Analysis of Correlation Structures: Current Status and Open Problems

Bentler, Peter M.; Savalei, Victoria

doi:10.1002/9780470583333.ch1

Cited by 11 publications

(7 citation statements)

References 104 publications

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“…A goodness‐of‐fit test can then be obtained by rescaling T so that, for example, its mean and variance equal those of a chi‐square variate with d degrees of freedom. In the latter case, T is generally not χ 2 ‐distributed, but can well be approximated by a χ 2 distribution with d degrees of freedom (Bentler & Savalei, 2010, p. 14). We obtained these mean‐ and‐variance‐adjusted statistics for the ULS and the DWLS estimators by implementing the formula as suggested, for instance, in Bentler and Savalei (2010, equation 1.25); for the PIV estimator, we used the equations given in Bollen and Maydeu‐Oilvares (2007).…”

Section: Methodsmentioning

confidence: 99%

“…To estimate the model parameters, Σ is substituted by the matrix of tetrachoric correlations between the binary responses, P, and Θ is set to Θ = I− ΛΨΛ T . The latter is done to identify the model but has the consequence that the error variances are no longer model parameters, and, more generally, that a correlation structure is analysed (see Bentler & Salavei, 2010, for an overview on the analysis of correlation structures; see also Muthén, & Asparouhov, 2002, for an approach for analysing covariance structures when there are binary indicators). Furthermore, it can be shown that the dichotomous factor analysis model is mathematically equivalent to the normal ogive version of the two‐parameter item response model and to the graded response model (see McDonald, 1999; Bollen, Bauer, Christ, & Edwards, 2010).…”

Section: The Dichotomous Factor Analysis Modelmentioning

confidence: 99%

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A Monte Carlo study comparing PIV, ULS and DWLS in the estimation of dichotomous confirmatory factor analysis

Nestler

2012

Brit J Math & Statis

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We conducted a Monte Carlo study to investigate the performance of the polychoric instrumental variable estimator (PIV) in comparison to unweighted least squares (ULS) and diagonally weighted least squares (DWLS) in the estimation of a confirmatory factor analysis model with dichotomous indicators. The simulation involved 144 conditions (1,000 replications per condition) that were defined by a combination of (a) two types of latent factor models, (b) four sample sizes (100, 250, 500, 1,000), (c) three factor loadings (low, moderate, strong), (d) three levels of non-normality (normal, moderately, and extremely non-normal), and (e) whether the factor model was correctly specified or misspecified. The results showed that when the model was correctly specified, PIV produced estimates that were as accurate as ULS and DWLS. Furthermore, the simulation showed that PIV was more robust to structural misspecifications than ULS and DWLS.

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Section: Methodsmentioning

confidence: 99%

Section: The Dichotomous Factor Analysis Modelmentioning

confidence: 99%

A Monte Carlo study comparing PIV, ULS and DWLS in the estimation of dichotomous confirmatory factor analysis

Nestler

2012

Brit J Math & Statis

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“…Cheung () proposed using the WLS estimation method to fit the model. The discrepancy function (e.g., Bentler & Savalei, ) is

F_{normalW normalL normalS} ((), θ) = {(r_{normalR} - ρ_{normalR} (θ))}^{T} V_{r}^{- 1} ((), r_{R} - ρ_{R} ((), θ)) .

…”

Section: Random‐effects Models In Meta‐analytic Structural Equation Mmentioning

confidence: 99%

“…which means that the average population correlation vector ρ R is a function of some parameters θ. M. W.-L. Cheung (2014) proposed using the WLS estimation method to fit the model. The discrepancy function (e.g., Bentler & Savalei, 2010) is…”

Section: Stage 2 Analysismentioning

confidence: 99%

Random‐effects models for meta‐analytic structural equation modeling: review, issues, and illustrations

Cheung

2016

Research Synthesis Methods

100

124

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Meta-analytic structural equation modeling (MASEM) combines the techniques of meta-analysis and structural equation modeling for the purpose of synthesizing correlation or covariance matrices and fitting structural equation models on the pooled correlation or covariance matrix. Both fixed-effects and random-effects models can be defined in MASEM. Random-effects models are well known in conventional meta-analysis but are less studied in MASEM. The primary objective of this paper was to address issues related to random-effects models in MASEM. Specifically, we compared two different random-effects models in MASEM-correlation-based MASEM and parameter-based MASEM-and explored their strengths and limitations. Two examples were used to illustrate the similarities and differences between these models. We offered some practical guidelines for choosing between these two models. Future directions for research on random-effects models in MASEM were also discussed. Copyright © 2016 John Wiley & Sons, Ltd.

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“…Of course, there are situations where variances matter, such as when testing invariance of factor structures across groups. For a summary on the role and limitations of correlation structures, see Bentler (2007) or Bentler and Savalei (2010).…”

Section: Simplicity Versus Complexity In Semmentioning

confidence: 99%

SEM with simplicity and accuracy

Bentler

2010

J Consum Psychol

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Professor Iacobucci has provided a useful introduction to the computer program LISREL, as well as to several technical topics in structural equation modeling (SEM). However, SEM has not been synonymous with LISREL for several decades, and focusing on LISREL’s 13 Greek matrices and vectors is not the most intuitive way to learn SEM. It is possible today to do model specification via a path diagram without any need for filling in matrix elements. The simplest alternative is based on the Bentler–Weeks model, whose basic concepts are reviewed. Selected additional SEM topics are discussed, including some recent developments and their practical implications. New simulation results on model fit under null and alternative hypotheses are also presented that are consistent with statistical theory but in part seem to contradict those reported by Iacobucci.

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Analysis of Correlation Structures: Current Status and Open Problems

Cited by 11 publications

References 104 publications

A Monte Carlo study comparing PIV, ULS and DWLS in the estimation of dichotomous confirmatory factor analysis

A Monte Carlo study comparing PIV, ULS and DWLS in the estimation of dichotomous confirmatory factor analysis

Random‐effects models for meta‐analytic structural equation modeling: review, issues, and illustrations

SEM with simplicity and accuracy

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