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) estimat...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.展开更多
Confirmatory factor analysis (CFA) refers to the FA procedure with some loadings constrained to be zeros. A difficulty in CFA is that the constraint must be specified by users in a subjective manner. For dealing with ...Confirmatory factor analysis (CFA) refers to the FA procedure with some loadings constrained to be zeros. A difficulty in CFA is that the constraint must be specified by users in a subjective manner. For dealing with this difficulty, we propose a computational method, in which the best CFA solution is obtained optimally without relying on users’ judgements. The method consists of the procedures at lower (L) and higher (H) levels: at the L level, for a fixed number of zero loadings, it is determined both which loadings are to be zeros and what values are to be given to the remaining nonzero parameters;at the H level, the procedure at the L level is performed over the different numbers of zero loadings, to provide the best solution. In the L level procedure, Kiers’ (1994) simplimax rotation fulfills a key role: the CFA solution under the constraint computationally specified by that rotation is used for initializing the parameters of a new FA procedure called simplimax FA. The task at the H level can be easily performed using information criteria. The usefulness of the proposed method is demonstrated numerically.展开更多
文摘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.
文摘Confirmatory factor analysis (CFA) refers to the FA procedure with some loadings constrained to be zeros. A difficulty in CFA is that the constraint must be specified by users in a subjective manner. For dealing with this difficulty, we propose a computational method, in which the best CFA solution is obtained optimally without relying on users’ judgements. The method consists of the procedures at lower (L) and higher (H) levels: at the L level, for a fixed number of zero loadings, it is determined both which loadings are to be zeros and what values are to be given to the remaining nonzero parameters;at the H level, the procedure at the L level is performed over the different numbers of zero loadings, to provide the best solution. In the L level procedure, Kiers’ (1994) simplimax rotation fulfills a key role: the CFA solution under the constraint computationally specified by that rotation is used for initializing the parameters of a new FA procedure called simplimax FA. The task at the H level can be easily performed using information criteria. The usefulness of the proposed method is demonstrated numerically.
