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

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.

Common psychiatric disorders share the same genetic origin: a multivariate sibling study of the Swedish population

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Exploiting spatial‐domain simplicity in spectral image analysis

“…A sampling of standard works [12,14,18] on these topics, together with more recent reviews [19,20] that focus on factor rotation methods, is included in the references. Over the past few decades, factor analysis has proved to be a powerful data analysis tool in the physical sciences as well, with broad application in, for instance, climatology, [21] geosciences, [22] and chemistry.…”

A structural analysis of deconversion processes in adolescence: The construction of the Adolescent Deconversion Scale

“…To verify the hypothesized structure of deconversion processes, we performed a factor analysis with oblique target rotation (Bernaards & Jennrich, 2005). This rotation makes it possible to transform the matrix of factor loadings in such a way that it is fitted as much as possible to another matrix.…”