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1.
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   

2.
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   

3.
Using a complex simulation study we investigated parameter recovery, classification accuracy, and performance of two item‐fit statistics for correct and misspecified diagnostic classification models within a log‐linear modeling framework. The basic manipulated test design factors included the number of respondents (1,000 vs. 10,000), attributes (3 vs. 5), and items (25 vs. 50) as well as different attribute correlations (.50 vs. .80) and marginal attribute difficulties (equal vs. different). We investigated misspecifications of interaction effect parameters under correct Q‐matrix specification and two types of Q‐matrix misspecification. While the misspecification of interaction effects had little impact on classification accuracy, invalid Q‐matrix specifications led to notably decreased classification accuracy. Two proposed item‐fit indexes were more strongly sensitive to overspecification of Q‐matrix entries for items than to underspecification. Information‐based fit indexes AIC and BIC were sensitive to both over‐ and underspecification.  相似文献   

4.
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   

5.
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   

6.
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   

7.
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8.
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   

9.
In the application of the Satorra–Bentler scaling correction, the choices of normal-theory weight matrices (i.e., the model-predicted vs. the sample covariance matrix) in the calculation of the correction remains unclear. Different software programs use different matrices by default. This simulation study investigates the discrepancies due to the weight matrices in the robust chi-square statistics, standard errors, and chi-square-based model fit indexes. This study varies the sample sizes at 100, 200, 500, and 1,000; kurtoses at 0, 7, and 21; and degrees of model misspecification, measured by the population root mean square error of approximation (RMSEA), at 0, .03, .05, .08, .10, and .15. The results favor the use of the model-predicted covariance matrix because it results in less false rejection rates under the correctly specified model, as well as more accurate standard errors across all conditions. For the sample-corrected robust RMSEA, comparative fit index (CFI) and Tucker–Lewis index (TLI), 2 matrices result in negligible differences.  相似文献   

10.
The power of the chi-square test statistic used in structural equation modeling decreases as the absolute value of excess kurtosis of the observed data increases. Excess kurtosis is more likely the smaller the number of item response categories. As a result, fit is likely to improve as the number of item response categories decreases, regardless of the true underlying factor structure or χ2-based fit index used to examine model fit. Equivalently, given a target value of approximate fit (e.g., root mean square error of approximation ≤ .05) a model with more factors is needed to reach it as the number of categories increases. This is true regardless of whether the data are treated as continuous (common factor analysis) or as discrete (ordinal factor analysis). We recommend using a large number of response alternatives (≥ 5) to increase the power to detect incorrect substantive models.  相似文献   

11.
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   

12.
An interval estimation procedure for proportion of explained observed variance in latent curve analysis is discussed, which can be used as an aid in the process of choosing between linear and nonlinear models. The method allows obtaining confidence intervals for the R 2 indexes associated with repeatedly followed measures in longitudinal studies. In addition to facilitating evaluation of local model fit, the approach is helpful for purposes of differentiating between plausible models stipulating different patterns of change over time, and in particular in empirical situations characterized by large samples and high statistical power. The procedure is also applicable in cross-sectional studies, as well as with general structural equation models. The method is illustrated using data from a nationally representative study of older adults.  相似文献   

13.
Structural equation modeling (SEM) techniques were used to compare 5 methods of assessing HIV/AIDS sexual risk in a large prediction model. These were: (a) multiple measures; (b) a single latent factor; (c) modifying the computation of the dependent variables used in Methods 1 and 2 to weight sexual encounters by specific partner risk; (d) use of risk composites, obtained by multiplying number of sexual partners by number of occasions of unprotected sex; and (e) use of risk indexes that assign a number based on responses to general questions about risk behaviors. Data from 452 at‐risk women from a New England community were analyzed in 5 versions of an HIV/AIDS sexual risk prediction model. Models were compared in terms of SEM empirical fit indexes (x2 [df], average absolute standardized residuals, and Comparative Fit Index); significant paths, explained variance, theoretical fit, and simplicity. Results indicate that: (a) multiple measures and latent factor models are preferable to all others by each of the standards of comparison, (b) in the composite dependent variable models, including information about the partners' number of partners provided little additional explained variance beyond knowing the number of occasions of unprotected sex, and (c) dependent measures that did not remain close to Centers for Disease Control criteria may not be adequately predicting HIV/AIDS sexual risk. Several recommendations are presented for selecting an appropriate conceptualization of HIV/AIDS sexual risk.  相似文献   

14.
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   

15.
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   

16.
In this study, the authors investigated incorporating adjusted model fit information into the root mean square error of approximation (RMSEA) fit index. Through Monte Carlo simulation, the usefulness of this adjusted index was evaluated for assessing model adequacy in structural equation modeling when the multivariate normality assumption underlying maximum likelihood estimation is violated. Adjustment to the RMSEA was considered in 2 forms: a rescaling adjustment via the Satorra-Bentler rescaled goodness-of-fit statistic and a bootstrap adjustment via the Bollen and Stine adjusted model p value. Both properly specified and misspecifed models were examined. The adjusted RMSEA was evaluated in terms of the average index value across study conditions and with respect to model rejection rates under tests of exact fit, close fit, and not-close fit.  相似文献   

17.
A paucity of research has compared estimation methods within a measurement invariance (MI) framework and determined if research conclusions using normal-theory maximum likelihood (ML) generalizes to the robust ML (MLR) and weighted least squares means and variance adjusted (WLSMV) estimators. Using ordered categorical data, this simulation study aimed to address these queries by investigating 342 conditions. When testing for metric and scalar invariance, Δχ2 results revealed that Type I error rates varied across estimators (ML, MLR, and WLSMV) with symmetric and asymmetric data. The Δχ2 power varied substantially based on the estimator selected, type of noninvariant indicator, number of noninvariant indicators, and sample size. Although some the changes in approximate fit indexes (ΔAFI) are relatively sample size independent, researchers who use the ΔAFI with WLSMV should use caution, as these statistics do not perform well with misspecified models. As a supplemental analysis, our results evaluate and suggest cutoff values based on previous research.  相似文献   

18.
This study examined the performance of the weighted root mean square residual (WRMR) through a simulation study using confirmatory factor analysis with ordinal data. Values and cut scores for the WRMR were examined, along with a comparison of its performance relative to commonly cited fit indexes. The findings showed that WRMR illustrated worse fit when sample size increased or model misspecification increased. Lower (i.e., better) values of WRMR were observed when nonnormal data were present, there were lower loadings, and when few categories were analyzed. WRMR generally illustrated expected patterns of relations to other well-known fit indexes. In general, a cutoff value of 1.0 appeared to work adequately under the tested conditions and the WRMR values of “good fit” were generally in agreement with other indexes. Users are cautioned that when the fitted model is misspeficifed, the index might provide misleading results under situations where extremely large sample sizes are used.  相似文献   

19.
In social science research, a common topic in multiple regression analysis is to compare the squared multiple correlation coefficients in different populations. Existing methods based on asymptotic theories (Olkin & Finn, 1995) and bootstrapping (Chan, 2009) are available but these can only handle a 2-group comparison. Another method based on structural equation modeling (SEM) has been proposed recently. However, this method has three disadvantages. First, it requires the user to explicitly specify the sample R2 as a function in terms of the basic SEM model parameters, which is sometimes troublesome and error prone. Second, it requires the specification of nonlinear constraints, which is not available in some popular SEM software programs. Third, it is for a 2-group comparison primarily. In this article, a 2-stage SEM method is proposed as an alternative. Unlike all other existing methods, the proposed method is simple to use, and it does not require any specific programming features such as the specification of nonlinear constraints. More important, the method allows a simultaneous comparison of 3 or more groups. A real example is given to illustrate the proposed method using EQS, a popular SEM software program.  相似文献   

20.
We compare the accuracy of confidence intervals (CIs) and tests of close fit based on the root mean square error of approximation (RMSEA) with those based on the standardized root mean square residual (SRMR). Investigations used normal and nonnormal data with models ranging from p = 10 to 60 observed variables. CIs and tests of close fit based on the SRMR are generally accurate across all conditions (even at p = 60 with nonnormal data). In contrast, CIs and tests of close fit based on the RMSEA are only accurate in small models. In larger models (p ≥ 30), they incorrectly suggest that models do not fit closely, particularly if sample size is less than 500.  相似文献   

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