Linear indices in nonlinear structural equation models: best fitting proper indices and other composites

Linear indices in nonlinear structural equation models: best fitting proper indices and other... The recent advent of nonlinear structural equation models with indices poses a new challenge to the measurement of scientific constructs. We discuss, exemplify and add to a family of statistical methods aimed at creating linear indices, and compare their suitability in a complex path model with linear and moderating relationships. The composites used include principal components, generalized canonical variables, partial least squares, factor extraction (‘LISREL’), and a newly developed method: best fitting proper indices. The latter involves the construction of linear combinations of indicators that maximize the fit of (non-)linear structural equations in terms of these indices; the weights as well as the loadings of the indicators are sign restricted so that each indicator contributes to as well as reflects its own index in a predefined way. We use cross-validation to evaluate the methods employed, and analyze the most general situation with a complete interaction specification using the bootstrap. The methods are exemplified using an empirical data set. An additional novel feature is the use of simulations to delineate the range of the possible parameter estimates. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quality & Quantity Springer Journals

Linear indices in nonlinear structural equation models: best fitting proper indices and other composites

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Publisher
Springer Journals
Copyright
Copyright © 2011 by Springer Science+Business Media B.V.
Subject
Social Sciences; Methodology of the Social Sciences; Social Sciences, general
ISSN
0033-5177
eISSN
1573-7845
D.O.I.
10.1007/s11135-010-9359-z
Publisher site
See Article on Publisher Site

Abstract

The recent advent of nonlinear structural equation models with indices poses a new challenge to the measurement of scientific constructs. We discuss, exemplify and add to a family of statistical methods aimed at creating linear indices, and compare their suitability in a complex path model with linear and moderating relationships. The composites used include principal components, generalized canonical variables, partial least squares, factor extraction (‘LISREL’), and a newly developed method: best fitting proper indices. The latter involves the construction of linear combinations of indicators that maximize the fit of (non-)linear structural equations in terms of these indices; the weights as well as the loadings of the indicators are sign restricted so that each indicator contributes to as well as reflects its own index in a predefined way. We use cross-validation to evaluate the methods employed, and analyze the most general situation with a complete interaction specification using the bootstrap. The methods are exemplified using an empirical data set. An additional novel feature is the use of simulations to delineate the range of the possible parameter estimates.

Journal

Quality & QuantitySpringer Journals

Published: Aug 11, 2011

References

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