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Psychometrika

, Volume 79, Issue 4, pp 585–604 | Cite as

Consistent Partial Least Squares for Nonlinear Structural Equation Models

  • Theo K. Dijkstra
  • Karin Schermelleh-Engel
Article

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.

Key words

consistent partial least squares latent moderated structural equations nonlinear structural equation model interaction effect quadratic effect 

Notes

Acknowledgements

The authors wish to acknowledge the constructive comments and suggestions by the editor, an associate editor, and three reviewers, which led to substantial improvements in contents and readability.

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Copyright information

© The Psychometric Society 2013

Authors and Affiliations

  1. 1.Department of Economics, Econometrics & FinanceUniversity of GroningenGroningenThe Netherlands
  2. 2.Department of PsychologyGoethe UniversityFrankfurt am MainGermany

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