Applied Multivariate Research v.13 no.1

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    Applied Multivariate Research, v.13 no.1 (complete version)
    (University of Windsor, Dept. of Psychology, 2009)
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    Multivariate models for three-dimensional data
    (University of Windsor, Department of Psychology, 2009) Grice, James W.; Grice, James W.
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    Three-way heirarchical classes: A comparison of the INDCLAS and Tucker3-HICLAS models
    (University of Windsor, Dept. of Psychology, 2009) Leenen, Iwin; Ceulemans, Eva
    Hierarchical classes (HICLAS) models for multi-way multi-mode data constitute a unique family of classification models in that (a) they simultaneously induce a hierarchical classification (of the elements) of each mode and (b) they link the hierarchical classifications together by an association relation that yields a predicted (or reconstructed) value for each cell in the data array. For the case of three-way three-mode binary data, the most prominent HICLAS models include INDCLAS and Tucker3-HICLAS. In this paper, we compare the latter two models, introducing the underlying theory of both in substantive terms and showing how a Tucker3-HICLAS analysis may result in a simpler model than that yielded by INDCLAS, although the former is mathematically more complex than the latter (which it includes as a special case). We illustrate by two applications: a study on anger responses in frustrating situations and a case-study on emotions in interpersonal relations.
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    Generalized Procrustes Analysis: A tool for exploring aggregates and persons
    (University of Windsor, Dept. of Psychology, 2009) Grice, James W.; Assad, Kimberly Kristine
    Gower (1975) introduced Generalized Procrustes Analysis (GPA) as a multivariate statistical technique for analyzing three-dimensional data matrices. The current paper presents a non-technical introduction to the logic underlying GPA and then presents a completely worked example using genuine data. Specifically, self and peer ratings obtained from students attending a Summer Science Academy are analyzed and discussed. It is shown that GPA offers a powerful set of tools for exploring data at both the aggregate and individual level. A number of issues regarding the current analysis methods are also discussed.
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    Analysing three-way profile data using the Parafac and Tucker3 models illustrated with views on parenting
    (University of Windsor, Dept. of Psychology, 2009) Kroonenberg, Pieter M.; Harshman, Richard A.; Murakami, Takashi
    In this paper two major models for three-way profile data, i.e., the Parafac model and the Tucker3 model are discussed from the point of view of application. Topics treated are handling the data before analysis, model choice, choice of dimensionality, model fit, algorithmic hazards during the analyses, and interpretation and validation of the results. These issues are discussed in some detail so that prospective users can take guidance for analysing their own data. The data provided by Japanese girls and their parents about the parenting style in their family are the major vehicle for demonstrating the issues touched upon. The general results from these data are that parental styles consisted of three groups of behaviours: Acceptance, Control and Rejection, and Discipline. Within families the parenting behaviours of fathers and mothers are seen as parallel rather than at cross purposes, both by the daughters and the parents themselves. Moreover, daughters and parents largely agree about the parenting style itself. Notwithstanding, there are also families in which daughters and parents disagree about the parenting style in particular about Acceptance and Control, but not about Discipline.