TY - JOUR
T1 - Advanced nonlinear latent variable modeling
T2 - Distribution analytic LMS and QML estimators of interaction and quadratic effects
AU - Kelava, Augustin
AU - Werner, Christina S.
AU - Schermelleh-Engel, Karin
AU - Moosbrugger, Helfried
AU - Zapf, Dieter
AU - Ma, Yue
AU - Cham, Heining
AU - Aiken, Leona S.
AU - West, Stephen
N1 - Funding Information:
We would like to thank Associate Editor Deborah Bandalos and the reviewers for providing comments that led to substantial improvements of the article. Stephen G. West was supported by a Forschungspreis (research prize) from the Alexander von Humboldt Foundation.
PY - 2011/7
Y1 - 2011/7
N2 - Interaction and quadratic effects in latent variable models have to date only rarely been tested in practice. Traditional product indicator approaches need to create product indicators (e.g., x21, x1x4) to serve as indicators of each nonlinear latent construct. These approaches require the use of complex nonlinear constraints and additional model specifications and do not directly address the nonnormal distribution of the product terms. In contrast, recently developed, easy-to-use distribution analytic approaches do not use product indicators, but rather directly model the nonlinear multivariate distribution of the measured indicators. This article outlines the theoretical properties of the distribution analytic Latent Moderated Structural Equations (LMS; Klein & Moosbrugger, 2000) and Quasi-Maximum Likelihood (QML; Klein & Muthén, 2007) estimators. It compares the properties of LMS and QML to those of the product indicator approaches.A small simulation study compares the two approaches and illustrates the advantages of the distribution analytic approaches as multicollinearity increases, particularly in complex models with multiple nonlinear terms. An empirical example from the field of work stress applies LMS and QML to a model with an interaction and 2 quadratic effects. Example syntax for the analyses with both approaches is provided.
AB - Interaction and quadratic effects in latent variable models have to date only rarely been tested in practice. Traditional product indicator approaches need to create product indicators (e.g., x21, x1x4) to serve as indicators of each nonlinear latent construct. These approaches require the use of complex nonlinear constraints and additional model specifications and do not directly address the nonnormal distribution of the product terms. In contrast, recently developed, easy-to-use distribution analytic approaches do not use product indicators, but rather directly model the nonlinear multivariate distribution of the measured indicators. This article outlines the theoretical properties of the distribution analytic Latent Moderated Structural Equations (LMS; Klein & Moosbrugger, 2000) and Quasi-Maximum Likelihood (QML; Klein & Muthén, 2007) estimators. It compares the properties of LMS and QML to those of the product indicator approaches.A small simulation study compares the two approaches and illustrates the advantages of the distribution analytic approaches as multicollinearity increases, particularly in complex models with multiple nonlinear terms. An empirical example from the field of work stress applies LMS and QML to a model with an interaction and 2 quadratic effects. Example syntax for the analyses with both approaches is provided.
KW - Estimators
KW - Interaction
KW - Multicollinearity
KW - Nonlinear structural equation models
KW - Quadratic
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U2 - 10.1080/10705511.2011.582408
DO - 10.1080/10705511.2011.582408
M3 - Article
AN - SCOPUS:79960658164
SN - 1070-5511
VL - 18
SP - 465
EP - 491
JO - Structural Equation Modeling
JF - Structural Equation Modeling
IS - 3
ER -