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Modeling Differences in the Dimensionality of Multiblock Data by Means of Clusterwise Simultaneous Component Analysis

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  • Kim De Roover
  • Eva Ceulemans
  • Marieke Timmerman
  • John Nezlek
  • Patrick Onghena

Abstract

Given multivariate multiblock data (e.g., subjects nested in groups are measured on multiple variables), one may be interested in the nature and number of dimensions that underlie the variables, and in differences in dimensional structure across data blocks. To this end, clusterwise simultaneous component analysis (SCA) was proposed which simultaneously clusters blocks with a similar structure and performs an SCA per cluster. However, the number of components was restricted to be the same across clusters, which is often unrealistic. In this paper, this restriction is removed. The resulting challenges with respect to model estimation and selection are resolved. Copyright The Psychometric Society 2013

Suggested Citation

  • Kim De Roover & Eva Ceulemans & Marieke Timmerman & John Nezlek & Patrick Onghena, 2013. "Modeling Differences in the Dimensionality of Multiblock Data by Means of Clusterwise Simultaneous Component Analysis," Psychometrika, Springer;The Psychometric Society, vol. 78(4), pages 648-668, October.
    • Handle: RePEc:spr:psycho:v:78:y:2013:i:4:p:648-668
    DOI: 10.1007/s11336-013-9318-4
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    References listed on IDEAS

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    1. Timmerman, Marieke E. & Ceulemans, Eva & Kiers, Henk A.L. & Vichi, Maurizio, 2010. "Factorial and reduced K-means reconsidered," Computational Statistics & Data Analysis, Elsevier, vol. 54(7), pages 1858-1871, July.
    2. Henry Kaiser, 1958. "The varimax criterion for analytic rotation in factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 23(3), pages 187-200, September.
    3. Yiu-Fai Yung, 1997. "Finite mixtures in confirmatory factor-analysis models," Psychometrika, Springer;The Psychometric Society, vol. 62(3), pages 297-330, September.
    4. 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.
    5. Michael Brusco & J. Cradit, 2001. "A variable-selection heuristic for K-means clustering," Psychometrika, Springer;The Psychometric Society, vol. 66(2), pages 249-270, June.
    6. William Meredith & Roger Millsap, 1985. "On component analyses," Psychometrika, Springer;The Psychometric Society, vol. 50(4), pages 495-507, December.
    7. 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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    Cited by:

    1. Alwin Stegeman, 2018. "Simultaneous Component Analysis by Means of Tucker3," Psychometrika, Springer;The Psychometric Society, vol. 83(1), pages 21-47, March.

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