Three-way SIMPLIMAX for oblique rotation of the three-mode factor analysis core to simple structure

Computational Statistics and Data Analysis

Volumn 28, Issue 3, 1998, Pages 307-324

  Kiers, Henk A L ^a  

^a UNIVERSITY OF GRONINGEN   (Netherlands)

Author keywords

Components analysis; Simple structure; Three way data

Indexed keywords

ALGORITHMS; COMPUTATIONAL METHODS; DATA STRUCTURES; MATRIX ALGEBRA;

COMPONENT ANALYSIS; THREE-MODE FACTOR ANALYSIS;

DATA REDUCTION;

EID: 0032483290     PISSN: 01679473     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-9473(98)00041-3     Document Type: Article

References (19)

1. Browne, M.W., 1972. Oblique rotation to a partially specified target. British J. Math. Statist. Psychol. 25, 207-212.
2. Cohen, H.S, 1974. Three-mode rotation to approximate INDSCAL structure (TRIAS). Paper presented at the Psychometric Society Meeting, Palo Alto.
3. Cohen, H.S., 1975. Further thoughts on three-mode rotation to INDSCAL structure, with jackknifed confidence regions for points. Paper presented at U.S.-Japan seminar on Theory, Methods and Applications of Multidimensional Scaling and Related Techniques, La Jolla.
4. Crawford, C.B., Ferguson, G.A., 1970. A general rotation criterion and its use in orthogonal rotation. Psychometrika 35, 321-332.
5. Jennrich, R.I., 1970. Orthogonal rotation algorithms. Psychometrika 35, 229-235.
6. Kiers, H.A.L., 1992. TUCKALS core rotations and constrained TUCKALS modelling. Statistica Applicata 4, 659-667.
7. Kiers, H.A.L., 1994. SIMPLIMAX: Oblique rotation to an optimal target with simple structure. Psychometrika 59, 567-579.
8. Kiers, H.A.L., 1997. Three-mode Orthomax rotation. Psychometrika 62, 579-598.
9. Kiers, H.A.L., Ten Berge, J.M.F., Rocci, R., 1997. Uniqueness of three-mode factor models with sparse cores: The 3 × 3 × 3 case. Psychometrika 62, 349-374.
10. Kroonenberg, P.M., 1983. Three-Mode Principal Component Analysis: Theory and Applications. DSWO press, Leiden.
11. Kroonenberg, P.M., 1994. The TUCKALS line: a suite of programs for three-way data analysis. Comput. Statist. Data Anal. 18, 73-96.
12. Kroonenberg, P.M., De Leeuw, J., 1980. Principal component analysis of three-mode data by means of alternating least squares algorithms. Psychometrika 45, 69-97.
13. Kroonenberg, P.M., Ten Berge, J.M.F., Brouwer, P., Kiers, H.A.L., 1989. Gram-Schmidt versus Bauer-Rutishauser in alternating least-squares algorithms for three-mode component analysis. Comput. Statist. Quart. 5, 81-87.
14. Kruskal, J.B., 1988. Simple structure for three-way data: a new method intermediate between 3-mode factor analysis and PARAFAC-CANDECOMP. Paper presented at the 53rd Annual Meeting of the Psychometric Society, Los Angeles.
15. MacCallum, R.C., 1976. Transformations of a three-mode multidimensional scaling solution to INDSCAL form. Psychometrika 41, 385-400.
16. Murakami, T., 1983. Quasi three-mode principal component analysis - A method for assessing factor change. Behaviormetrika 14, 27-48.
17. Murakami, T., Ten Berge, J.M.F., Kiers, H.A.L., 1998. A case of extreme simplicity of the core matrix in three-mode principal components analysis. Psychometrika 63.
18. Ten Berge, J.M.F., 1996. Some general results for Murakami zeros in p × p × 2 arrays (p ≤ 5). Unpublished note.
19. Tucker, L.R., 1966. Some mathematical notes on three-mode factor analysis. Psychometrika 31, 279-311.