Conditions for factor (in)determinacy in factor analysis

Abstract

The subject of factor indeterminacy has a vast history in factor analysis Wilson Lederman Guttman It has lead to strong dierences in opinion Steiger The current paper gives necessary and sucient conditions for observability of factors in terms of the parameter matrices and a nite number of variables Five conditions are given which rigorously dene indeterminacy It is shown that un observable factors are in determinate Specically the indeterminacy proof by Guttman is extended to Heywood cases The results are illustrated by two examples and implications for indeterminacy are discussed