Author(s)

Kohei Adachi

Graduate School of Human Sciences, Osaka University, Osaka, Japan.

Factor analysis (FA) is a time-honored multivariate analysis procedure for exploring the factors underlying observed variables. In this paper, we propose a new algorithm for the generalized least squares (GLS) estimation in FA. In the algorithm, a majorization step and diagonal steps are alternately iterated until convergence is reached, where Kiers and ten Berge’s (1992) majorization technique is used for the former step, and the latter ones are formulated as minimizing simple quadratic functions of diagonal matrices. This procedure is named a majorizing-diagonal (MD) algorithm. In contrast to the existing gradient approaches, differential calculus is not used and only elmentary matrix computations are required in the MD algorithm. A simuation study shows that the proposed MD algorithm recovers parameters better than the existing algorithms.

Exploratory Factor Analysis, Generalized Least Squares Estimation, Matrix Computations, Majorization

Adachi, K. (2015) A New Algorithm for Generalized Least Squares Factor Analysis with a Majorization Technique. Open Journal of Statistics, 5, 165-172. doi: 10.4236/ojs.2015.53020.