Hierarchical relations among principal component and factor analysis procedures elucidated from a comprehensive model

Kohei Adachi ()
Additional contact information
Kohei Adachi: Kyoto Women’s University

Computational Statistics, 2025, vol. 40, issue 7, No 20, 3946 pages

Abstract: Abstract In this review article, the term “hierarchy” is related to constrained-ness, but not to superiority. Procedures A and B forming a hierarchy means that A is a constrained variant of B or vice versa. A goal of this article is to present a hierarchy of principal component analysis (PCA) and factor analysis (FA) procedures, which follows from a comprehensive FA (CompFA) model. This model can be regarded as a hybrid of PCA and prevalent FA models. First, we show how a non-random version of the CompFA model leads to the following hierarchy: PCA is a constrained variant of completely decomposed FA, which itself is a constrained variant of matrix decomposition FA. Then, we prove that a random version of the CompFA model leads to minimum rank FA (MRFA) and constraining MRFA leads to random PCA (RPCA), so as to present the following hierarchy: Probabilistic PCA is a constrained variant of prevalent FA, and the latter is a constrained variant of RPCA, which is itself a constrained variant of MRFA. Finally, this hierarchy and the above hierarchy following from the non-random version are unified into one. We further utilize the unified hierarchy to present a strategy for selecting a procedure suitable to a data set.

Keywords: Comprehensive factor analysis model; Principal component analysis; Matrix decomposition factor analysis; Minimum rank factor analysis; Random principal component analysis (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s00180-025-01611-8 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:compst:v:40:y:2025:i:7:d:10.1007_s00180-025-01611-8

Ordering information: This journal article can be ordered from
http://www.springer.com/statistics/journal/180/PS2

DOI: 10.1007/s00180-025-01611-8

Access Statistics for this article

Computational Statistics is currently edited by Wataru Sakamoto, Ricardo Cao and Jürgen Symanzik

More articles in Computational Statistics from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().