors are not complete.
