Gradient Projection Algorithms and Software for Arbitrary Rotation Criteria in Factor Analysis
Top Cited Papers
- 1 October 2005
- journal article
- Published by SAGE Publications in Educational and Psychological Measurement
- Vol. 65 (5), 676-696
- https://doi.org/10.1177/0013164404272507
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.Keywords
This publication has 17 references indexed in Scilit:
- A simple general method for oblique rotationPsychometrika, 2002
- A simple general procedure for orthogonal rotationPsychometrika, 2001
- Factor Structure and Construct Validity of Scores on the Hopelessness Scale for Children with Students with Cognitive DisabilitiesEducational and Psychological Measurement, 1998
- Simplimax: Oblique rotation to an optimal target with simple structurePsychometrika, 1994
- OBLIQUE ROTATION TO A PARTIALLY SPECIFIED TARGETBritish Journal of Mathematical and Statistical Psychology, 1972
- ORTHOGONAL ROTATION TO A PARTIALLY SPECIFIED TARGETBritish Journal of Mathematical and Statistical Psychology, 1972
- Principal Component Analysis and its Application in Large-Scale Correlation StudiesThe Journal of Geology, 1966
- The varimax criterion for analytic rotation in factor analysisPsychometrika, 1958
- THE QUARTIMAX METHODBritish Journal of Statistical Psychology, 1954
- An analytical solution for approximating simple structure in factor analysisPsychometrika, 1953