Beauducel André, Hilger Norbert
Institute of Psychology, University of Bonn, Bonn, Germany.
Front Psychol. 2019 Aug 16;10:1895. doi: 10.3389/fpsyg.2019.01895. eCollection 2019.
The non-diagonal elements of the observed covariances are more exactly reproduced by the factor loadings than by the model implied by the corresponding factor score predictors. This is a limitation to the validity of factor score predictors. It is therefore investigated whether it is possible to estimate factor loadings for which the model implied by the factor score predictors optimally reproduces the non-diagonal elements of the observed covariance matrix. Accordingly, loading estimates are proposed for which the model implied by the factor score predictors allows for a least-squares approximation of the non-diagonal elements of the observed covariance matrix. This estimation method is termed score predictor factor analysis and algebraically compared with Minres factor analysis as well as principal component analysis. A population-based and a sample-based simulation study was performed in order to compare score predictor factor analysis, Minres factor analysis, and principal component analysis. It turns out that the non-diagonal elements of the observed covariance matrix can more exactly be reproduced from the factor score predictors computed from score predictor factor analysis than from the factor score predictors computed from Minres factor analysis and from principal components.
与由相应因子得分预测变量所隐含的模型相比，因子载荷能更精确地重现观测协方差的非对角元素。这是因子得分预测变量有效性的一个限制。因此，研究了是否有可能估计因子载荷，使得由因子得分预测变量所隐含的模型能最优地重现观测协方差矩阵的非对角元素。相应地，提出了载荷估计方法，使得由因子得分预测变量所隐含的模型能够对观测协方差矩阵的非对角元素进行最小二乘近似。这种估计方法被称为得分预测变量因子分析，并在代数上与最小残差因子分析以及主成分分析进行比较。为了比较得分预测变量因子分析、最小残差因子分析和主成分分析，进行了基于总体和基于样本的模拟研究。结果表明，与从最小残差因子分析和主成分计算出的因子得分预测变量相比，从得分预测变量因子分析计算出的因子得分预测变量能更精确地重现观测协方差矩阵的非对角元素。
