Selecting among three-mode principal component models of different types and complexities: A numerical convex hull based method

British Journal of Mathematical and Statistical Psychology

Volumn 59, Issue 1, 2006, Pages 133-150

  Ceulemans, Eva ^a,c   Kiers, Henk A L ^b  

^a UNIVERSITY OF LEUVEN   (Belgium)

^b UNIVERSITY OF GRONINGEN   (Netherlands)

^c Department of Psychology ^*  (Belgium)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; HUMAN; PSYCHOLOGICAL MODEL; PSYCHOLOGY; STATISTICS; THEORETICAL MODEL;

HUMANS; MODELS, PSYCHOLOGICAL; MODELS, THEORETICAL; PSYCHOLOGY;

EID: 33745135758     PISSN: 00071102     EISSN: None     Source Type: Journal    
DOI: 10.1348/000711005X64817     Document Type: Article

References (19)

1. Bro, R., & Kiers, H. A. L. (2003). A new efficient method for determining the number of components in PARAFAC models. Journal of Chemometrics, 17, 274-286.
2. Carroll, J. D., & Chang, J. J. (1970). Analysis of individual differences in multidimensional scaling via an n-way generalization of 'Eckart-Young' decomposition. Psychometrika, 35, 283-319.
3. Ceulemans, E., & Van Mechelen, I. (2005). Hierarchical classes models for three-way three-mode binary data: Interrelations and model selection. Psychometrika, 70, 461-480.
4. Fowlkes, E. B., Freeny, A. E., & Landwehr, J. M. (1988). Evaluating logistic models for large contingency tables. Journal of the American Statistical Association, 83, 611-622.
5. Harshman, R. A. (1970). Foundations of the PARAFAC procedure: Models and conditions for an explanatory multi-modal factor analysis. UCLA Working Papers in Phonetics, 16, 1-84.
6. Kiers, H. A. L. (1991). Hierarchical relations among three-way methods. Psychometrika, 56, 449-470.
7. Kiers, H. A. L., & der Kinderen, A. (2003). A fast method for choosing the numbers of components in Tucker3 analysis. British Journal of Mathematical and Statistical Psychology, 56, 119-125.
8. Kiers, H. A. L., & Harshman, R. A. (1997). Relating two proposed methods for speedup of algorithms for fitting two- and three-way principal component and related multilinear models. Chemometrics and Intelligent Laboratory Systems, 36, 31-40.
9. Kroonenberg, P. M. (1983). Three-mode principal component analysis: Theory and applications. Leiden: DSWO.
10. 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.
11. Kroonenberg, P. M., & Oort, F. J. (2003). Three-mode analysis of multimode covariance matrices. British Journal of Mathematical and Statistical Psychology, 56, 305-336.
12. Kroonenberg, P. M., & Van der Voort, T. H. A. (1987). Multiplicatieve decompositie van interacties bij oordelen over de werkelijkheidswaarde van televisiefilms [Multiplicative decomposition of interactions for judgements of realism of television films]. Kwantitatieve Methoden, 8, 117-144.
13. p. Technometrics, 15, 661-675.
14. Murakami, T., & Kroonenberg, P. M. (2003). Three-mode models and individual differences in semantic differential data. Multivariate Behavioral Research, 38, 247-283.
15. Timmerman, M. E., & Kiers, H. A. L. (2000). Three-mode principal components analysis: Choosing the numbers of components and sensitivity to local minima. British Journal of Mathematical and Statistical Psychology, 53, 1-16.
16. Tucker, L. R. (1966). Some mathematical notes on three-mode factor analysis. Psychometrika, 31, 279-311.
17. Verbeek, A. (1984). The geometry of model selection in regression. In T. K. Dijkstra (Ed.), Misspecification analysis (pp. 20-36). Berlin: Springer.
18. Wansbeek, T., & Verhees, J. (1989). Models for multidimensional matrices in econometrics and psychometrics. In R. Coppi & S. Bolasco (Eds.), Multiway data analysis (pp. 543-552). Amsterdam: North Holland.
19. Weesie, J., & Van Houwelingen, H. (1983). GEPCAM users' manual (first draft). Utrecht, The Netherlands: Institute of Mathematical Statistics, State University of Utrecht.