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The SIMCLAS Model: Simultaneous Analysis of Coupled Binary Data Matrices with Noise Heterogeneity Between and Within Data Blocks

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  • Tom Wilderjans
  • E. Ceulemans
  • I. Mechelen

Abstract

In many research domains different pieces of information are collected regarding the same set of objects. Each piece of information constitutes a data block, and all these (coupled) blocks have the object mode in common. When analyzing such data, an important aim is to obtain an overall picture of the structure underlying the whole set of coupled data blocks. A further challenge consists of accounting for the differences in information value that exist between and within (i.e., between the objects of a single block) data blocks. To tackle these issues, analysis techniques may be useful in which all available pieces of information are integrated and in which at the same time noise heterogeneity is taken into account. For the case of binary coupled data, however, only methods exist that go for a simultaneous analysis of all data blocks but that do not account for noise heterogeneity. Therefore, in this paper, the SIMCLAS model, being a Hierarchical Classes model for the simultaneous analysis of coupled binary two-way matrices, is presented. In this model, noise heterogeneity between and within the data blocks is accounted for by downweighting entries from noisy blocks/objects within a block. In a simulation study it is shown that (1) the SIMCLAS technique recovers the underlying structure of coupled data to a very large extent, and (2) the SIMCLAS technique outperforms a Hierarchical Classes technique in which all entries contribute equally to the analysis (i.e., noise homogeneity within and between blocks). The latter is also demonstrated in an application of both techniques to empirical data on categorization of semantic concepts. Copyright The Psychometric Society 2012

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  • Tom Wilderjans & E. Ceulemans & I. Mechelen, 2012. "The SIMCLAS Model: Simultaneous Analysis of Coupled Binary Data Matrices with Noise Heterogeneity Between and Within Data Blocks," Psychometrika, Springer;The Psychometric Society, vol. 77(4), pages 724-740, October.
    • Handle: RePEc:spr:psycho:v:77:y:2012:i:4:p:724-740
    DOI: 10.1007/s11336-012-9275-3
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    References listed on IDEAS

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    1. Iwin Leenen & Iven Mechelen & Andrew Gelman & Stijn Knop, 2008. "Bayesian Hierarchical Classes Analysis," Psychometrika, Springer;The Psychometric Society, vol. 73(1), pages 39-64, March.
    2. Roger Millsap & William Meredith, 1988. "Component analysis in cross-sectional and longitudinal data," Psychometrika, Springer;The Psychometric Society, vol. 53(1), pages 123-134, March.
    3. Tom Wilderjans & Eva Ceulemans & Iven Mechelen, 2008. "The CHIC Model: A Global Model for Coupled Binary Data," Psychometrika, Springer;The Psychometric Society, vol. 73(4), pages 729-751, December.
    4. Iwin Leenen & Iven Van Mechelen, 2001. "An Evaluation of Two Algorithms for Hierarchical Classes Analysis," Journal of Classification, Springer;The Classification Society, vol. 18(1), pages 57-80, January.
    5. Eva Ceulemans & Iven Mechelen & Iwin Leenen, 2003. "Tucker3 hierarchical classes analysis," Psychometrika, Springer;The Psychometric Society, vol. 68(3), pages 413-433, September.
    6. Iwin Leenen & Iven Mechelen & Paul Boeck & Seymour Rosenberg, 1999. "Indclas: A three-way hierarchical classes model," Psychometrika, Springer;The Psychometric Society, vol. 64(1), pages 9-24, March.
    7. Eva Ceulemans & Iven Mechelen, 2005. "Hierarchical classes models for three-way three-mode binary data: interrelations and model selection," Psychometrika, Springer;The Psychometric Society, vol. 70(3), pages 461-480, September.
    8. Eva Ceulemans & Iven Mechelen, 2004. "Tucker2 hierarchical classes analysis," Psychometrika, Springer;The Psychometric Society, vol. 69(3), pages 375-399, September.
    9. Eva Ceulemans & Iven Mechelen & Iwin Leenen, 2007. "The Local Minima Problem in Hierarchical Classes Analysis: An Evaluation of a Simulated Annealing Algorithm and Various Multistart Procedures," Psychometrika, Springer;The Psychometric Society, vol. 72(3), pages 377-391, September.
    10. Marieke Timmerman & Henk Kiers, 2003. "Four simultaneous component models for the analysis of multivariate time series from more than one subject to model intraindividual and interindividual differences," Psychometrika, Springer;The Psychometric Society, vol. 68(1), pages 105-121, March.
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    13. Iven Mechelen & Paul Boeck & Seymour Rosenberg, 1995. "The conjunctive model of hierarchical classes," Psychometrika, Springer;The Psychometric Society, vol. 60(4), pages 505-521, December.
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    3. Jerzy Grobelny & Rafal Michalski & Gerhard-Wilhelm Weber, 2021. "Modeling human thinking about similarities by neuromatrices in the perspective of fuzzy logic," WORking papers in Management Science (WORMS) WORMS/21/09, Department of Operations Research and Business Intelligence, Wroclaw University of Science and Technology.

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