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Multidimensional Exploratory Analysis of a Structural Model Using a Class of Generalized Covariance Criteria

In: Proceedings of COMPSTAT'2010

Author

Listed:
  • Xavier Bry

    (I3M, UM2)

  • Thomas Verron

    (SEITA-ITG, SCR)

  • Patrick Redont

    (I3M, UM2)

Abstract

Our aim is to explore a structural model: several variable groups describing the same observations are assumed to be structured around latent dimensions that are linked through a linear model that may have several equations. This type of model is commonly dealt with by methods assuming that the latent dimension in each group is unique. However, conceptual models generally link concepts which are multidimensional. We propose a general class of criteria suitable to measure the quality of a Structural Equation Model (SEM). This class contains the covariance criteria used in PLS Regression and the Multiple Covariance criterion of the SEER method. It also contains quartimax-related criteria. All criteria in the class must be maximized under a unit norm constraint. We give an equivalent unconstrained maximization program, and algorithms to solve it. This maximization is used within a general algorithm named THEME (Thematic Equation Model Exploration), which allows to search the structures of groups for all dimensions useful to the model. THEME extracts locally nested structural component models.

Suggested Citation

  • Xavier Bry & Thomas Verron & Patrick Redont, 2010. "Multidimensional Exploratory Analysis of a Structural Model Using a Class of Generalized Covariance Criteria," Springer Books, in: Yves Lechevallier & Gilbert Saporta (ed.), Proceedings of COMPSTAT'2010, pages 405-412, Springer.
    • Handle: RePEc:spr:sprchp:978-3-7908-2604-3_38
    DOI: 10.1007/978-3-7908-2604-3_38
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