A1165
Title: A nesting relation among principal component and factor analysis procedures
Authors: Kohei Adachi - Kyoto Women\'s University (Japan) [presenting]
Abstract: Relationships among three procedures for principal component analysis (PCA) and four procedures for factor analysis (FA) are examined, which amount to seven procedures named as follows: [1] standard PCA (PCA), [2] random PCA (RPCA), [3] probabilistic PCA (PPCA), [4] classic FA (CFA), [5] minimum rank FA (MRFA), [6] matrix decomposed FA (MDFA), and [7] completely decomposed FA (CDFA). Procedures [1] and [4] were prevalent from the last century, while [2], [6], and [7] were proposed in this century, with [3] and [5] presented in the last century. Two nesting relations are demonstrated: [6] MDFA > [7] CDFA > [1] PCA, and [5] MRFA > [2] RPCA > [4] CFA > [3] PPCA. In these relations, the procedure after > is a constrained variant of the one before >, with factor or PC scores being nonrandom parameters in [1], [6], and [7], but random variables in [2] through [5]. The two relations are unified into a single relation: [6] MDFA > [7] CDFA / [5] MRFA > [1] PCA / [2] RPCA > [4] CFA > [3] PPCA, based on the equivalences of [7] to [5] and [1] to [2].
