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1.
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   

2.
Contamination of responses due to extreme and midpoint response style can confound the interpretation of scores, threatening the validity of inferences made from survey responses. This study incorporated person-level covariates in the multidimensional item response tree model to explain heterogeneity in response style. We include an empirical example and two simulation studies to support the use and interpretation of the model: parameter recovery using Markov chain Monte Carlo (MCMC) estimation and performance of the model under conditions with and without response styles present. Item intercepts mean bias and root mean square error were small at all sample sizes. Item discrimination mean bias and root mean square error were also small but tended to be smaller when covariates were unrelated to, or had a weak relationship with, the latent traits. Item and regression parameters are estimated with sufficient accuracy when sample sizes are greater than approximately 1,000 and MCMC estimation with the Gibbs sampler is used. The empirical example uses the National Longitudinal Study of Adolescent to Adult Health’s sexual knowledge scale. Meaningful predictors associated with high levels of extreme response latent trait included being non-White, being male, and having high levels of parental support and relationships. Meaningful predictors associated with high levels of the midpoint response latent trait included having low levels of parental support and relationships. Item-level covariates indicate the response style pseudo-items were less easy to endorse for self-oriented items, whereas the trait of interest pseudo-items were easier to endorse for self-oriented items.  相似文献   

3.
Kelley and Lai (2011) recently proposed the use of accuracy in parameter estimation (AIPE) for sample size planning in structural equation modeling. The sample size that reaches the desired width for the confidence interval of root mean square error of approximation (RMSEA) is suggested. This study proposes a graphical extension with the AIPE approach, abbreviated as GAIPE, on RMSEA to facilitate sample size planning in structural equation modeling. GAIPE simultaneously displays the expected width of a confidence interval of RMSEA, the necessary sample size to reach the desired width, and the RMSEA values covered in the confidence interval. Power analysis for hypothesis tests related to RMSEA can also be integrated into the GAIPE framework to allow for a concurrent consideration of accuracy in estimation and statistical power to plan sample sizes. A package written in R has been developed to implement GAIPE. Examples and instructions for using the GAIPE package are presented to help readers make use of this flexible framework. With the capacity of incorporating information on accuracy in RMSEA estimation, values of RMSEA, and power for hypothesis testing on RMSEA in a single graphical representation, the GAIPE extension offers an informative and practical approach for sample size planning in structural equation modeling.  相似文献   

4.
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   

5.
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   

6.
This article examines the effects of clustering in latent class analysis. A comprehensive simulation study is conducted, which begins by specifying a true multilevel latent class model with varying within- and between-cluster sample sizes, varying latent class proportions, and varying intraclass correlations. These models are then estimated under the assumption of a single-level latent class model. The outcomes of interest are measures of bias in the Bayesian Information Criterion (BIC) and the entropy R 2 statistic relative to accounting for the multilevel structure of the data. The results indicate that the size of the intraclass correlation as well as between- and within-cluster sizes are the most prominent factors in determining the amount of bias in these outcome measures, with increasing intraclass correlations combined with small between-cluster sizes resulting in increased bias. Bias is particularly noticeable in the BIC. In addition, there is evidence that class separation interacts with the size of the intraclass correlations and cluster sizes in producing bias in these measures.  相似文献   

7.
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   

8.
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   

9.
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   

10.
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   

11.
Using Monte Carlo simulations, this research examined the performance of four missing data methods in SEM under different multivariate distributional conditions. The effects of four independent variables (sample size, missing proportion, distribution shape, and factor loading magnitude) were investigated on six outcome variables: convergence rate, parameter estimate bias, MSE of parameter estimates, standard error coverage, model rejection rate, and model goodness of fit—RMSEA. A three-factor CFA model was used. Findings indicated that FIML outperformed the other methods in MCAR, and MI should be used to increase the plausibility of MAR. SRPI was not comparable to the other three methods in either MCAR or MAR.  相似文献   

12.
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   

13.
Abstract

Recently, researchers have used multilevel models for estimating intervention effects in single-case experiments that include replications across participants (e.g., multiple baseline designs) or for combining results across multiple single-case studies. Researchers estimating these multilevel models have primarily relied on restricted maximum likelihood (REML) techniques, but Bayesian approaches have also been suggested. The purpose of this Monte Carlo simulation study was to examine the impact of estimation method (REML versus Bayesian with noninformative priors) on the estimation of treatment effects (relative bias, root mean square error) and on the inferences about those effects (interval coverage) for autocorrelated multiple-baseline data. Simulated conditions varied with regard to the number of participants, series length, and distribution of the variance within and across participants. REML and Bayesian estimation led to estimates of the fixed effects that showed little to no bias but that differentially impacted the inferences about the fixed effects and the estimates of the variances. Implications for applied researchers and methodologists are discussed.  相似文献   

14.
A multilevel meta-analysis can combine the results of several single-subject experimental design studies. However, the estimated effects are biased if the effect sizes are standardized and the number of measurement occasions is small. In this study, the authors investigated 4 approaches to correct for this bias. First, the standardized effect sizes are adjusted using Hedges’ small sample bias correction. Next, the within-subject standard deviation is estimated by a 2-level model per study or by using a regression model with the subjects identified using dummy predictor variables. The effect sizes are corrected using an iterative raw data parametric bootstrap procedure. The results indicate that the first and last approach succeed in reducing the bias of the fixed effects estimates. Given the difference in complexity, we recommend the first approach.  相似文献   

15.
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   

16.
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   

17.
This study compared diagonal weighted least squares robust estimation techniques available in 2 popular statistical programs: diagonal weighted least squares (DWLS; LISREL version 8.80) and weighted least squares–mean (WLSM) and weighted least squares—mean and variance adjusted (WLSMV; Mplus version 6.11). A 20-item confirmatory factor analysis was estimated using item-level ordered categorical data. Three different nonnormality conditions were applied to 2- to 7-category data with sample sizes of 200, 400, and 800. Convergence problems were seen with nonnormal data when DWLS was used with few categories. Both DWLS and WLSMV produced accurate parameter estimates; however, bias in standard errors of parameter estimates was extreme for select conditions when nonnormal data were present. The robust estimators generally reported acceptable model–data fit, unless few categories were used with nonnormal data at smaller sample sizes; WLSMV yielded better fit than WLSM for most indices.  相似文献   

18.
The central purposes of this study were to review the development and evolution of the Scientific Attitude Inventory (SAI) and then reevaluate the psychometric properties of the revised form of the SAI, the Scientific Attitude Inventory II (SAI‐II). The SAI‐II was administered to a convenience sample of 543 middle and high school students from five teachers in four schools in four school districts in San Antonio, Texas, at the beginning of the 2004–2005 school year. Confirmatory factor analysis on the full data set failed to support the existence of a 12‐factor structure (as proposed by the scale developers) or a one‐factor structure. The data were then randomly divided into exploratory [exploratory factor analysis (EFA)] validation and confirmatory [confirmatory factor analysis (CFA)] cross‐validation sets. Exploratory and confirmatory models yielded a three‐factor solution that did not fit the data well [χ2 (321) = 646, p < .001; RMSEA = .061 (.90 CI = .054–.068); and CFI = .81]. The three factors were labeled “Science is About Understanding and Explaining” (13 items), “Science is Rigid” (6 items), and “I Want to Be a Scientist” (8 items). The α‐coefficients for these three factors ranged from 0.59 to 0.85. Whether these identified subscales are valid will require independent investigation. In this sample, and consistent with prior publications, the SAI‐II in its current form did not have satisfactory psychometric properties and cannot be recommended for further use. © 2008 Wiley Periodicals, Inc. J Res Sci Teach 45: 600–616, 2008  相似文献   

19.
The study of measurement invariance in latent profile analysis (LPA) indicates whether the latent profiles differ across known subgroups (e.g., gender). The purpose of the present study was to examine the impact of noninvariance on the relative bias of LPA parameter estimates and on the ability of the likelihood ratio test (LRT) and information criteria statistics to reject the hypothesis of invariance. A Monte Carlo simulation study was conducted in which noninvariance was defined as known group differences in the indicator means in each profile. Results indicated that parameter estimates were biased in conditions with medium and large noninvariance. The LRT and AIC detected noninvariance in most conditions with small sample sizes, while the BIC and adjusted BIC needed larger sample sizes to detect noninvariance. Implications of the results are discussed along with recommendations for future research.  相似文献   

20.
There is a need for effect sizes that are readily interpretable by a broad audience. One index that might fill this need is π, which represents the proportion of scores in one group that exceed the mean of another group. The robustness of estimates of π to violations of normality had not been explored. Using simulated data, three estimates of π (π? direct, r, and rrobust) were studied under varying conditions of sample size, distribution shape, and group mean difference. This study demonstrated that r and rrobust were biased estimates of π when data were nonnormal. We recommend that neither be used in estimating π unless data are normally distributed.  相似文献   

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