Conjugate gradient methods in confirmatory factor analysis

Abstract In the search for more efficient algorithms for covariance structure analysis we investigate the use of variable metric conjugate gradient (VMCG) algorithms. The key to success of these algorithms is the metric that defines them. Several metrics for maximum likelihood estimation in confirmatory factor analysis are introduced. Some of these produce algorithms that appear to be more efficient than the Fletcher-Powell algorithm used by LISREL and the Fisher scoring algorithm used by EQS. The EM algorithm of Rubin and Thayer [Psychometrica 47 (1982) 60–76] is generalized to handle additional specified value restrictions and the VMCG algorithm is used to accelerate the generalized algorithm. A careful comparison of the performance of Fisher scoring, Fletcher-Powell, EM, simple conjugate gradient, and several versions of algorithms introduced here is given.