Hostname: page-component-745bb68f8f-grxwn Total loading time: 0 Render date: 2025-01-08T04:50:57.110Z Has data issue: false hasContentIssue false
  • English
  • Français

The CHIC Model: A Global Model for Coupled Binary Data

Published online by Cambridge University Press:  01 January 2025

Tom Wilderjans ,
Eva Ceulemans  and
Iven Van Mechelen
Tom Wilderjans*
Affiliation:
Katholieke Universiteit Leuven
Eva Ceulemans
Affiliation:
Katholieke Universiteit Leuven
Iven Van Mechelen
Affiliation:
Katholieke Universiteit Leuven
*
Requests for reprints should be sent to Tom Wilderjans, Department of Psychology, Katholieke Universiteit Leuven, Tiensestraat 102, 3000 Leuven, Belgium. E-mail: Tom.Wilderjans@psy.kuleuven.be
Get access Rights & Permissions [Opens in a new window]

Abstract

Often problems result in the collection of coupled data, which consist of different N-way N-mode data blocks that have one or more modes in common. To reveal the structure underlying such data, an integrated modeling strategy, with a single set of parameters for the common mode(s), that is estimated based on the information in all data blocks, may be most appropriate. Such a strategy implies a global model, consisting of different N-way N-mode submodels, and a global loss function that is a (weighted) sum of the partial loss functions associated with the different submodels. In this paper, such a global model for an integrated analysis of a three-way three-mode binary data array and a two-way two-mode binary data matrix that have one mode in common is presented. A simulated annealing algorithm to estimate the model parameters is described and evaluated in a simulation study. An application of the model to real psychological data is discussed.

Keywords

coupled datathree-way three-mode databinary datahierarchical classesmulti-way data analysisclusteringdata fusion
Type
Original Paper
Information
Psychometrika , Volume 73 , Issue 4 , December 2008 , pp. 729 - 751
Copyright
Copyright © 2008 The Psychometric Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

T. Wilderjans is a Research Assistant of the Fund for Scientific Research—Flanders (Belgium). The research reported in this paper was partially supported by the Research Council of K.U. Leuven (GOA/2005/04). We are grateful to Kristof Vansteelandt for providing us with an interesting data set. We also thank three anonymous reviewers for their useful comments.

References

Aarts, E.H.L., Korst, J.H.M., Van Laarhoven, P.J.M. (1997). Simulated annealing. In Aarts, E.H.L., & Lenstra, J.K. (Eds.), Local search in combinatorial optimization (pp. 91–120). Chichester: Wiley.Google Scholar
Akaike, H. (1973). Information theory and an extension of the maximum likelihood principle. In Petrov, B.N., & Csaki, F. (Eds.), Second international symposium on information theory (pp. 267–281). Budapest: Academiai Kiado.Google Scholar
Barbut, M., & Monjardet, B. (1970). Ordre et classification: algèbre et combinatoire, Paris: Hachette.Google Scholar
Birkhoff, G. (1940). Lattice theory, Providence: American Mathematical Society.Google Scholar
Boqué, R., & Smilde, A.K. (1999). Monitoring and diagnosing batch processes with multiway covariates regression models. AIChE Journal, 45, 1504–1520.CrossRefGoogle Scholar
Bozdogan, H. (1987). Model selection and Akaike’s information criterion (AIC): the general theory and its analytical extensions. Psychometrika, 52, 345–370.CrossRefGoogle Scholar
Bozdogan, H. (2000). Akaike’s information criterion and recent developments in informational complexity. Journal of Mathematical Psychology, 44, 62–91.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
Cattell, R.B. (1966). The meaning and strategic use of factor analysis. In Cattell, R.B. (Eds.), Handbook of multivariate experimental psychology (pp. 174–243). Chicago: Rand McNally.Google Scholar
Ceulemans, E., & Van Mechelen, I. (2004). Tucker2 hierarchical classes analysis. Psychometrika, 69, 375–399.CrossRefGoogle Scholar
Ceulemans, E., & Van Mechelen, I. (2005). Hierarchical classes models for three-way three-mode binary data: interrelations and model selection. Psychometrika, 70, 461–480.CrossRefGoogle Scholar
Ceulemans, E., Van Mechelen, I., & Leenen, I. (2003). Tucker3 hierarchical classes analysis. Psychometrika, 68, 413–433.CrossRefGoogle Scholar
Ceulemans, E., Van Mechelen, I., & Leenen, I. (2007). The local minima problem in hierarchical classes analysis: An evaluation of a simulated annealing algorithm and various multistart procedures. Psychometrika, 72, 377–391.CrossRefGoogle Scholar
Cohen, J. (1960). A coefficient of agreement for nominal scales. Educational and Psychological Measurement, 20, 37–46.CrossRefGoogle Scholar
Coxe, K.L. (1986). Principal components regression analysis. In Johnson, N.L., & Kotz, S. (Eds.), Encyclopedia of statistical science (pp. 181–186). New York: Wiley.Google Scholar
De Boeck, P., & Rosenberg, S. (1988). Hierarchical classes: model & data analysis. Psychometrika, 53, 361–381.CrossRefGoogle Scholar
Gati, I., & Tversky, A. (1982). Representations of qualitative and quantitative dimensions. Journal of Experimental Psychology: Human Perception and Performance, 8, 325–340.Google ScholarPubMed
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.Google Scholar
Hubert, L., & Arabie, P. (1985). Comparing partitions. Journal of Classification, 2, 193–218.CrossRefGoogle Scholar
Kirkpatrick, S., Gelatt, C.D. Jr., & Vecchi, M.P. (1983). Optimization by simulated annealing. Science, 220, 671–680.CrossRefGoogle ScholarPubMed
Leenen, I., & Van Mechelen, I. (2001). An evaluation of two algorithms for hierarchical classes analysis. Journal of Classification, 18, 57–80.CrossRefGoogle Scholar
Leenen, I., Van Mechelen, I., De Boeck, P., & Rosenberg, S. (1999). indclas: A three-way hierarchical classes model. Psychometrika, 64, 9–24.CrossRefGoogle Scholar
McKenzie, D.M., Clarke, D.M., & Low, L.H. (1992). A method of constructing parsimonious diagnostic and screening tests. International Journal of Methods in Psychiatric Research, 2, 71–79.Google Scholar
Smilde, A.K., & Kiers, H.A.L. (1999). Multiway covariates regression models. Journal of Chemometrics, 13, 31–48.3.0.CO;2-P>CrossRefGoogle Scholar
Smilde, A.K., Westerhuis, J.A., & Boqué, R. (2000). Multiway multiblock component and covariates regression models. Journal of Chemometrics, 14, 301–331.3.0.CO;2-H>CrossRefGoogle Scholar
Ten Berge, J.M.F. (1986). Rotation to perfect congruence and the cross-validation of component weights across populations. Multivariate Behavioral Research, 21, 41–64.CrossRefGoogle ScholarPubMed
Van Mechelen, I., De Boeck, P., & Rosenberg, S. (1995). The conjunctive model of hierarchical classes. Psychometrika, 60, 505–521.CrossRefGoogle Scholar
Van Mechelen, I., Lombardi, L., & Ceulemans, E. (2007). Hierarchical classes modeling of rating data. Psychometrika, 72, 475–488.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar