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1.
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   

2.
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   

3.
An alternative method for determining the goodness of fit of a proposed theoretical model is presented and applied to a simple case to illustrate its 0use. The method is based on the application of the binomial distribution to the number of paths in a model that are supported by the data. This method is a different conceptual approach than those traditionally used in structural equation modeling studies.  相似文献   

4.
Bollen and Ting (1993) proposed confirmatory tetrad analysis (CTA) as a method for testing structural equation models. CTA holds promise as a complementary method to the conventional model testing methodology. It applies to some underidentified models and nonnested models that cannot be tested in the conventional approach, and it is a noniterative estimator that does not have nonconvergence problems. This article illustrates an SAS macro, named CTA‐SAS, that implements the CTA testing methodology. Essential elements of the test and the syntax of the program are discussed, and an example is used to illustrate the application of the program.  相似文献   

5.
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   

6.
Given the relationships of item response theory (IRT) models to confirmatory factor analysis (CFA) models, IRT model misspecifications might be detectable through model fit indexes commonly used in categorical CFA. The purpose of this study is to investigate the sensitivity of weighted least squares with adjusted means and variance (WLSMV)-based root mean square error of approximation, comparative fit index, and Tucker–Lewis Index model fit indexes to IRT models that are misspecified due to local dependence (LD). It was found that WLSMV-based fit indexes have some functional relationships to parameter estimate bias in 2-parameter logistic models caused by violations of LD. Continued exploration into these functional relationships and development of LD-detection methods based on such relationships could hold much promise for providing IRT practitioners with global information on violations of local independence.  相似文献   

7.
Many mechanistic rules of thumb for evaluating the goodness of fit of structural equation models (SEM) emphasize model parsimony; all other things being equal, a simpler, more parsimonious model with fewer estimated parameters is better than a more complex model Although this is usually good advice, in the present article a heuristic counterexample is demonstrated in which parsimony as typically operationalized in indices of fit may be undesirable. Specifically, in simplex models of longitudinal data, the failure to include correlated uniquenesses relating the same indicators administered on different occasions will typically lead to systematically inflated estimates of stability. Although simplex models with correlated uniquenesses are substantially less parsimonious and may be unacceptable according to mechanistic decision rules that penalize model complexity, it can be argued a priori that these additional parameter estimates should be included. Simulated data . are used to support this claim and to evaluate the behavior of a variety of fit indices and decision rules. The results demonstrate the validity of Bollen and Long’s (1993) conclusion that “test statistics and fit indices are very beneficial, but they are no replacement for sound judgment and substantive expertise” (p. 8).  相似文献   

8.
This research was designed to investigate how much more suitable moving average (MA) and autoregressive-moving average (ARMA) models are for longitudinal panel data in which measurement errors correlate than AR, quasi-simplex, and 1-factor models. The conclusions include (a) when testing for a stochastic process hypothesized to occur in a longitudinal data set, testing for other processes is necessary, because incorrect models often fit other processes well enough to be deceiving; (b) when measurement error correlations are flagged to be relatively high in panel data, the fit and propriety of an MA or ARMA model should be considered and compared to the fit and propriety of other models; (c) when an MA model is fit to AR data, measurement error correlations may nonetheless be deceptively high, though fortunately MA model fit indexes are almost always lower than those for an AR model; and (d) the assumption that longitudinal panel data always contain measurement error correlations is patently false. In summary, whenever evaluating longitudinal panel data, the fit, propriety, and parsimony of all 5 models should be considered jointly and compared before a particular model is endorsed as most suitable.  相似文献   

9.
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10.
This article compares two statistical approaches for modeling growth across time. The two statistical approaches are the multilevel model (MLM) and latent curve analysis (LCA), which have been proposed to depict change or growth adequately. These two approaches were compared in terms of the estimation of growth profiles represented by the parameters of initial status and the rate of growth. A longitudinal data set obtained from a school‐based substance‐use prevention trial for adolescents was used to illustrate the similarities and differences between the two approaches. The results indicated that the two approaches yielded very compatible results. The parameter estimates associated with regression weights are the same, whereas those associated with variances and covariances are similar. The MLM approach is easier for model specification and is more efficient computationally in yielding results. The LCA approach, however, has the advantage of providing model evaluation, that is, an overall test of goodness of fit, and is more flexible in modeling and hypothesis testing as demonstrated in this study.  相似文献   

11.
A 30-item survey was devised to determine Chinese TEFL (Teaching English as a Foreign Language) academics’ potential for conducting research. A five-part Likert scale was used to gather data from 182 academics on four factors: (1) perceptions on teaching–research nexus, (2) personal perspectives for conducting research, (3) predispositions for conducting research and (4) workplace contexts for conducting research. Data were subjected to confirmatory factor analysis (CFA) for structural equation modelling using various fit indices. The independence model was rejected. Accordingly, the CFA model proposed that the four factors covaried and were associated with each indicated item. The hypothesized CFA model demonstrated an acceptable model fit. After statistical analysis, a revised CFA model presented more reliable fit measures, which required a reduction in survey item numbers. This instrument will require further testing but may be used to draw comparisons between past and present data and determine areas for enhancing research productivity.  相似文献   

12.
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   

13.
The purpose of this study was to examine the behavior of 8 measures of fit used to evaluate confirmatory factor analysis models. This study employed Monte Carlo simulation to determine to what extent sample size, model size, estimation procedure, and level of nonnormality affected fit when polytomous data were analyzed. The 3 indexes least affected by the design conditions were the comparative fit index, incremental fit index, and nonnormed fit index, which were affected only by level of nonnormality. The measure of centrality was most affected by the design variables, with values of n2>. 10 for sample size, model size, and level of nonnormality and interaction effects for Model Size x Level of Nonnormality and Estimation x Level of Nonnormality. Findings from this study should alert applied researchers to exercise caution when evaluating model fit with nonnormal, polytomous data.  相似文献   

14.
This simulation study investigated the sensitivity of commonly used cutoff values for global-model-fit indexes, with regard to different degrees of violations of the assumption of uncorrelated errors in confirmatory factor analysis. It is shown that the global-model-fit indexes fell short in identifying weak to strong model misspecifications under both different degrees of correlated error terms, and various simulation conditions. On the basis of an example misspecification search, it is argued that global model testing must be supplemented by this procedure. Implications for the use of structural equation modeling are discussed.  相似文献   

15.
The recovery of weak factors has been extensively studied in the context of exploratory factor analysis. This article presents the results of a Monte Carlo simulation study of recovery of weak factor loadings in confirmatory factor analysis under conditions of estimation method (maximum likelihood vs. unweighted least squares), sample size, loading size, factor correlation, and model specification (correct vs. incorrect). The effects of these variables on goodness of fit and convergence are also examined. Results show that recovery of weak factor loadings, goodness of fit, and convergence are improved when factors are correlated and models are correctly specified. Additionally, unweighted least squares produces more convergent solutions and successfully recovers the weak factor loadings in some instances where maximum likelihood fails. The implications of these findings are discussed and compared to previous research.  相似文献   

16.
This study discusses a procedure for testing the equivalence among different item response formats used in personality and attitude measurement. The procedure is based on the assumption that latent response variables underlie the observed item responses (underlying variables approach) and uses a nested series of confirmatory factor analysis models derived from Joreskog's (1971) method for estimating the dissatenuated correlation. The different stages of the procedure are illustrated using real data.  相似文献   

17.
The effects of levels of aggregation on measures of goodness of fit and higher order parameter estimates obtained from confirmatory factor analysis (CFA) were investigated. For a higher order model of academic self‐concept, 3 levels of aggregation were considered—disaggregated, partially disaggregated, and partially aggregated. In the disaggregated model, measured variables represented individual items. In the partially disaggregated model, testlets (groups of 4 items) represented measured variables. In the partially aggregated model, subscale scores represented measured variables. Three indexes of fit were employed: the Tucker‐Lewis Index (TLI), the Comparative Fit Index (CFI), and chi‐square. Solutions for the disaggregated models consistently evidenced poor fit. TLI and CFI values for partially disaggregated and partially aggregated solutions were satisfactory. Standardized parameter estimates were similar across all solutions. Implications of these findings are discussed with consideration of other research on model complexity in CFA.  相似文献   

18.
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   

19.
This article is concerned with the difference in noncentrality parameters of nested structural equation models and their utility in evaluating statistical power associated with the pertinent restriction test. Based on the seminal work by Browne and Du Toit (1992), Steiger (1989, 1990), Steiger and Lind (1980), and Steiger, Shapiro, and Browne (1985), asymptotic confidence intervals for that difference are discussed. The intervals represent a useful adjunct to widely employed goodness‐of‐fit indexes and test statistics when assessing plausibility of constraints in nested models. The approach also permits estimating power of the test of validity of the nesting restrictions (cf. MacCallum, Browne, & Sugawara, 1996). It is illustrated on data from a 2‐group cognitive training study.  相似文献   

20.
The primary purpose of this research is to explore the impacts of knowledge creation practices on organizational performance improvement. Research has been empirically assessed on the basis of the collected data from three Korean private organizations. The concept of knowledge creation theory was adapted as the theoretical framework of this research (Nonaka & Takeuchi, 1995). Structural equation modeling has been used in order to assess the fit of the hypothesized model with the collected data. The result of the confirmatory factor analysis suggests that the hypothesized measurement model is a reliable and valid construct in the Korean context; multiple regression analysis reveals that knowledge creation practices have a positive and strong influence on performance improvement. Conclusions, limitations, and implications for human resource development are discussed.  相似文献   

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