Introduction of a new measure for detecting poor fit due to omitted nonlinear terms in SEM
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The model chi-square that is used in linear structural equation modeling compares the fitted covariance matrix of a target model to an unstructured covariance matrix to assess global fit. For models with nonlinear terms, i.e., interaction or quadratic terms, this comparison is very problematic because these models are not nested within the saturated model that is represented by the unstructured covariance matrix. We propose a novel measure that quantifies the heteroscedasticity of residuals in structural equation models. It is based on a comparison of the likelihood for the residuals under the assumption of heteroscedasticity with the likelihood under the assumption of homoscedasticity. The measure is designed to respond to omitted nonlinear terms in the structural part of the model that result in heteroscedastic residual scores. In a small Monte Carlo study, we demonstrate that the measure appears to detect omitted nonlinear terms reliably when falsely a linear model is analyzed and the omitted nonlinear terms account for substantial nonlinear effects. The results also indicate that the measure did not respond when the correct model or an overparameterized model were used.
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- Introduction of a new measure for detecting poor fit due to omitted nonlinear terms in SEM
AStA Advances in Statistical Analysis
Volume 94, Issue 2 , pp 157-166
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- Print ISSN
- Online ISSN
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- Monte Carlo study
- Nonlinear model
- Structural equation modeling
- Interaction effect
- Quadratic effect
- Industry Sectors
- Author Affiliations
- 1. Department of Psychology, University of Western Ontario, SSC, London, Ontario, N6A 5C2, Canada
- 2. Division of Psychological Research Methods and Evaluation, Department of Psychology, Goethe University, Mertonstrasse 17, Frankfurt am Main, Germany