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1.
Bootstrapping approximate fit indexes in structural equation modeling (SEM) is of great importance because most fit indexes do not have tractable analytic distributions. Model-based bootstrap, which has been proposed to obtain the distribution of the model chi-square statistic under the null hypothesis (Bollen & Stine, 1992), is not theoretically appropriate for obtaining confidence intervals (CIs) for fit indexes because it assumes the null is exactly true. On the other hand, naive bootstrap is not expected to work well for those fit indexes that are based on the chi-square statistic, such as the root mean square error of approximation (RMSEA) and the comparative fit index (CFI), because sample noncentrality is a biased estimate of the population noncentrality. In this article we argue that a recently proposed bootstrap approach due to Yuan, Hayashi, and Yanagihara (YHY; 2007) is ideal for bootstrapping fit indexes that are based on the chi-square. This method transforms the data so that the “parent” population has the population noncentrality parameter equal to the estimated noncentrality in the original sample. We conducted a simulation study to evaluate the performance of the YHY bootstrap and the naive bootstrap for 4 indexes: RMSEA, CFI, goodness-of-fit index (GFI), and standardized root mean square residual (SRMR). We found that for RMSEA and CFI, the CIs under the YHY bootstrap had relatively good coverage rates for all conditions, whereas the CIs under the naive bootstrap had very low coverage rates when the fitted model had large degrees of freedom. However, for GFI and SRMR, the CIs under both bootstrap methods had poor coverage rates in most conditions.  相似文献   

2.
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   

3.
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   

4.
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   

5.
This article considers the implications for other noncentrality parameter-based statistics from Steiger's (1998) multiple sample adjustment to the root mean square error of approximation (RMSEA) measure. When a structural equation model is fitted simultaneously in more than 1 sample, it is shown that the calculation of the noncentrality parameter used in tests of approximate fit and in point and interval estimators of other noncentral fit statistics (except the expected cross-validation index) also requires a likeminded adjustment. Furthermore, it is shown that an adjustment is needed in multiple sample models for correctly calculating MacCallum, Browne, and Sugawara's (1996) approach to power analysis. The accuracy of these proposals is investigated and demonstrated in a small Monte Carlo study in which particular attention is paid to using appropriately constructed covariance matrices that give specified nonzero population discrepancy values under maximum likelihood estimation.  相似文献   

6.
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   

7.
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   

8.
Two Monte Carlo studies were conducted to examine the sensitivity of goodness of fit indexes to lack of measurement invariance at 3 commonly tested levels: factor loadings, intercepts, and residual variances. Standardized root mean square residual (SRMR) appears to be more sensitive to lack of invariance in factor loadings than in intercepts or residual variances. Comparative fit index (CFI) and root mean square error of approximation (RMSEA) appear to be equally sensitive to all 3 types of lack of invariance. The most intriguing finding is that changes in fit statistics are affected by the interaction between the pattern of invariance and the proportion of invariant items: when the pattern of lack of invariance is uniform, the relation is nonmonotonic, whereas when the pattern of lack of invariance is mixed, the relation is monotonic. Unequal sample sizes affect changes across all 3 levels of invariance: Changes are bigger when sample sizes are equal rather than when they are unequal. Cutoff points for testing invariance at different levels are recommended.  相似文献   

9.
The Classroom Appraisal of Resources and Demands (CARD) was designed to evaluate teacher stress based on subjective evaluations of classroom demands and resources. However, the CARD has been mostly utilized in western countries. The aim of the current study was to provide aspects of the validity of responses to a Chinese version of the CARD that considers Chinese teachers’ unique vocational conditions in the classroom. A sample of 580 Chinese elementary school teachers (510 female teachers and 70 male teachers) were asked to respond to the Chinese version of the CARD. Confirmatory factor analyses showed that the data fit the theoretical model very well (e.g., CFI: .982; NFI: .977; GFI: .968; SRMR: .028; RMSEA: .075; where CFI is comparative fit index, NFI is normed fit index, GFI is goodness of fit, SRMR is standardized root mean square residual, RMSEA is root mean square error of approximation), thus providing evidence of construct validity. Latent constructs of the Chinese version of the CARD were also found to be significantly associated with other measures that are related to teacher stress such as self‐efficacy, job satisfaction, personal habits to deal with stress, and intention to leave their current job.  相似文献   

10.
Research Findings: Empathy, or the ability to understand what others are thinking or feeling, can be observed in early developmental stages. The purpose of this study was to validate the Spanish version of the Empathy Questionnaire (EmQue) and examine its longitudinal measurement invariance (LMI) at 2 time points. Parents of 103 children completed the EmQue when their children were 3 (M = 41.76) and 4 (M = 51.65) years old. Confirmatory factor analyses revealed that Grazzani, Ornaghi, Pepe, Brazzelli and Rieffe’s (2016) 3-factor model of emotional contagion (EC), attention to others’ feelings, and prosocial actions (PA) presented the best fit indices at both time points (Time 1: CFI = .931, TLI = .914, and RMSEA = .070; Time 2: CFI = .941, TLI = .935, and RMSEA = .064). Moreover, preliminary evidence was obtained for the LMI of this model. PA scores increased over time. Score reliability ranged from .60 (EC) to .83 (PA). Positive correlations were found between PA and emotional regulation at each time point and across time.Practice or Policy: The great relevance of empathy and prosocial behavior in academic achievement and psychological adjustment justifies the development of reliable instruments to evaluate these constructs from early ages.  相似文献   

11.
As a prerequisite for meaningful comparison of latent variables across multiple populations, measurement invariance or specifically factorial invariance has often been evaluated in social science research. Alongside with the changes in the model chi-square values, the comparative fit index (CFI; Bentler, 1990) is a widely used fit index for evaluating different stages of factorial invariance, including metric invariance (equal factor loadings), scalar invariance (equal intercepts), and strict invariance (equal unique factor variances). Although previous literature generally showed that the CFI performed well for single-group structural equation modeling analyses, its applicability to multiple group analyses such as factorial invariance studies has not been examined. In this study we argue that the commonly used default baseline model for the CFI might not be suitable for factorial invariance studies because (a) it is not nested within the scalar invariance model, and thus (b) the resulting CFI values might not be sensitive to the group differences in the measurement model. We therefore proposed a modified version of the CFI with an alternative (and less restrictive) baseline model that allows observed variables to be correlated. Monte Carlo simulation studies were conducted to evaluate the utility of this modified CFI across various conditions including varying degree of noninvariance and different factorial invariance models. Results showed that the modified CFI outperformed both the conventional CFI and the ΔCFI (Cheung & Rensvold, 2002) in terms of sensitivity to small and medium noninvariance.  相似文献   

12.
Model fit indices are being increasingly recommended and used to select the number of factors in an exploratory factor analysis. Growing evidence suggests that the recommended cutoff values for common model fit indices are not appropriate for use in an exploratory factor analysis context. A particularly prominent problem in scale evaluation is the ubiquity of correlated residuals and imperfect model specification. Our research focuses on a scale evaluation context and the performance of four standard model fit indices: root mean square error of approximate (RMSEA), standardized root mean square residual (SRMR), comparative fit index (CFI), and Tucker–Lewis index (TLI), and two equivalence test-based model fit indices: RMSEAt and CFIt. We use Monte Carlo simulation to generate and analyze data based on a substantive example using the positive and negative affective schedule (N = 1,000). We systematically vary the number and magnitude of correlated residuals as well as nonspecific misspecification, to evaluate the impact on model fit indices in fitting a two-factor exploratory factor analysis. Our results show that all fit indices, except SRMR, are overly sensitive to correlated residuals and nonspecific error, resulting in solutions that are overfactored. SRMR performed well, consistently selecting the correct number of factors; however, previous research suggests it does not perform well with categorical data. In general, we do not recommend using model fit indices to select number of factors in a scale evaluation framework.  相似文献   

13.
ObjectiveThe Childhood Trauma Questionnaire-Short Form (CTQ-SF) is a self-report questionnaire that retrospectively provides screening for a history of childhood abuse and neglect, and which is widely used throughout the world. The current study aimed to examine the psychometric properties of the Chinese version of the CTQ-SF.MethodsParticipants included 3431 undergraduates from Hunan provinces and 234 depressive patients from psychological clinics. Confirmatory factor analysis was performed to examine how well the original five-factor model fit the data and the measurement equivalence of CTQ-SF across gender. Internal consistency was also evaluated.ResultsThe five-factor model achieved satisfactory fit (Undergraduate sample TLI = 0.925, CFI = 0.936, RMSEA = 0.034, SRMR = 0.046; depressive sample TLI = 0.912, CFI = 0.923, RMSEA = 0.044, SRMR = 0.062). Measurement invariance of the five-factor model across gender was supported fully assuming different degrees of invariance. The CTQ-SF also showed acceptable internal consistency and good stability.ConclusionThe current study provides that the Chinese version of the Childhood Trauma questionnaire-short form has good reliability and validity among Chinese undergraduates and depressive samples, which also indicates that the CTQ-SF is a good tool for child trauma assessment.  相似文献   

14.
Abstract

An increasing number of K–12 schools have adopted blended learning approaches. Current empirical research has been sparse regarding preparing teachers for blended teaching, including the skills they must develop to teach in blended contexts. This research is focused on that weakness, with the purposes of systematically identifying the skills needed for teaching in a blended learning context and of developing and testing an instrument that can be used to determine individual and school-wide readiness for blended teaching. In this study we present a measurement model used to develop items for measuring K–12 blended learning readiness. Specifically the instrument contained the following top-level areas: (a) foundational knowledge, skills, and dispositions, (b) instructional planning, (c) instructional methods and strategies, (d) assessment and evaluation, and (e) management. Each top-level construct also had two to four subconstructs. Through confirmatory factor analysis using survey responses from 2,290?K–12 teachers we found that the data met all four fit statistics cutoffs set forth in the literature (root mean square error of approximation [RMSEA]= 0.041, comparative fit index [CFI]?=?0.926, Tucker–Lewis index [TLI]?=?0.923, standardized root mean square residual [SRMR]?=?0.041, X2?=?978.934, df?=?1992).  相似文献   

15.
Hayduk and Glaser (2000) asserted that the most commonly used point estimate of the Root Mean Square Error of Approximation index of fit (Steiger & Lind, 1980) has two significant problems: (a) The frequently cited target value of. 05 is not a stable target, but a "sample size adjustment"; and (b) the truncated point estimate Rt = max(R, 0) effectively throws away a substantial part of the sampling distribution of the test statistic with "proper models," rendering it useless a substantial portion of the time. In this article, I demonstrate that both issues discussed by Hayduk and Glaser are actually not problems at all. The first "problem" derives from a false premise by Hayduk and Glaser that Steiger (1995) specifically warned about in an earlier publication. The second so-called problem results from the point estimate satisfying a fundamental property of a good estimator and can be shown to have virtually no negative implications for statistical practice.  相似文献   

16.
This paper emphasizes the following points regarding the appropriate role of rough-and-tumble play (R & T) in educational settings. (1) There has been an important secular trend toward an increasing importance of adult supervision of children's play. As a result, children's R & T must be considered in the context of social values regarding the expected developmental significance of children's play. (2) R & T is an aspect of evolved systems that propel the children into enthusiastic interaction with their environment and can be reasonably supposed to have several beneficial influences on children's cognitive and social development. (3) R & T can be distinguished from aggression, and adult supervised R & T is potentially an important arena for learning the limits of appropriate R & T. (4) It is suggested that supervised educational settings should be concerned with socializing several discrete systems that underlie children's development, including the present emphasis on socializing children to be able to focus attention, inhibit behavior, and be neat and orderly. However, the purpose of the present paper is to present a case for socializing the systems underlying stimulus seeking, extroversion, sociability, and intellectual creativity as well.  相似文献   

17.
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   

18.
Parental involvement is well documented as a significant contributor to the self‐efficacy and academic achievement of students. A structural equation model of parent involvement with family socioeconomic status, student gender, parents’ aspirations for their children, mathematics efficacy, and mathematics achievement was tested to examine whether parent involvement in the 10th grade remains relevant to achievement. A sample of data pertaining to 8,673 10th graders from the Educational Longitudinal Study was analyzed. The results indicated that the fit of the measurement model to the data was good (χ2 = 3081.62, df = 87, p = .0, normed fit index [NFI] = .96, comparative fit index [CFI] = .96, root mean square error of approximation [RMSEA] = .064), as was the structural model (χ2 = 3470.69, df = 94, p = .00, NFI = .96, CFI = .96, RMSEA = .065). Although the effect was small in magnitude, parent involvement in advising had a significant indirect relationship with mathematics achievement via mathematics efficacy of 10th graders.  相似文献   

19.
We proposed a higher order latent construct of parenting young children, parenting quality. This higher-order latent construct comprises five component constructs: demographic protection, psychological distress, psychosocial maturity, moral and cognitive reflectivity, and parenting attitudes and beliefs. We evaluated this model with data provided by 199 mothers of 4-year-old children enrolled in Head Start. The model was confirmed with only one adjustment suggested by modification indices. Final RMSEA was .05, CFI .96, and NNFI .94, indicating good model fit. Results were interpreted as emphasizing the interdependence of psychological and environmental demands on parenting. Implications of the model for teachers, early interventionists, and public policy are discussed.  相似文献   

20.
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   

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