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On insensitivity of the chi-square model test to non-linear misspecification in structural equation models
Ab Mooijaart,Albert Satorra +1 more
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In this paper, the authors show that the classical chi-square goodness-of-fit test is unable to detect the presence of interaction (non-linear) terms in the model and explain this phenomenon by exploiting results on asymptotic robustness (AR) in structural equation models.Abstract:
In this note we show that for some structural equation models (SEM), the classical chi-square goodness-of-fit test is unable to detect the presence of interaction (non-linear) terms in the model. Not only the model test has zero power against that type of misspecifications, but even the theoretical (chi-square) distribution of the test is not distorted when severe interaction term misspecification is present in the postulated model. We explain this phenomenon by exploiting results on asymptotic robustness (AR) in structural equation models. The importance of this paper is to warn against the conclusion that if a proposed linear model fits the data well according to the chi-quare goodness-of-fit test, then the underlying model is linear indeed; it will be shown that the underlying model may in fact be be severely nonlinear. In addition, the present paper shows that such insensitivity to interaction terms is only a particular instance of a more general problem, namely, the incapacity of the classical chi-square goodness-of-fit test to detect deviations from zero correlation among exogenous regressors (either being them observable, or latent) when the structural part of the model is just saturated.read more
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MonographDOI
Structural Equation Modeling
TL;DR: Structural equation modeling, structural equation modeling (SEM), Structural equation modelling (SME), this paper, Structural EDE (SDE), structural equation model (SEM)
Journal ArticleDOI
Probing for the multiplicative term in modern expectancy-value theory: a latent interaction modeling study
Ulrich Trautwein,Herbert W. Marsh,Benjamin Nagengast,Oliver Lüdtke,Gabriel Nagy,Kathrin Jonkmann +5 more
TL;DR: In this article, the authors used latent moderated structural equation modeling to explore whether there is empirical support for a multiplicative effect in a sample of 2,508 students at the end of secondary education.
Reference EntryDOI
23 Structural Equation Modeling
Jodie B. Ullman,Peter M. Bentler +1 more
TL;DR: The first half of this chapter presents an overview of the type hypotheses, statistical theory, and major issues relevant to specifying, estimating, evaluating, and interpreting structural equation models as discussed by the authors.
Journal ArticleDOI
Toward a comprehensive understanding of executive cognitive function in implicit racial bias.
Tiffany A. Ito,Naomi P. Friedman,Bruce D. Bartholow,Joshua Correll,Chris Loersch,Lee J. Altamirano,Akira Miyake +6 more
TL;DR: The main findings were that measures of implicit bias were only weakly intercorrelated, and EF and estimates of automatic processes both predicted implicit bias and also interacted, such that the relation between automatic processes and bias expression was reduced at higher levels of EF.
Journal ArticleDOI
Estimating Latent Variable Interactions With Nonnormal Observed Data: A Comparison of Four Approaches
TL;DR: A Monte Carlo simulation was conducted to investigate the robustness of 4 latent variable interaction modeling approaches under high degrees of nonnormality of the observed exogenous variables, showing that the CPI and LMS approaches yielded biased estimates of the interaction effect when theExogenous variables were highly nonnormal.
References
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Measures of multivariate skewness and kurtosis with applications
TL;DR: In this article, the authors developed measures of multivariate skewness and kurtosis by extending certain studies on robustness of the t statistic, and the asymptotic distributions of the measures for samples from a multivariate normal population are derived and a test for multivariate normality is proposed.
Corrections to test statistics and standard errors in covariance structure analysis. In: Eye AV, Clogg CC ed. Latent variables analysis: Applications for developmental research. Thousand Oaks, CA: Sage.
A Satorra,PM Bentler +1 more
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Asymptotically distribution‐free methods for the analysis of covariance structures
TL;DR: Methods for obtaining tests of fit of structural models for covariance matrices and estimator standard errors which are asymptotically distribution free are derived.
Journal ArticleDOI
Maximum likelihood estimation of latent interaction effects with the LMS method
TL;DR: The Latent Moderated Structural Equations (LMS) as mentioned in this paper approach is a new method developed for the analysis of the general interaction model that utilizes the mixture distribution and provides a ML estimation of model parameters by adapting the EM algorithm.
BookDOI
Advanced structural equation modeling : issues and techniques
TL;DR: In this article, the Kenny-Judd model with interaction effects is used for cross-domain analysis of change over time, combining growth modeling and covariance structure analysis, and a limited-information estimator for LISREL models with or without Heteroscedastic Errors is presented.