Krijnen Wim P
University of Amsterdam, Amsterdam.
Department of Psychology, Psychological Methods, University of Amsterdam, Roetersstraat 15, 1018 WB, Amsterdam, The Netherlands.
Psychometrika. 2006 Jun;71(2):395-409. doi: 10.1007/s11336-004-1220-7. Epub 2017 Feb 11.
For the confirmatory factor model a series of inequalities is given with respect to the mean square error (MSE) of three main factor score predictors. The eigenvalues of these MSE matrices are a monotonic function of the eigenvalues of the matrix Γ = Φ Λ 'Ψ Λ Φ . This matrix increases with the number of observable variables p. A necessary and sufficient condition for mean square convergence of predictors is divergence of the smallest eigenvalue of Γ or, equivalently, divergence of signal-to-noise (Schneeweiss & Mathes, 1995). The same condition is necessary and sufficient for convergence to zero of the positive definite MSE differences of factor predictors, convergence to zero of the distance between factor predictors, and convergence to the unit value of the relative efficiencies of predictors. Various illustrations and examples of the convergence are given as well as explicit recommendations on the problem of choosing between the three main factor score predictors.
对于验证性因子模型，给出了一系列关于三种主要因子得分预测器的均方误差（MSE）的不等式。这些MSE矩阵的特征值是矩阵Γ = Φ Λ 'Ψ Λ Φ 的特征值的单调函数。该矩阵随着可观测变量p的数量增加而增大。预测器均方收敛的充要条件是Γ 的最小特征值发散，或者等价地，信噪比发散（施内维斯和马西斯，1995）。对于因子预测器正定MSE差异收敛到零、因子预测器之间的距离收敛到零以及预测器相对效率收敛到单位值，同样的条件也是充要的。给出了收敛的各种说明和示例，以及关于在三种主要因子得分预测器之间进行选择问题的明确建议。
