Gradient Projection Algorithms and Software for Arbitrary Rotation Criteria in Factor Analysis

2005/10/01 by Coen A. Bernaards, Coen Bernaards, Robert I. Jennrich · 611 citations
Engineering · Mathematics · #Algorithm #Artificial intelligence #Computer science #Factor (programming language) #Mathematics #Matrix (chemical analysis) #Mechanical Engineering and Vibrations Research #Oblique case #Oblique projection #Orthographic projection #Projection (relational algebra) #Rotation (mathematics) #Rotation matrix #Software #Statistical and numerical algorithms #Vehicle Noise and Vibration Control

paper · doi:10.1177/0013164404272507

published in Educational and Psychological Measurement 65(5), 676-696 (SAGE Publishing)

openalex publication_date 2005/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30

Abstract

Almost all modern rotation of factor loadings is based on optimizing a criterion, for example, the quartimax criterion for quartimax rotation. Recent advancements in numerical methods have led to general orthogonal and oblique algorithms for optimizing essentially any rotation criterion. All that is required for a specific application is a definition of the criterion and its gradient. The authors present the implementations of gradient projection algorithms, both orthogonal and oblique, as well as a catalogue of rotation criteria and corresponding gradients. Software for these is downloadable and free; a specific version is given for each of the computing environments used most by statisticians. Examples of rotation methods are presented by applying them to a loading matrix from Wehmeyer and Palmer.

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