Uniqueness of N-way N-mode hierarchical classes models

Journal of Mathematical Psychology

Volumn 47, Issue 3, 2003, Pages 259-264

  Ceulemans, Eva ^a   Mechelen, Iven Van ^a  

^a UNIVERSITY OF LEUVEN   (Belgium)

Author keywords

Hierarchical classes; PARAFAC CANDECOMP; PCA; TUCKER3; Uniqueness

Indexed keywords

EID: 12344304847     PISSN: 00222496     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-2496(03)00002-6     Document Type: Article

References (25)

1. Bro, R., & De Jong, S. (1997). A fast non-negativity-constrained least squares algorithm. Journal of Chemometrics, 11, 393-401.
2. Bro, R., & Sidiropoulos, N. D. (1998). Least squares algorithms under unimodality and non-negativity constraints. Journal of Chemometrics, 12, 223-247.
3. 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.
4. Carroll, J. D., & Pruzansky, S. (1984). The Candecomp-Candelinc family of models and methods for multidimensional data analysis. In H. G. Law, J. C. W. Snyder, J. Hattie, & R. P. McDonald (Eds.), Research methods for multimode data analysis (pp. 372-402). New York: Praeger.
5. Ceulemans, E., Van Mechelen, I., & Leenen, I (in press). Tucker3 hierarchical classes analysis. Psychometrika, in press.
6. De Boeck, P., & Rosenberg, S. (1988). Hierarchical classes: Model and data analysis. Psychometrika, 53, 361-381.
7. Falmagne, J.-C., Koppen, M., Vilano, M., Doignon, J.-P., & Johannesen, L. (1990). Introduction to knowledge spaces: How to build, test and search them. Psychological Review, 97, 201-224.
8. Gara, M., & Rosenberg, S. (1990). A set-theoretical model of person perception. Behavioral research, 25, 275-293.
9. Harshman, R. A. (1970). Foundations of the PARAFAC procedure: Models and conditions for an explanatory multi-modal factor analysis. UCLA Working Papers in Phonetics, Vol. 16 (pp. 1-84).
10. Harshman, R. A., & Lundy, M. E. (1984). The Parafac model for three-way factor analysis and multidimensional scaling. In H. G. Law, J. C. W. Snyder, J. Hattie, & R. P. McDonald (Eds.), Research methods for multimode data analysis (pp. 122-215). New York: Praeger.
11. Kiers, H. A. L. (2000). Towards a standardized notation and terminology in multiway analysis. Journal of Chemometrics, 14, 105-122.
12. Kiers, H. A. L., & Smilde, A. K. (1998). Constrained three-mode factor analysis as a tool for parameter estimation with second-order instrumental data. Journal of Chemometrics, 12, 125-147.
13. 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.
14. Kim, K. H. (1982). Boolean matrix theory. New York: Marcel Dekker.
15. Kruskal, J. B. (1977). Three-way arrays: Rank and uniqueness of trilinear decompositions, with applications to arithmetic complexity and statistics. Linear Algebra and its Applications, 18, 95-138.
16. Kruskal, J. B. (1989). Rank, decomposition, and uniqueness for 3-way and n-way arrays. In R. Coppi, & S. Bolasco (Eds.), Multiway data analysis (pp. 8-18). Amsterdam: Elsevier.
17. Leenen, I., Van Mechelen, I., De Boeck, P., & Rosenberg, S. (1999). INDCLAS: A three-way hierarchical classes model. Psychometrika, 64, 9-24.
18. Luce, R. D. (1952). A note on Boolean matrix theory. Proceedings of the American Mathematical Society, 3, 382-388.
19. Rutherford, D. E. (1963). Inverse of Boolean matrices. Proceedings of the Glasgow Mathematical Association, 6, 49-53.
20. Sidiropoulos, N. D., & Bro, R. (2000). On the uniqueness of multilinear decomposition of n-way arrays. Journal of Chemometrics, 14, 229-239.
21. Tucker, L. R. (1966). Some mathematical notes on three-mode factor analysis. Psychometrika, 31, 279-311.
22. Van Mechelen, I., & De Boeck, P. (1989). Implicit taxonomy in psychiatric diagnosis: A case study. Journal of Social and Clinical Psychology, 8, 276-287.
23. Van Mechelen, I., De Boeck, P., & Rosenberg, S. (1995). The conjunctive model of hierarchical classes. Psychometrika, 60, 505-521.
24. Van Mechelen, I., & Van Damme, G. (1994). A latent criteria model for choice data. Acta Psychologica, 87, 85-94.
25. Vansteelandt, K., & Van Mechelen, I. (1998). Individual differences in situation-behavior profiles: A triple typology model. Journal of Personality and Social Psychology, 75, 751-765.