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Consistent Partial Least Squares for Nonlinear Structural Equation Models

Published online by Cambridge University Press:  01 January 2025

Theo K. Dijkstra  and
Karin Schermelleh-Engel
Theo K. Dijkstra*
Affiliation:
University of Groningen
Karin Schermelleh-Engel
Affiliation:
University of Frankfurt
*
Requests for reprints should be sent to Theo K. Dijkstra, Department of Economics, Econometrics & Finance, University of Groningen, Groningen, The Netherlands. E-mail: t.k.dijkstra@rug.nl
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Abstract

Partial Least Squares as applied to models with latent variables, measured indirectly by indicators, is well-known to be inconsistent. The linear compounds of indicators that PLS substitutes for the latent variables do not obey the equations that the latter satisfy. We propose simple, non-iterative corrections leading to consistent and asymptotically normal (CAN)-estimators for the loadings and for the correlations between the latent variables. Moreover, we show how to obtain CAN-estimators for the parameters of structural recursive systems of equations, containing linear and interaction terms, without the need to specify a particular joint distribution. If quadratic and higher order terms are included, the approach will produce CAN-estimators as well when predictor variables and error terms are jointly normal. We compare the adjusted PLS, denoted by PLSc, with Latent Moderated Structural Equations (LMS), using Monte Carlo studies and an empirical application.

Keywords

consistent partial least squareslatent moderated structural equationsnonlinear structural equation modelinteraction effectquadratic effect
Type
Original Paper
Information
Psychometrika , Volume 79 , Issue 4 , October 2014 , pp. 585 - 604
Copyright
Copyright © 2013 The Psychometric Society

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