scholarly journals Two-Level Dynamic Structural Equation Models with Small Samples

2019 ◽  
Vol 26 (6) ◽  
pp. 948-966 ◽  
Author(s):  
Daniel McNeish
Keyword(s):  
Structural Equation ◽  
Structural Equation Models ◽  
Small Samples

scholarly journals Correcting measurement error bias in interaction models with small samples

2006 ◽  
Vol 3 (2) ◽  
Author(s):  
Josep Bisbe ◽  
Germà Coenders ◽  
Willem Saris ◽  
Joan Batista-Foguet
Keyword(s):  
Measurement Error ◽  
Least Squares ◽  
Structural Equation ◽  
Structural Equation Models ◽  
Ordinary Least Squares ◽  
Alternative Methods ◽  
Small Samples ◽  
Least Squares Regression ◽  
Interaction Terms ◽  
Error Bias

Several methods have been suggested to estimate non-linear models with interaction terms in the presence of measurement error. Structural equation models eliminate measurement error bias, but require large samples. Ordinary least squares regression on summated scales, regression on factor scores and partial least squares are appropriate for small samples but do not correct measurement error bias. Two stage least squares regression does correct measurement error bias but the results strongly depend on the instrumental variable choice. This article discusses the old disattenuated regression method as an alternative for correcting measurement error in small samples. The method is extended to the case of interaction terms and is illustrated on a model that examines the interaction effect of innovation and style of use of budgets on business performance. Alternative reliability estimates that can be used to disattenuate the estimates are discussed. A comparison is made with the alternative methods. Methods that do not correct for measurement error bias perform very similarly and considerably worse than disattenuated regression.

scholarly journals Using the Standardized Root Mean Squared Residual (SRMR) to Assess Exact Fit in Structural Equation Models

2020 ◽  
pp. 001316442092623 ◽  
Author(s):  
Goran Pavlov ◽  
Alberto Maydeu-Olivares ◽  
Dexin Shi
Keyword(s):  
Asymptotic Approximation ◽  
Structural Equation ◽  
Structural Equation Models ◽  
Small Samples ◽  
Type I ◽  
Current Standard ◽  
Type I Errors ◽  
P Values ◽  
Lr Test ◽  
Small Models

We examine the accuracy of p values obtained using the asymptotic mean and variance (MV) correction to the distribution of the sample standardized root mean squared residual (SRMR) proposed by Maydeu-Olivares to assess the exact fit of SEM models. In a simulation study, we found that under normality, the MV-corrected SRMR statistic provides reasonably accurate Type I errors even in small samples and for large models, clearly outperforming the current standard, that is, the likelihood ratio (LR) test. When data shows excess kurtosis, MV-corrected SRMR p values are only accurate in small models ( p = 10), or in medium-sized models ( p = 30) if no skewness is present and sample sizes are at least 500. Overall, when data are not normal, the MV-corrected LR test seems to outperform the MV-corrected SRMR. We elaborate on these findings by showing that the asymptotic approximation to the mean of the SRMR sampling distribution is quite accurate, while the asymptotic approximation to the standard deviation is not.

scholarly journals Dangers of the Defaults: A Tutorial on the Impact of Default Priors When Using Bayesian SEM With Small Samples

2020 ◽  
Vol 11 ◽  
Author(s):  
Sanne C. Smid ◽  
Sonja D. Winter
Keyword(s):  
Sample Size ◽  
Structural Equation ◽  
Structural Equation Models ◽  
Small Sample ◽  
Small Samples ◽  
Informative Priors ◽  
Prior Distributions ◽  
Shiny App ◽  
Technical Discussion ◽  
The Impact

When Bayesian estimation is used to analyze Structural Equation Models (SEMs), prior distributions need to be specified for all parameters in the model. Many popular software programs offer default prior distributions, which is helpful for novel users and makes Bayesian SEM accessible for a broad audience. However, when the sample size is small, those prior distributions are not always suitable and can lead to untrustworthy results. In this tutorial, we provide a non-technical discussion of the risks associated with the use of default priors in small sample contexts. We discuss how default priors can unintentionally behave as highly informative priors when samples are small. Also, we demonstrate an online educational Shiny app, in which users can explore the impact of varying prior distributions and sample sizes on model results. We discuss how the Shiny app can be used in teaching; provide a reading list with literature on how to specify suitable prior distributions; and discuss guidelines on how to recognize (mis)behaving priors. It is our hope that this tutorial helps to spread awareness of the importance of specifying suitable priors when Bayesian SEM is used with small samples.

Effect Sizes of Model Misfit in Structural Equation Models

Methodology ◽  
2017 ◽  
Vol 13 (Supplement 1) ◽  
pp. 23-30 ◽  
Author(s):  
Alberto Maydeu-Olivares ◽  
Dexin Shi
Keyword(s):  
Structural Equation ◽  
Structural Equation Models ◽  
Model Misspecification ◽  
Covariance Structure ◽  
Effect Sizes ◽  
Small Samples ◽  
Type I ◽  
Model Misfit ◽  
Covariance Structure Models ◽  
Residual Correlations

Abstract. Residual correlations and covariances provide effect sizes of the misfit of covariance structure models. In a simulation study, we found that accurate confidence intervals (CIs) for standardized residual covariances are obtained even in small samples (N = 100), regardless of model size, degree of model misspecification, and data distribution. Standardized residual covariances also provide information about the source of misfit in poorly fitting models. From this viewpoint, they may be considered an alternative to modification indices. We compared the empirical Type I errors and power rates of standardized residual covariances and modification indices and found that both procedures provide nearly identical rates across the simulation conditions investigated. Residual correlations and standardized residual covariances provide very similar results.

Measuring the Big Five in Self-Report and Other Ratings

2000 ◽  
Vol 16 (1) ◽  
pp. 31-43 ◽  
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.

Collective Efficacy and Organizational Commitment in an Italian City Hall

2009 ◽  
Vol 14 (4) ◽  
pp. 363-371 ◽  
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.

A Cautionary Note on Incremental Fit Indices Reported by LISREL

Methodology ◽  
2005 ◽  
Vol 1 (2) ◽  
pp. 81-85 ◽  
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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