Conditions for factor (in)determinacy in factor analysis

The subject of factor indeterminacy has a vast history in factor analysis ( Guttman, 1955; Lederman, 1938; Wilson, 1928). It has lead to strong differe nces in opinion (Steiger, 1979). The current paper gives necessary and suff icient conditions for observability of factors in terms of the parameter ma trices and a finite number of variables. Five conditions are given which ri gorously define indeterminacy. It is shown that (un)observable factors are (in)determinate. Specifically, the indeterminacy proof by Guttman is extend ed to Heywood cases. The results are illustrated by two examples and implic ations for indeterminacy are discussed.