Abstract #300226

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JSM 2003 Abstract #300226
Activity Number: 294
Type: Contributed
Date/Time: Tuesday, August 5, 2003 : 2:00 PM to 3:50 PM
Sponsor: Section on Statistical Computing
Abstract - #300226
Title: Gradient Projection Algorithms for Arbitrary Rotation Criteria in Factor Analysis with Examples
Author(s): Coen A. Bernaards*+ and Robert I. Jennrich
Companies: University of California, Los Angeles and University of California
Address: Department of Statistics, Los Angeles, CA, 90095-1554,
Keywords: factor analysis ; factor rotation ; oblique ; orthogonal ; quartimin ; varimax
Abstract:

Almost all modern rotation of factor loadings is based on optimizing a criterion, for example the quartimax criterion for quartimax rotation. For most methods, tailored optimization algorithms were designed. Consequently, a new method required designing and programming new algorithms. Recent advancements (Jennrich 2001, 2002) 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. Here, we present implementations of gradient projection algorithms, both orthogonal and oblique, as well as a catalog of rotation criteria and corresponding gradients. Examples of rotation methods are presented by applying them to Thurstone's box problem. Methods are compared using sorted absolute loading plots. It is found that popular rotation methods do not always perform as well as less popular rotation methods.

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