Computational Aspects of the Greatest Lower Bound to the Reliability and Constrained Minimum Trace Factor Analysis
Jos M. F. ten Berge, Tom A. B. Snijders, Frits E. Zegers · Psychometrika · 1981
In the last decade several algorithms for computing the greatest lower bound to reliability or the constrained minimum-trace communality solution in factor analysis have been developed. In this paper convergence properties of these methods are examined. Instead of using Lagrange multipliers a new theorem is applied that gives a sufficient condition for a symmetric matrix to be Gramian. Whereas computational pitfalls for two methods suggested by Woodhouse and Jackson can be constructed it is shown that a slightly modified version of one method suggested by Bentler and Woodward can safely be applied to any set of data. A uniqueness proof for the solution desired is offered.