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1.
A Monte Carlo simulation study was conducted to investigate the effects on structural equation modeling (SEM) fit indexes of sample size, estimation method, and model specification. Based on a balanced experimental design, samples were generated from a prespecified population covariance matrix and fitted to structural equation models with different degrees of model misspecification. Ten SEM fit indexes were studied. Two primary conclusions were suggested: (a) some fit indexes appear to be noncomparable in terms of the information they provide about model fit for misspecified models and (b) estimation method strongly influenced almost all the fit indexes examined, especially for misspecified models. These 2 issues do not seem to have drawn enough attention from SEM practitioners. Future research should study not only different models vis‐à‐vis model complexity, but a wider range of model specification conditions, including correctly specified models and models specified incorrectly to varying degrees.  相似文献   

2.
Fit indexes are an important tool in the evaluation of model fit in structural equation modeling (SEM). Currently, the newest confidence interval (CI) for fit indexes proposed by Zhang and Savalei (2016) is based on the quantiles of a bootstrap sampling distribution at a single level of misspecification. This method, despite a great improvement over naive and model-based bootstrap methods, still suffers from unsatisfactory coverage. In this work, we propose a new method of constructing bootstrap CIs for various fit indexes. This method directly inverts a bootstrap test and produces a CI that involves levels of misspecification that would not be rejected in a bootstrap test. Similar in rationale to a parametric CI of root mean square error of approximation (RMSEA) based on a noncentral χ2 distribution and a profile-likelihood CI of model parameters, this approach is shown to have better performance than the approach of Zhang and Savalei (2016), with more accurate coverage and more efficient widths.  相似文献   

3.
Abstract

Covariance structure analysis provides a useful methodology to test hypotheses about competing structural models. The chi-square goodness of fit test is basically an appropriate test for model evaluation. However, methodologists are particularly concerned about the validity of the test to detect misspecified models in small samples. At the same time, there is the concern of rejecting models with reasonably good fit in large samples. The present Monte Carlo study examined the validity of the chi-square test in different instances of misspecification and sample size. The usefulness of the chi-square difference statistic to compare competing structures and improvement in fit is also addressed.  相似文献   

4.
This study investigated the performance of fit indexes in selecting a covariance structure for longitudinal data. Data were simulated to follow a compound symmetry, first-order autoregressive, first-order moving average, or random-coefficients covariance structure. We examined the ability of the likelihood ratio test (LRT), root mean square error of approximation (RMSEA), comparative fit index (CFI), and Tucker–Lewis Index (TLI) to reject misspecified models with varying degrees of misspecification. With a sample size of 20, RMSEA, CFI, and TLI are high in both Type I and Type II error rates, whereas LRT has a high Type II error rate. With a sample size of 100, these indexes generally have satisfactory performance, but CFI and TLI are affected by a confounding effect of their baseline model. Akaike's Information Criterion (AIC) and Bayesian Information Criterion (BIC) have high success rates in identifying the true model when sample size is 100. A comparison with the mixed model approach indicates that separately modeling the means and covariance structures in structural equation modeling dramatically improves the success rate of AIC and BIC.  相似文献   

5.
Confirmatory factor analytic procedures are routinely implemented to provide evidence of measurement invariance. Current lines of research focus on the accuracy of common analytic steps used in confirmatory factor analysis for invariance testing. However, the few studies that have examined this procedure have done so with perfectly or near perfectly fitting models. In the present study, the authors examined procedures for detecting simulated test structure differences across groups under model misspecification conditions. In particular, they manipulated sample size, number of factors, number of indicators per factor, percentage of a lack of invariance, and model misspecification. Model misspecification was introduced at the factor loading level. They evaluated three criteria for detection of invariance, including the chi-square difference test, the difference in comparative fit index values, and the combination of the two. Results indicate that misspecification was associated with elevated Type I error rates in measurement invariance testing.  相似文献   

6.
Despite its importance to structural equation modeling, model evaluation remains underdeveloped in the Bayesian SEM framework. Posterior predictive p-values (PPP) and deviance information criteria (DIC) are now available in popular software for Bayesian model evaluation, but they remain underutilized. This is largely due to the lack of recommendations for their use. To address this problem, PPP and DIC were evaluated in a series of Monte Carlo simulation studies. The results show that both PPP and DIC are influenced by severity of model misspecification, sample size, model size, and choice of prior. The cutoffs PPP < 0.10 and ?DIC > 7 work best in the conditions and models tested here to maintain low false detection rates and misspecified model selection rates, respectively. The recommendations provided in this study will help researchers evaluate their models in a Bayesian SEM analysis and set the stage for future development and evaluation of Bayesian SEM fit indices.  相似文献   

7.
Data collected from questionnaires are often in ordinal scale. Unweighted least squares (ULS), diagonally weighted least squares (DWLS) and normal-theory maximum likelihood (ML) are commonly used methods to fit structural equation models. Consistency of these estimators demands no structural misspecification. In this article, we conduct a simulation study to compare the equation-by-equation polychoric instrumental variable (PIV) estimation with ULS, DWLS, and ML. Accuracy of PIV for the correctly specified model and robustness of PIV for misspecified models are investigated through a confirmatory factor analysis (CFA) model and a structural equation model with ordinal indicators. The effects of sample size and nonnormality of the underlying continuous variables are also examined. The simulation results show that PIV produces robust factor loading estimates in the CFA model and in structural equation models. PIV also produces robust path coefficient estimates in the model where valid instruments are used. However, robustness highly depends on the validity of instruments.  相似文献   

8.
In previous research (Hu & Bentler, 1998, 1999), 2 conclusions were drawn: standardized root mean squared residual (SRMR) was the most sensitive to misspecified factor covariances, and a group of other fit indexes were most sensitive to misspecified factor loadings. Based on these findings, a 2-index strategy-that is, SRMR coupled with another index-was proposed in model fit assessment to detect potential misspecification in both the structural and measurement model parameters. Based on our reasoning and empirical work presented in this article, we conclude that SRMR is not necessarily most sensitive to misspecified factor covariances (structural model misspecification), the group of indexes (TLI, BL89, RNI, CFI, Gamma hat, Mc, or RMSEA) are not necessarily more sensitive to misspecified factor loadings (measurement model misspecification), and the rationale for the 2-index presentation strategy appears to have questionable validity.  相似文献   

9.
The relation among fit indexes, power, and sample size in structural equation modeling is examined. The noncentrality parameter is required to compute power. The 2 existing methods of computing power have estimated the noncentrality parameter by specifying an alternative hypothesis or alternative fit. These methods cannot be implemented easily and reliably. In this study, 4 fit indexes (RMSEA, CFI, McDonald's Fit Index, and Steiger's gamma) were used to compute the noncentrality parameter and sample size to achieve certain level of power. The resulting power and sample size varied as a function of (a) choice of fit index, (b) number of variables/degrees of freedom, (c) relation among the variables, and (d) value of the fit index. However, if the level of misspecification were held constant, then the resulting power and sample size would be identical.  相似文献   

10.
Goodness-of-fit (GOF) indexes provide "rules of thumb"—recommended cutoff values for assessing fit in structural equation modeling. Hu and Bentler (1999) proposed a more rigorous approach to evaluating decision rules based on GOF indexes and, on this basis, proposed new and more stringent cutoff values for many indexes. This article discusses potential problems underlying the hypothesis-testing rationale of their research, which is more appropriate to testing statistical significance than evaluating GOF. Many of their misspecified models resulted in a fit that should have been deemed acceptable according to even their new, more demanding criteria. Hence, rejection of these acceptable-misspecified models should have constituted a Type 1 error (incorrect rejection of an "acceptable" model), leading to the seemingly paradoxical results whereby the probability of correctly rejecting misspecified models decreased substantially with increasing N. In contrast to the application of cutoff values to evaluate each solution in isolation, all the GOF indexes were more effective at identifying differences in misspecification based on nested models. Whereas Hu and Bentler (1999) offered cautions about the use of GOF indexes, current practice seems to have incorporated their new guidelines without sufficient attention to the limitations noted by Hu and Bentler (1999).  相似文献   

11.
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12.
Most researchers acknowledge that virtually all structural equation models (SEMs) are approximations due to violating distributional assumptions and structural misspecifications. There is a large literature on the unmet distributional assumptions, but much less on structural misspecifications. In this paper, we examine the robustness to structural misspecification of the model implied instrumental variable, two-stage least square (MIIV-2SLS) estimator of SEMs. We introduce two types of robustness: robust-unchanged and robust-consistent. We develop new robustness analytic conditions for MIIV-2SLS and illustrate these with hypothetical models, simulated data, and an empirical example. Our conditions enable a researcher to know whether, for example, a structural misspecification in the latent variable model influences the MIIV-2SLS estimator for measurement model equations and vice versa. Similarly, we establish robustness conditions for correlated errors. The new robustness conditions provide guidance on the types of structural misspecifications that affect parameter estimates and they assist in diagnosing the source of detected problems with MIIVs.  相似文献   

13.
Proper model specification is an issue for researchers, regardless of the estimation framework being utilized. Typically, indexes are used to compare the fit of one model to the fit of an alternate model. These indexes only provide an indication of relative fit and do not necessarily point toward proper model specification. There is a procedure in the Bayesian framework called posterior predictive checking that is designed theoretically to detect model misspecification for observed data. However, the performance of the posterior predictive check procedure has thus far not been directly examined under different conditions of mixture model misspecification. This article addresses this task and aims to provide additional insight into whether or not posterior predictive checks can detect model misspecification within the context of Bayesian growth mixture modeling. Results indicate that this procedure can only identify mixture model misspecification under very extreme cases of misspecification.  相似文献   

14.
A problem central to structural equation modeling is measurement model specification error and its propagation into the structural part of nonrecursive latent variable models. Full-information estimation techniques such as maximum likelihood are consistent when the model is correctly specified and the sample size large enough; however, any misspecification within the model can affect parameter estimates in other parts of the model. The goals of this study included comparing the bias, efficiency, and accuracy of hypothesis tests in nonrecursive latent variable models with indirect and direct feedback loops. We compare the performance of maximum likelihood, two-stage least-squares and Bayesian estimators in nonrecursive latent variable models with indirect and direct feedback loops under various degrees of misspecification in small to moderate sample size conditions.  相似文献   

15.
Approximations to the distributions of goodness-of-fit indexes in structural equation modeling are derived with the assumption of multivariate normality and slight misspecification of models. The fit indexes considered in this article are Joreskog and Sorbom's goodness-of-fit index (GFI) and the adjusted GFI, McDonald's absolute GFI, Steiger and Lind's root mean squared error of approximation, Steiger's Γ1 and Γ2, Bentler and Bonett's normed fit index, Bollen's incremental fit index and ρ1, Tucker and Lewis's index ρ2, and Bentler's fit index (McDonald and Marsh's relative noncentrality index). An approximation to the asymptotic covariance matrix for the fit indexes is derived by using the delta method. Furthermore, approximations to the densities of the fit indexes are obtained from the transformations of the asymptotically noncentral chi-square distributed variable. A simulation is carried out to confirm the accuracy of the approximations.  相似文献   

16.
McDonald goodness‐of‐fit indices based on maximum likelihood, asymptotic distribution free, and the Satorra‐Bentler scale correction estimation methods are investigated. Sampling experiments are conducted to assess the magnitude of error for each index under variations in distributional misspecification, structural misspecification, and sample size. The Satorra‐Bentler correction‐based index is shown to have the least error under each distributional misspecification level when the model has correct structural specification. The scaled index also performs adequately when there is minor structural misspecification and distributional misspecification. However, when a model has major structural misspecification with distributional misspecification, none of the estimation methods perform adequately.  相似文献   

17.
Information fit indexes such as Akaike Information Criterion, Consistent Akaike Information Criterion, Bayesian Information Criterion, and the expected cross validation index can be valuable in assessing the relative fit of structural equation models that differ regarding restrictiveness. In cases in which models without mean restrictions (i.e., saturated mean structure) are compared to models with restricted (i.e., modeled) means, one should take account of the presence of means, even if the model is saturated with respect to the means. The failure to do this can result in an incorrect rank order of models in terms of the information fit indexes. We demonstrate this point by an analysis of measurement invariance in a multigroup confirmatory factor model.  相似文献   

18.
The objective was to offer guidelines for applied researchers on how to weigh the consequences of errors made in evaluating measurement invariance (MI) on the assessment of factor mean differences. We conducted a simulation study to supplement the MI literature by focusing on choosing among analysis models with different number of between-group constraints imposed on loadings and intercepts of indicators. Data were generated with varying proportions, patterns, and magnitudes of differences in loadings and intercepts as well as factor mean differences and sample size. Based on the findings, we concluded that researchers who conduct MI analyses should recognize that relaxing as well as imposing constraints can affect Type I error rate, power, and bias of estimates in factor mean differences. In addition, fit indexes can be misleading in making decisions about constraints of loadings and intercepts. We offer suggestions for making MI decisions under uncertainty when assessing factor mean differences.  相似文献   

19.
This study examined the performance of 4 correlation-based fit indexes (marginal and conditional pseudo R 2s; average and conditional concordance correlations) in detecting misspecification in mean structures in growth curve models. Their performance was also compared to that of 4 traditional SEM fit indexes. We found that the marginal pseudo R 2 and average concordance correlation were able to detect misspecification in the marginal mean structure (average change trajectory). The conditional pseudo R 2 and concordance correlation could detect misspecification when it occurred in the conditional mean structure (individual change trajectory) or in both mean structures. Compared to the SEM fit indexes, the correlation-based fit indexes were more robust to sample size but were less robust to data properties such as magnitude of population mean and measurement error. Theoretical and practical implications of the results and directions for future research are discussed.  相似文献   

20.
Conventional null hypothesis testing (NHT) is a very important tool if the ultimate goal is to find a difference or to reject a model. However, the purpose of structural equation modeling (SEM) is to identify a model and use it to account for the relationship among substantive variables. With the setup of NHT, a nonsignificant test statistic does not necessarily imply that the model is correctly specified or the size of misspecification is properly controlled. To overcome this problem, this article proposes to replace NHT by equivalence testing, the goal of which is to endorse a model under a null hypothesis rather than to reject it. Differences and similarities between equivalence testing and NHT are discussed, and new “T-size” terminology is introduced to convey the goodness of the current model under equivalence testing. Adjusted cutoff values of root mean square error of approximation (RMSEA) and comparative fit index (CFI) corresponding to those conventionally used in the literature are obtained to facilitate the understanding of T-size RMSEA and CFI. The single most notable property of equivalence testing is that it allows a researcher to confidently claim that the size of misspecification in the current model is below the T-size RMSEA or CFI, which gives SEM a desirable property to be a scientific methodology. R code for conducting equivalence testing is provided in an appendix.  相似文献   

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