# An algorithm for sparse factor analysis with common factors and/or specific factors dissociated from errors

An algorithm for sparse factor analysis with common factors and/or specific factors dissociated... Two new approaches to factor analysis (FA) were presented in this century. One of them is developing the FA procedure underlain by a comprehensive FA (CompFA) model. In this model, a multivariate observation is decomposed into common factor, specific factor, and errors parts, with the three parts assumed to be uncorrelated mutually. The other approach is modifying FA so as to provide a sparse loading matrix. Such a modification is called sparse FA. The two approaches are combined in this note: its purpose is to present an algorithm for the sparse FA procedure underlain by the CompFA model, with the algorithm based on an alternating direction method of multipliers. The algorithm also covers the variants of the procedure, in which the model assumption is relaxed so that either common or specific factor part may be correlated with the error part. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Behaviormetrika Springer Journals

# An algorithm for sparse factor analysis with common factors and/or specific factors dissociated from errors

, Volume OnlineFirst – Feb 1, 2023
12 pages

/lp/springer-journals/an-algorithm-for-sparse-factor-analysis-with-common-factors-and-or-YZepHmG1Zw
Publisher
Springer Journals
ISSN
0385-7417
eISSN
1349-6964
DOI
10.1007/s41237-023-00195-1
Publisher site
See Article on Publisher Site

### Abstract

Two new approaches to factor analysis (FA) were presented in this century. One of them is developing the FA procedure underlain by a comprehensive FA (CompFA) model. In this model, a multivariate observation is decomposed into common factor, specific factor, and errors parts, with the three parts assumed to be uncorrelated mutually. The other approach is modifying FA so as to provide a sparse loading matrix. Such a modification is called sparse FA. The two approaches are combined in this note: its purpose is to present an algorithm for the sparse FA procedure underlain by the CompFA model, with the algorithm based on an alternating direction method of multipliers. The algorithm also covers the variants of the procedure, in which the model assumption is relaxed so that either common or specific factor part may be correlated with the error part.

### Journal

BehaviormetrikaSpringer Journals

Published: Feb 1, 2023

Keywords: Sparse factor analysis; Comprehensive factor analysis model; Completely decomposed factor analysis; Alternating direction method of multipliers; Unpenalized approach; Extended orthogonal Procrustes rotation

### References

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