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has been cited by the following article:

• TITLE: A New Algorithm for Generalized Least Squares Factor Analysis with a Majorization Technique

  AUTHORS: Kohei Adachi

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

  JOURNAL NAME: Open Journal of Statistics, Vol.5 No.3, April 27, 2015

  ABSTRACT: 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.