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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
ABSIL, P.-A., MAHOMY, R. and ANDREWS, B. (2005): Convergence of the Iterates of Descent Methods for Analytic Cost Functions, SIAM J. OPTIM., Vol. 16, No. 2, pp. 531-547.
BONNANS, J. F., GILBERT, J. C, LEMARÉCHAL, C. and SAGASTIZÁBAL, C. (1997): Optimisation Numérique, Springer, Mathématiques et Applications, 27.
BRY X., VERRON T.and CAZES P. (2009): Exploring a physico-chemical multi-array explanatory model with a new multiple covariance-based technique: Structural equation exploratory regression, Anal. Chim. Acta, 642, 45–58.
CHIN, W.W., NEWSTED, P.R., (1999): Structural equation modeling analysis with small samples using partial least squares. In: Statistical Strategies for Small Sample Research. Sage, 307–341.
HWANG, H., and TAKANE, Y. (2004): Generalized structured component analysis. Psychometrika, 69, 81-99.
JÖRESKOG, K. G. and WOLD, H. (1982): The ML and PLS techniques for modeling with latent variables: historical and competitive aspects, in Systems under indirect observation, Part 1, 263–270.
LAGEMAN, Ch. (2007): Pointwise convergence of gradient-like systems, Math. Nachr. 280, No. 13-14, 1543-1558.
LOHMÖLLER J.-B. (1989): Latent Variables Path Modeling with Partial Least Squares, Physica-Verlag, Heidelberg.
NOCEDAL, J., WRIGHT, S. J. (1999): Numerical Optimization, Springer, Series in Operations Research.
SMILDE, A.K., WESTERHUIS, J.A. and BOQUÉE, R., (2000): Multiway multiblock component and covariates regression models. J. Chem. 14, 301–331.
TENENHAUS M., VINZI V.E., CHATELIN Y-M. and LAURO C. (2005): PLS path modeling - CSDA, 48, 159-205.
WANGEN L., KOWALSKI B. (1988): A multiblock partial least squares algorithm for investigating complex chemical systems. J. Chem.; 3: 3–20.
WESTERHUIS, J.A., KOURTI and K., MACGREGOR, J.F., (1998): Analysis of multiblock and hierarchical PCA and PLS models. J. Chem. 12, 301–321.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bry, X., Verron, T., Redont, P. (2010). Multidimensional Exploratory Analysis of a Structural Model Using a Class of Generalized Covariance Criteria. In: Lechevallier, Y., Saporta, G. (eds) Proceedings of COMPSTAT'2010. Physica-Verlag HD. https://doi.org/10.1007/978-3-7908-2604-3_38
Download citation
DOI: https://doi.org/10.1007/978-3-7908-2604-3_38
Published:
Publisher Name: Physica-Verlag HD
Print ISBN: 978-3-7908-2603-6
Online ISBN: 978-3-7908-2604-3
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)