Tucker3 hierarchical classes analysis. This paper presents a new model for binary three-way three-mode data, called Tucker3 hierarchical classes model (Tucker3-HICLAS). This new model generalizes I. Leenen, I. van Mechelen, P. De Boeck and S. Rosenberg’s individual differences hierarchical classes model (INDCLAS) [Psychometrika 64, No. 1, 9–24 (1999; Zbl 06318576)]. Like the INDCLAS model, the Tucker3-HICLAS model includes a hierarchical classification of the elements of each mode, and a linking structure among the three hierarchies. Unlike INDCLAS, Tucker3-HICLAS (a) does not restrict the hierarchical classifications of the three modes to have the same rank, and (b) allows for more complex linking structures among the three hierarchies. An algorithm to fit the Tucker3-HICLAS model is described and evaluated in an extensive simulation study. An application of the model to hostility data is discussed.

References in zbMATH (referenced in 15 articles , 1 standard article )

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  1. Depril, Dirk; Van Mechelen, Iven; Wilderjans, Tom F.: Lowdimensional additive overlapping clustering (2012)
  2. Wilderjans, Tom F.; Ceulemans, E.; Van Mechelen, I.: The SIMCLAS model: simultaneous analysis of coupled binary data matrices with noise heterogeneity between and within data blocks (2012)
  3. Glodeanu, Cynthia Vera: Factorization with hierarchical classes analysis and with formal concept analysis (2011)
  4. Maruotti, Antonello: Mixed hidden Markov models for longitudinal data: an overview (2011)
  5. Schepers, Jan; Van Mechelen, Iven; Ceulemans, Eva: The real-valued model of hierarchical classes (2011)
  6. Schepers, Jan; van Mechelen, Iven: Uniqueness of real-valued hierarchical classes models (2010)
  7. Leenen, Iwin; van Mechelen, Iven; Gelman, Andrew; de Knop, Stijn: Bayesian hierarchical classes analysis (2008)
  8. Wilderjans, Tom; Ceulemans, Eva; Van Mechelen, Iven: The CHIC model: a global model for coupled binary data (2008)
  9. Ceulemans, Eva; Van Mechelen, Iven; Leenen, Iwin: The local minima problem in hierarchical classes analysis: an evaluation of a simulated annealing algorithm and various multistart procedures (2007)
  10. Van Mechelen, Iven; Lombardi, Luigi; Ceulemans, Eva: Hierarchical classes modeling of rating data (2007)
  11. van Mechelen, Iven; Schepers, Jan: A unifying model involving a categorical and/or dimensional reduction for multimode data (2007)
  12. Ceulemans, Eva; Van Mechelen, Iven: Hierarchical classes models for three-way three-mode binary data: interrelations and model selection (2005)
  13. Kiers, Henk A.L.: Clustering all three modes of three-mode data: computational possibilities and problems (2004)
  14. Ceulemans, Eva; Van Mechelen, Iven: Uniqueness of $N$-way $N$-mode hierarchical classes models. (2003)
  15. Ceulemans, Eva; Van Mechelen, Iven; Leenen, Iwin: Tucker3 hierarchical classes analysis (2003)