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Journal ArticleDOI: 10.1080/10705511.2020.1761808

Bayesian estimation of single and multilevel models with latent variable interactions

04 Mar 2021-Structural Equation Modeling (Routledge)-Vol. 28, Iss: 2, pp 314-328
Abstract: In this article, we discuss single and multilevel SEM models with latent variable interactions We describe the Bayesian estimation for these models and show through simulation studies that the Bay

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Topics: Latent variable (63%), Multilevel model (61%), Bayesian probability (54%) ... show more

13 results found

Open access
09 Oct 2008-
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.

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Topics: Linear model (57%)

38 Citations

Journal ArticleDOI: 10.1080/10705511.2020.1855076
Steffen Zitzmann1, Christoph HelmInstitutions (1)
Abstract: In the analysis of hierarchical data, multilevel structural equation modeling (multilevel SEM) has become the standard in the social sciences. To estimate these models, maximum likelihood (ML) appr...

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7 Citations

Open accessJournal ArticleDOI: 10.1177/2397002220968188
Abstract: Information and communication technologies facilitate connectivity to work-related matters after official working hours. Therefore, more and more employees engage in technology-assisted supplementa...

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4 Citations

Journal ArticleDOI: 10.1080/10705511.2021.1922283
Kyle Cox1, Benjamin Kelcey2Institutions (2)
Abstract: Estimation of structural equation model (SEM) parameters is frequently complicated by the inclusion of latent interactions. A computationally simple sequential estimation approach using corrections...

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Topics: Sequential estimation (64%), Bayes estimator (51%)

2 Citations


25 results found

Open access
01 Jan 2016-
Abstract: Thank you for downloading introduction to multivariate statistical analysis. Maybe you have knowledge that, people have look hundreds times for their favorite books like this introduction to multivariate statistical analysis, but end up in infectious downloads. Rather than reading a good book with a cup of tea in the afternoon, instead they cope with some harmful bugs inside their desktop computer. introduction to multivariate statistical analysis is available in our digital library an online access to it is set as public so you can get it instantly. Our books collection hosts in multiple countries, allowing you to get the most less latency time to download any of our books like this one. Merely said, the introduction to multivariate statistical analysis is universally compatible with any devices to read.

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Topics: Multivariate analysis (74%)

3,066 Citations

Journal ArticleDOI: 10.1007/BF02296338
01 Dec 2000-Psychometrika
Abstract: In the context of structural equation modeling, a general interaction model with multiple latent interaction effects is introduced. A stochastic analysis represents the nonnormal distribution of the joint indicator vector as a finite mixture of normal distributions. The Latent Moderated Structural Equations (LMS) 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. The finite sample properties and the robustness of LMS are discussed. Finally, the applicability of the new method is illustrated by an empirical example.

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965 Citations

Journal ArticleDOI: 10.1037/A0026802
Abstract: This article proposes a new approach to factor analysis and structural equation modeling using Bayesian analysis. The new approach replaces parameter specifications of exact zeros with approximate zeros based on informative, small-variance priors. It is argued that this produces an analysis that better reflects substantive theories. The proposed Bayesian approach is particularly beneficial in applications where parameters are added to a conventional model such that a nonidentified model is obtained if maximum-likelihood estimation is applied. This approach is useful for measurement aspects of latent variable modeling, such as with confirmatory factor analysis, and the measurement part of structural equation modeling. Two application areas are studied, cross-loadings and residual correlations in confirmatory factor analysis. An example using a full structural equation model is also presented, showing an efficient way to find model misspecification. The approach encompasses 3 elements: model testing using posterior predictive checking, model estimation, and model modification. Monte Carlo simulations and real data are analyzed using Mplus. The real-data analyses use data from Holzinger and Swineford's (1939) classic mental abilities study, Big Five personality factor data from a British survey, and science achievement data from the National Educational Longitudinal Study of 1988.

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852 Citations

Journal ArticleDOI: 10.1037/1082-989X.9.3.275
Herbert W. Marsh1, Zhonglin Wen2, Kit-Tai Hau3Institutions (3)
Abstract: Interactions between (multiple indicator) latent variables are rarely used because of implementation complexity and competing strategies. Based on 4 simulation studies, the traditional constrained approach performed more poorly than did 3 new approaches--unconstrained, generalized appended product indicator, and quasi-maximum-likelihood (QML). The authors' new unconstrained approach was easiest to apply. All 4 approaches were relatively unbiased for normally distributed indicators, but the constrained and QML approaches were more biased for nonnormal data; the size and direction of the bias varied with the distribution but not with the sample size. QML had more power, but this advantage was qualified by consistently higher Type I error rates. The authors also compared general strategies for defining product indicators to represent the latent interaction factor.

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770 Citations

Open accessJournal ArticleDOI: 10.1037/A0012869
Abstract: In multilevel modeling (MLM), group-level (L2) characteristics are often measured by aggregating individual-level (L1) characteristics within each group so as to assess contextual effects (e.g., group-average effects of socioeconomic status, achievement, climate). Most previous applications have used a multilevel manifest covariate (MMC) approach, in which the observed (manifest) group mean is assumed to be perfectly reliable. This article demonstrates mathematically and with simulation results that this MMC approach can result in substantially biased estimates of contextual effects and can substantially underestimate the associated standard errors, depending on the number of L1 individuals per group, the number of groups, the intraclass correlation, the sampling ratio (the percentage of cases within each group sampled), and the nature of the data. To address this pervasive problem, the authors introduce a new multilevel latent covariate (MLC) approach that corrects for unreliability at L2 and results in unbiased estimates of L2 constructs under appropriate conditions. However, under some circumstances when the sampling ratio approaches 100%, the MMC approach provides more accurate estimates. Based on 3 simulations and 2 real-data applications, the authors evaluate the MMC and MLC approaches and suggest when researchers should most appropriately use one, the other, or a combination of both approaches.

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Topics: Covariate (57%), Latent variable model (53%), Multilevel model (52%)

529 Citations

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