A Note on Testing Mediated Effects in Structural Equation Models

Methods to assess the significance of mediated effects in education and the social sciences are well studied and fall into two categories: single sample methods and computer-intensive methods. A popular single sample method to detect the significance of the mediated effect is the test of joint significance, and a popular computer-intensive method to detect the significance of the mediated effect is the bias-corrected bootstrap method. Both these methods are used for testing the significance of mediated effects in structural equation models (SEMs). A recent study by Leth-Steensen and Gallitto 2016 provided evidence that the test of joint significance was more powerful than the bias-corrected bootstrap method for detecting mediated effects in SEMs, which is inconsistent with previous research on the topic. The goal of this article was to investigate this surprising result and describe two issues related to testing the significance of mediated effects in SEMs which explain the inconsistent results regarding the power of the test of joint significance and the bias-corrected bootstrap found by Leth-Steensen and Gallitto 2016. The first issue was that the bias-corrected bootstrap method was conducted incorrectly. The bias-corrected bootstrap was used to estimate the standard error of the mediated effect as opposed to creating confidence intervals. The second issue was that the correlation between the path coefficients of the mediated effect was ignored as an important aspect of testing the significance of the mediated effect in SEMs. The results of the replication study confirmed prior research on testing the significance of mediated effects. That is, the bias-corrected bootstrap method was more powerful than the test of joint significance, and the bias-corrected bootstrap method had elevated Type 1 error rates in some cases. Additional methods for testing the significance of mediated effects in SEMs were considered and limitations and future directions were discussed.

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The Robustness of the Likelihood Ratio Chi-Square Test for Structural Equation Models: A Meta-Analysis

Journal of Educational and Behavioral Statistics ◽

10.3102/10769986026001105 ◽

2001 ◽

Vol 26 (1) ◽

pp. 105-132 ◽

Cited By ~ 30

Author(s):

Douglas A. Powell ◽

William D. Schafer

Keyword(s):

Structural Equation ◽

Structural Equation Models ◽

Type I Error ◽

Meta Analysis ◽

Generalized Least Squares ◽

Error Rates ◽

Type I ◽

Chi Square ◽

Distribution Free ◽

Projection Techniques

The robustness literature for the structural equation model was synthesized following the method of Harwell which employs meta-analysis as developed by Hedges and Vevea. The study focused on the explanation of empirical Type I error rates for six principal classes of estimators: two that assume multivariate normality (maximum likelihood and generalized least squares), elliptical estimators, two distribution-free estimators (asymptotic and others), and latent projection. Generally, the chi-square tests for overall model fit were found to be sensitive to non-normality and the size of the model for all estimators (with the possible exception of the elliptical estimators with respect to model size and the latent projection techniques with respect to non-normality). The asymptotic distribution-free (ADF) and latent projection techniques were also found to be sensitive to sample sizes. Distribution-free methods other than ADF showed, in general, much less sensitivity to all factors considered.

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The influence of culture on care receivers’ satisfaction and aggressive tendencies in the emergency department

PLoS ONE ◽

10.1371/journal.pone.0256513 ◽

2021 ◽

Vol 16 (9) ◽

pp. e0256513

Author(s):

Alon Lisak ◽

Dorit Efrat-Treister ◽

Ella Glikson ◽

Vladimir Zeldetz ◽

Dan Schwarzfuchs

Keyword(s):

Emergency Department ◽

Structural Equation ◽

Structural Equation Models ◽

Bootstrap Method ◽

Minority Group ◽

Psychological Benefits ◽

Cultural Characteristics ◽

Cultural Affiliation ◽

Cultural Minority ◽

Survey Responses

Introduction Reducing aggressive tendencies among care receivers in the emergency department has great economic and psychological benefits for care receivers, staff, and health care organizations. In a study conducted in a large multicultural hospital emergency department, we examined how cultural factors relating to ethnicity interact to enhance care receivers’ satisfaction and reduce their aggressive tendencies. Specifically, we explored how care receivers’ cultural affiliation, individual cultural characteristics, and the cultural situational setting interact to increase care receivers’ satisfaction and reduce their aggressive tendencies. Method Data were collected using survey responses from 214 care receivers. We use structural equation models and the bootstrap method to analyze the data. Results Care receivers’ openness to diversity (an individual cultural characteristic) was positively related to their satisfaction that was associated with lower aggressive tendencies, only when they were affiliated with a cultural minority group and when the cultural situational setting included language accessibility. Conclusion Our results demonstrate that cultural affiliation, individual cultural characteristics, and cultural situational setting can affect care receivers’ satisfaction and aggressive tendencies in a multicultural emergency department context. In particular, high cultural openness of care receivers, and making information accessible in their native language, increased satisfaction and reduced aggressive tendencies among cultural minority care receivers in our study.

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Measuring the Big Five in Self-Report and Other Ratings

European Journal of Psychological Assessment ◽

10.1027//1015-5759.16.1.31 ◽

2000 ◽

Vol 16 (1) ◽

pp. 31-43 ◽

Cited By ~ 24

Author(s):

Claudio Barbaranelli ◽

Gian Vittorio Caprara

Keyword(s):

Big Five ◽

Structural Equation ◽

Structural Equation Models ◽

Error Variance ◽

The Self ◽

Self Report ◽

Sources Of Information ◽

Third Person ◽

Fit Indexes ◽

Response Modes

Summary: The aim of the study is to assess the construct validity of two different measures of the Big Five, matching two “response modes” (phrase-questionnaire and list of adjectives) and two sources of information or raters (self-report and other ratings). Two-hundred subjects, equally divided in males and females, were administered the self-report versions of the Big Five Questionnaire (BFQ) and the Big Five Observer (BFO), a list of bipolar pairs of adjectives ( Caprara, Barbaranelli, & Borgogni, 1993 , 1994 ). Every subject was rated by six acquaintances, then aggregated by means of the same instruments used for the self-report, but worded in a third-person format. The multitrait-multimethod matrix derived from these measures was then analyzed via Structural Equation Models according to the criteria proposed by Widaman (1985) , Marsh (1989) , and Bagozzi (1994) . In particular, four different models were compared. While the global fit indexes of the models were only moderate, convergent and discriminant validities were clearly supported, and method and error variance were moderate or low.

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Collective Efficacy and Organizational Commitment in an Italian City Hall

European Psychologist ◽

10.1027/1016-9040.14.4.363 ◽

2009 ◽

Vol 14 (4) ◽

pp. 363-371 ◽

Cited By ~ 14

Author(s):

Laura Borgogni ◽

Silvia Dello Russo ◽

Laura Petitta ◽

Gary P. Latham

Keyword(s):

Organizational Commitment ◽

Collective Efficacy ◽

Structural Equation ◽

Structural Equation Models ◽

Practical Significance ◽

City Hall ◽

Italian City ◽

Public Sector Managers ◽

The Individual ◽

Level Group

Employees (N = 170) of a City Hall in Italy were administered a questionnaire measuring collective efficacy (CE), perceptions of context (PoC), and organizational commitment (OC). Two facets of collective efficacy were identified, namely group and organizational. Structural equation models revealed that perceptions of top management display a stronger relationship with organizational collective efficacy, whereas employees’ perceptions of their colleagues and their direct superior are related to collective efficacy at the group level. Group collective efficacy had a stronger relationship with affective organizational commitment than did organizational collective efficacy. The theoretical significance of this study is in showing that CE is two-dimensional rather than unidimensional. The practical significance of this finding is that the PoC model provides a framework that public sector managers can use to increase the efficacy of the organization as a whole as well as the individual groups that compose it.

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A Cautionary Note on Incremental Fit Indices Reported by LISREL

Methodology ◽

10.1027/1614-1881.1.2.81 ◽

2005 ◽

Vol 1 (2) ◽

pp. 81-85 ◽

Cited By ~ 5

Author(s):

Stefan C. Schmukle ◽

Jochen Hardt

Keyword(s):

Factor Analysis ◽

Maximum Likelihood ◽

Structural Equation ◽

Structural Equation Models ◽

Null Model ◽

Likelihood Estimation ◽

Parameter Estimates ◽

Fit Indices ◽

Cautionary Note ◽

Confirmatory Factor

Abstract. Incremental fit indices (IFIs) are regularly used when assessing the fit of structural equation models. IFIs are based on the comparison of the fit of a target model with that of a null model. For maximum-likelihood estimation, IFIs are usually computed by using the χ2 statistics of the maximum-likelihood fitting function (ML-χ2). However, LISREL recently changed the computation of IFIs. Since version 8.52, IFIs reported by LISREL are based on the χ2 statistics of the reweighted least squares fitting function (RLS-χ2). Although both functions lead to the same maximum-likelihood parameter estimates, the two χ2 statistics reach different values. Because these differences are especially large for null models, IFIs are affected in particular. Consequently, RLS-χ2 based IFIs in combination with conventional cut-off values explored for ML-χ2 based IFIs may lead to a wrong acceptance of models. We demonstrate this point by a confirmatory factor analysis in a sample of 2449 subjects.

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Forced Zero Cross-Loading Misspecifications in Measurement Component of Structural Equation Models

Methodology ◽

10.1027/1614-2241/a000084 ◽

2014 ◽

Vol 10 (4) ◽

pp. 138-152 ◽

Cited By ~ 5

Author(s):

Hsien-Yuan Hsu ◽

Susan Troncoso Skidmore ◽

Yan Li ◽

Bruce Thompson

Keyword(s):

Structural Equation ◽

Structural Model ◽

Structural Equation Models ◽

Equation Model ◽

Model Fit ◽

Model Specification ◽

Simulation Design ◽

Measurement Models ◽

Fit Statistics ◽

Path Coefficients

The purpose of the present paper was to evaluate the effect of constraining near-zero parameter cross-loadings to zero in the measurement component of a structural equation model. A Monte Carlo 3 × 5 × 2 simulation design was conducted (i.e., sample sizes of 200, 600, and 1,000; parameter cross-loadings of 0.07, 0.10, 0.13, 0.16, and 0.19 misspecified to be zero; and parameter path coefficients in the structural model of either 0.50 or 0.70). Results indicated that factor pattern coefficients and factor covariances were overestimated in measurement models when near-zero parameter cross-loadings constrained to zero were higher than 0.13 in the population. Moreover, the path coefficients between factors were misestimated when the near-zero parameter cross-loadings constrained to zero were noteworthy. Our results add to the literature detailing the importance of testing individual model specification decisions, and not simply evaluating omnibus model fit statistics.

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