Abstract
A new approach to structural equation modelling based on so-called Extended Redundancy Analysis has been recently proposed in literature, enhanced with the added characteristic of generalizing Redundancy Analysis and Reduced-Rank Regression models for more than two blocks. However, in presence of direct effects linking exogenous and endogenous variables, the latent composite scores are estimated by ignoring the presence of the specified direct effects. In this paper, we extend Extended Redundancy Analysis, permitting us to specify and fit a variety of relationships among latent composites and endogenous variables. In particular, covariates are allowed to affect endogenous indicators indirectly through the latent composites and/or directly.
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
References
Bougeard, S., Hanafi, M., Lupo, C., & Qannari, E. M. (2008). From multiblock Partial Least Squares to multiblock redundancy analysis. In A continuum approach. International Conference on Computational Statistics. Porto, Portugal.
Davies, P., & Tso, M. (1982). Procedures for reduced-rank regression. Applied Statistics, 31, 244–255.
Izenman, A. J. (1975). Reduced-rank regression for the multivariate linear model. Journal of Multivariate Analysis, 5, 248–264.
Jôreskog, K. G. (1970). A general method for analysis of covariance structures. Biometrika, 57, 409–426.
Kiers, H. A. L., Takane, Y., & ten Berge, J. M. F. (1996). The analysis of multitrait-multimethod matrices via constrained components analysis. Psychometrika, 61, 601–628.
McDonald, R. P. (1996). Path analysis with composite variables. Multivariate Behavioral Research, 31, 239–270.
Millsap, R. E., & Meredith, W. (1988). Component analysis in cross-sectional and longitudinal data. Psychometrika, 53, 123–134.
Reinsel, G. C., & Velu, R. P. (1998). Multivariate reduced-rank regression. New York: Springer.
Schônemann, P. H., & Steiger, J. H. (1976). Regression component analysis. British Journal of Mathematical and Statistical Psychology, 29, 175–189.
Takane, Y., & Hwang, H. (2005). An extended redundancy analysis and its applications to two practical examples. CSDA, 49(3), 785–808.
ten Berge, J. M. F. (1993). Least squares optimization in multivariate analysis. Leiden: DSWO.
van den Wollenberg, A. L. (1977). Redundancy analysis: an alternative for canonical analysis. Psychometrika, 42, 207–219.
Wold, H. (1982). Soft modeling: The basic design and some extensions. In K. G Jôreskog and H. Wold (Eds.). Systems under indirect observations: causality, structure, prediction. Part 2, (pp. 1–54). North-Holland, Amsterdam.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer International Publishing Switzerland
About this paper
Cite this paper
Lovaglio, P.G., Vittadini, G. (2013). Component Analysis for Structural Equation Models with Concomitant Indicators. In: Giudici, P., Ingrassia, S., Vichi, M. (eds) Statistical Models for Data Analysis. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Heidelberg. https://doi.org/10.1007/978-3-319-00032-9_24
Download citation
DOI: https://doi.org/10.1007/978-3-319-00032-9_24
Published:
Publisher Name: Springer, Heidelberg
Print ISBN: 978-3-319-00031-2
Online ISBN: 978-3-319-00032-9
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)