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Constrained Multilevel Latent Class Models for the Analysis of Three-Way Three-Mode Binary Data

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  • Michel Meulders
  • Francis Tuerlinckx
  • Wolf Vanpaemel

Abstract

Probabilistic feature models (PFMs) can be used to explain binary rater judgements about the associations between two types of elements (e.g., objects and attributes) on the basis of binary latent features. In particular, to explain observed object-attribute associations PFMs assume that respondents classify both objects and attributes with respect to a, usually small, number of binary latent features, and that the observed object-attribute association is derived as a specific mapping of these classifications. Standard PFMs assume that the object-attribute association probability is the same according to all respondents, and that all observations are statistically independent. As both assumptions may be unrealistic, a multilevel latent class extension of PFMs is proposed which allows objects and/or attribute parameters to be different across latent rater classes, and which allows to model dependencies between associations with a common object (attribute) by assuming that the link between features and objects (attributes) is fixed across judgements. Formal relationships with existing multilevel latent class models for binary three-way data are described. As an illustration, the models are used to study rater differences in product perception and to investigate individual differences in the situational determinants of anger-related behavior. Copyright Springer Science+Business Media New York 2013

Suggested Citation

  • Michel Meulders & Francis Tuerlinckx & Wolf Vanpaemel, 2013. "Constrained Multilevel Latent Class Models for the Analysis of Three-Way Three-Mode Binary Data," Journal of Classification, Springer;The Classification Society, vol. 30(3), pages 306-337, October.
    • Handle: RePEc:spr:jclass:v:30:y:2013:i:3:p:306-337
    DOI: 10.1007/s00357-013-9141-8
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    References listed on IDEAS

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    1. E. Maris, 1999. "Estimating multiple classification latent class models," Psychometrika, Springer;The Psychometric Society, vol. 64(2), pages 187-212, June.
    2. Michel Meulders & Paul De Boeck & Iven Van Mechelen & Andrew Gelman, 2005. "Probabilistic feature analysis of facial perception of emotions," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 54(4), pages 781-793, August.
    3. Torres, Anna & Bijmolt, Tammo H.A., 2009. "Assessing brand image through communalities and asymmetries in brand-to-attribute and attribute-to-brand associations," European Journal of Operational Research, Elsevier, vol. 195(2), pages 628-640, June.
    4. Vermunt, Jeroen K., 2007. "A hierarchical mixture model for clustering three-way data sets," Computational Statistics & Data Analysis, Elsevier, vol. 51(11), pages 5368-5376, July.
    5. Meulders, Michel & Boeck, Paul De & Mechelen, Iven Van, 2001. "Probability matrix decomposition models and main-effects generalized linear models for the analysis of replicated binary associations," Computational Statistics & Data Analysis, Elsevier, vol. 38(2), pages 217-233, December.
    6. Even Mechelen & Paul Boeck, 1990. "Projection of a binary criterion into a model of hierarchical classes," Psychometrika, Springer;The Psychometric Society, vol. 55(4), pages 677-694, December.
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