Some Mathematical Properties of the Matrix Decomposition Solution in Factor Analysis
Some Mathematical Properties of the Matrix Decomposition Solution in Factor Analysis
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DOI：
10.1007/s11336-017-9600-y
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发表时间：
2018-06-01
期刊：
影响因子：
3
通讯作者：
Trendafilov, Nickolay T.
中科院分区：
文献类型：
--
作者：
Adachi, Kohei;Trendafilov, Nickolay T.
最近提出了一种新的因子分析（FA）方法，称为矩阵分解FA（MDFA）。所有FA模型参数（公共和唯一因子、载荷和唯一方差）都被视为固定的未知矩阵。然后，MDFA模型简单地成为特定的数据矩阵分解。通过最小化数据与MDFA模型之间的差异来找到MDFA参数。已经开发了几种算法，并且在文献中讨论了一些属性（特别是Stegeman在Comput Stat Data Anal 99：189-203，2016中），但是，作为一个整体，MDFA尚未得到充分研究。本文发现了一些新的性质，并更明确地导出了一些现有的性质。所提供的属性涉及结果的唯一性，共同因素之间的协方差，独特的因素，和残差，以及共同和独特的因素得分的不确定性程度的评估。使用一个真实的数据的例子来说明的属性。
A new factor analysis (FA) procedure has recently been proposed which can be called matrix decomposition FA (MDFA). All FA model parameters (common and unique factors, loadings, and unique variances) are treated as fixed unknown matrices. Then, the MDFA model simply becomes a specific data matrix decomposition. The MDFA parameters are found by minimizing the discrepancy between the data and the MDFA model. Several algorithms have been developed and some properties have been discussed in the literature (notably by Stegeman in Comput Stat Data Anal 99:189-203, 2016), but, as a whole, MDFA has not been studied fully yet. A number of new properties are discovered in this paper, and some existing ones are derived more explicitly. The properties provided concern the uniqueness of results, covariances among common factors, unique factors, and residuals, and assessment of the degree of indeterminacy of common and unique factor scores. The properties are illustrated using a real data example.