Skip to main content
SpringerLink
Log in

The Real-Valued Model of Hierarchical Classes

  • Published:
Journal of Classification Aims and scope Submit manuscript

Abstract

We propose a non-negative real-valued model of hierarchical classes (HICLAS) for two-way two-mode data. Like the other members of the HICLAS family, the non-negative real-valued model (NNRV-HICLAS) implies simultaneous hierarchically organized classifications of all modes involved in the data. A distinctive feature of the novel model is that it yields continuous, non-negative real-valued reconstructed data, which considerably expands the application range of the HICLAS family. The expansion implies a major algorithmic challenge as it involves a move from the typical discrete optimization problems in HICLAS to a mixed discrete-continuous one. To solve this mixed discrete-continuous optimization problem, a two-stage algorithm combining a simulated annealing and an alternating local descent stage is proposed. Subsequently it is evaluated in a simulation study. Finally, the NNRVHICLAS model is applied to an empirical data set on anger.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • AARTS, E.H.L., and LENSTRA, J.K. (1997), Local Search in Combinatorial Optimization, New York: Wiley.

    MATH  Google Scholar 

  • BACCELLI, F., COHEN, G., OLSDER, G.-J., and QUADRAT, J.-P. (1993), Synchronization and Linearity: An Algebra for Discrete Event Systems, London: John Wiley & Sons.

    Google Scholar 

  • BRUSCO,M.J. (2001), “A Simulated Annealing Heuristic for Unidimensional and Multidimensional (City-Block) Scaling of Symmetric Proximity Matrices”, Journal of Classification, 18, 3–33.

    MathSciNet  MATH  Google Scholar 

  • CARROLL, J.D., and ARABIE, P. (1980), “Multidimensional Scaling”, Annual Review of Psychology, 31, 607–649.

    Article  Google Scholar 

  • CEULEMANS, E., and KIERS, H.A.L. (2006), “Selecting Among Three-Mode Principal Component Models of Different Types and Complexities: A Numerical Convex Hull Based Method”, British Journal of Mathematical and Statistical Psychology, 59, 133–150.

    Article  MathSciNet  Google Scholar 

  • CEULEMANS, E., and VAN MECHELEN, I. (2003), “Uniqueness of N-Way N-Mode Hierarchical Classes Models”, Journal of Mathematical Psychology, 47, 259–264.

    Article  MathSciNet  MATH  Google Scholar 

  • CEULEMANS, E., and VAN MECHELEN, I. (2004), “Tucker2 Hierarchical Classes Analysis”, Psychometrika, 69, 375–399.

    Article  MathSciNet  Google Scholar 

  • CEULEMANS, E., VAN MECHELEN, I., and KUPPENS, P. (2004), “Adapting the Formal to the Substantive: Constrained Tucker3-HICLAS”, Journal of Classification, 21, 19–50.

    Article  MathSciNet  MATH  Google Scholar 

  • CEULEMANS, E., VAN MECHELEN, I., and LEENEN, I. (2003), “Tucker3 Hierarchical Classes Analysis”, Psychometrika, 68, 413–433.

    Article  MathSciNet  Google Scholar 

  • CEULEMANS, E., VAN MECHELEN, I., and 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.

    Article  MathSciNet  MATH  Google Scholar 

  • CHATURVEDI,A., and CARROLL, J.D. (1994), “An Alternating Combinatorial Optimization Approach to Fitting the INDCLUS and Generalized INDCLUS Models”, Journal of Classification, 11, 155–170.

    Article  MATH  Google Scholar 

  • DE BOECK, P., and ROSENBERG, S. (1988), “Hierarchical Classes: Model and Data Analysis”, Psychometrika, 53, 361–381.

    Article  MATH  Google Scholar 

  • DE BOECK, P., and VANMECHELEN, I. (1990), “Traits and Taxonomies: A Hierarchical Classes Approach”, European Journal of Personality, 4, 147–156.

    Article  Google Scholar 

  • GARA, M.A., SILVER, R.C., ESCOBAR, J.I., HOLMAN, A., and WAITZKIN, H. (1998), “A Hierarchical Classes Analysis (HICLAS) of Primary Care PatientsWith Medically Unexplained Somatic Symptoms”, Psychiatry Research, 81, 77–86.

    Article  Google Scholar 

  • KUPPENS, P., and VAN MECHELEN, I. (2007), “Interactional Appraisal Models for the Anger Appraisals of Threatened Self-Esteem, Other-Blame, and Frustration”, Cognition & Emotion, 21, 56–77.

    Article  Google Scholar 

  • KUPPENS, P., VAN MECHELEN, I., SMITS, D. J.M., and DE BOECK, P. (2003), “The Appraisal Basis of Anger: Specificity, Necessity and Sufficiency of Components”, Emotion, 3, 254–269.

    Article  Google Scholar 

  • KUPPENS, P., VAN MECHELEN, I., SMITS, D. J.M., DE BOECK, P., and CEULEMANS, E. (2007), “Individual Differences in Patterns of Appraisal and Anger Experience”, Cognition & Emotion, 21, 689–713.

    Article  Google Scholar 

  • LEENEN, I., VAN MECHELEN, I., DE BOECK, P., and ROSENBERG, S. (1999), “INDCLAS: A Three-Way Hierarchical Classes Model”, Psychometrika, 64, 9–24.

    Article  Google Scholar 

  • MISCHEL,W., and SHODA, Y. (1998), “Reconciling Processing Dynamics and Personality Dispositions”, Annual Review of Psychology, 49, 229–258.

    Article  Google Scholar 

  • MURILLO, A., VERA, J.F., and HEISER, W.J. (2005), “A Permutation-Translation Simulated Annealing Algorithm for L1 and L2 Unidimensional Scaling”, Journal of Classification, 22, 119–138.

    Article  MathSciNet  MATH  Google Scholar 

  • NOCEDAL, J., and WRIGHT, S.J. (1999), Numerical Optimization, New York: Springer.

    Book  MATH  Google Scholar 

  • REID, A., and DEAUX, K. (1996), “Relationship Between Social and Personal Identities: Segregation or Integration?”, Journal of Personality and Social Psychology, 71, 1084–1091.

    Article  Google Scholar 

  • SCHEPERS, J., and HOFMANS, J. (2009), “TwoMP: aMATLAB Graphical User Interface for Two-Mode Partitioning”, Behavior Research Methods, 41, 507–514.

    Article  Google Scholar 

  • SCHEPERS, J., CEULEMANS, E., and VAN MECHELEN, I. (2008), “Selecting Among Multi-Mode Partitioning Models of Different Complexities: A Comparison of Four Model Selection Criteria”, Journal of Classification, 25, 67–85.

    Article  MathSciNet  MATH  Google Scholar 

  • SCHEPERS, J., and VAN MECHELEN, I. (2010), “Uniqueness of Real-Valued Hierarchical Classes Models”, Journal of Mathematical Psychology, 54, 215–221.

    Article  MathSciNet  MATH  Google Scholar 

  • STIRRATT, M.J., MEYER, I.H., OUELLETTE, S.C., and GARA, M.A. (2008), “Measuring Identity Multiplicity and Intersectionality: Hierarchical Classes Analysis (HICLAS) of Sexual, Racial, and Gender Identities”, Self and Identity, 7, 89–111.

    Article  Google Scholar 

  • VAN MECHELEN, I., and DE BOECK, P. (1989), “Implicit Taxonomy in Psychiatric Diagnosis: A Case Study”, Journal of Social and Clinical Psychology, 8, 276–287.

    Article  Google Scholar 

  • VAN MECHELEN, I., DE BOECK, P., and ROSENBERG, S. (1995), “The Conjunctive Model of Hierarchical Classes”, Psychometrika, 60, 505–521.

    Article  MATH  Google Scholar 

  • VANMECHELEN, I., LOMBARDI, L., and CEULEMANS, E. (2007), “Hierarchical Classes Modeling of Rating Data”, Psychometrika, 72, 475–488.

    Article  MathSciNet  Google Scholar 

  • VAN ROSMALEN, J., GROENEN, P.J.F., TREJOS, J. and CASTILLO W. (2009), “Optimization Strategies for Two-Mode Partitioning”, Journal of Classification, 26, 155–181.

    Article  MathSciNet  Google Scholar 

  • VANSTEELANDT,K., and VANMECHELEN, I. (1998), “Individual Differences in Situation-Behavior Profiles: A Triple Typology Model”, Journal of Personality and Social Psychology, 75, 751–765.

    Article  Google Scholar 

  • VANSTEELANDT,K., and VANMECHELEN, I. (2006), “Individual Differences in Anger and Sadness: In Pursuit of Active Situational Features and Psychological Processes”, Journal of Personality, 74, 871–910.

    Article  Google Scholar 

  • VERA, J.F., MACIAS, R., and HEISER, W.J. (2009), “A Dual Latent Class Unfolding Model for Two-Way Two-Mode Preference Rating Data”, Computational Statistics and Data Analysis, 53, 3231–3244.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. K.U.Leuven, Leuven, Belgium

    Jan Schepers, Iven Van Mechelen & Eva Ceulemans

  2. Faculty of Psychology and Neuroscience, Maastricht University, P.O. Box 616, 6200 MD, Maastricht, The Netherlands

    Jan Schepers

Authors
  1. Jan Schepers
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Iven Van Mechelen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Eva Ceulemans
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jan Schepers.

Additional information

J. Schepers and I. van Mechelen were supported by the Fund for Scientific Research-Flanders (Belgium), Project No. G.0146.06 awarded to Iven van Mechelen and by the Research Council KULeuven (GOA/2005/04). The authors would like to thank Peter Kuppens for providing the data set on anger.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Schepers, J., Van Mechelen, I. & Ceulemans, E. The Real-Valued Model of Hierarchical Classes. J Classif 28, 363–389 (2011). https://doi.org/10.1007/s00357-011-9089-5

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00357-011-9089-5

Keywords

Search

Navigation