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1.
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
2.
In testing factorial invariance, researchers have often used a reference variable strategy in which the factor loading for a variable (i.e., reference variable) is fixed to 1 for identification. This commonly used method can be misleading if the chosen reference variable is actually a noninvariant item. This simulation study suggests an alternative method for testing factorial invariance and evaluates the performance of the method in specification searches based on the modification index. The results of the study showed that the proposed specification searches performed well when the number of noninvariant variables was relatively small and this performance improved as sample size increased and the size of group differences increased. When the number of noninvariant variables was relatively large, however, the method rarely succeeded in detecting the noninvariant items in the specification searches. Implications of the findings are discussed along with the limitations of the study. 相似文献
3.
Testing factorial invariance has recently gained more attention in different social science disciplines. Nevertheless, when examining factorial invariance, it is generally assumed that the observations are independent of each other, which might not be always true. In this study, we examined the impact of testing factorial invariance in multilevel data, especially when the dependency issue is not taken into account. We considered a set of design factors, including number of clusters, cluster size, and intraclass correlation (ICC) at different levels. The simulation results showed that the test of factorial invariance became more liberal (or had inflated Type I error rate) in terms of rejecting the null hypothesis of invariance held between groups when the dependency was not considered in the analysis. Additionally, the magnitude of the inflation in the Type I error rate was a function of both ICC and cluster size. Implications of the findings and limitations are discussed. 相似文献
4.
This study investigates the effects of sample size, factor overdetermination, and communality on the precision of factor loading estimates and the power of the likelihood ratio test of factorial invariance in multigroup confirmatory factor analysis. Although sample sizes are typically thought to be the primary determinant of precision and power, the degree of factor overdetermination and the level of indicator communalities also play important roles. Based on these findings, no single rule of thumb regarding the ratio of sample size to number of indicators can ensure adequate power to detect a lack of measurement invariance. 相似文献
5.
Several structural equation modeling (SEM) strategies were developed for assessing measurement invariance (MI) across groups relaxing the assumptions of strict MI to partial, approximate, and partial approximate MI. Nonetheless, applied researchers still do not know if and under what conditions these strategies might provide results that allow for valid comparisons across groups in large-scale comparative surveys. We perform a comprehensive Monte Carlo simulation study to assess the conditions under which various SEM methods are appropriate to estimate latent means and path coefficients and their differences across groups. We find that while SEM path coefficients are relatively robust to violations of full MI and can be rather effectively recovered, recovering latent means and their group rankings might be difficult. Our results suggest that, contrary to some previous recommendations, partial invariance may rather effectively recover both path coefficients and latent means even when the majority of items are noninvariant. Although it is more difficult to recover latent means using approximate and partial approximate MI methods, it is possible under specific conditions and using appropriate models. These models also have the advantage of providing accurate standard errors. Alignment is recommended for recovering latent means in cases where there are only a few noninvariant parameters across groups. 相似文献
6.
We examine the power associated with the test of factor mean differences when the assumption of factorial invariance is violated. Utilizing the Wald test for obtaining power, issues of model size, sample size, and total versus partial noninvariance are considered along with variation of actual factor mean differences. Results of a population study show that power is profoundly affected by true factor mean differences but is relatively unaffected by the degree of factor loading noninvariance. Inequality of sample size has a profound effect on power probabilities with power decreasing as sample sizes become increasingly disparate. Sample size variations operate such that power is uniformly lower when the group with the smaller generalized variance is associated with the smaller sample size. An increase in the number of variables yields uniformly larger power probabilities. No substantial differences are found between total and partial noninvariance. Results are related to work in the area of robustness of Hotelling's T 2 statistic and discussed in terms of asymptotic covariability of factor means and factor loadings. Implications for practice are considered. 相似文献
7.
Keith F. Widaman Kevin J. Grimm Dawnté R. Early Richard W. Robins Rand D. Conger 《Structural equation modeling》2013,20(3):384-408
Difficulties arise in multiple-group evaluations of factorial invariance if particular manifest variables are missing completely in certain groups. Ad hoc analytic alternatives can be used in such situations (e.g., deleting manifest variables), but some common approaches, such as multiple imputation, are not viable. At least 3 solutions to this problem are viable: analyzing differing sets of variables across groups, using pattern mixture approaches, and a new method using random number generation. The latter solution, proposed in this article, is to generate pseudo-random normal deviates for all observations for manifest variables that are missing completely in a given sample and then to specify multiple-group models in a way that respects the random nature of these values. An empirical example is presented in detail comparing the 3 approaches. The proposed solution can enable quantitative comparisons at the latent variable level between groups using programs that require the same number of manifest variables in each group. 相似文献
8.
When factorial invariance is violated, a possible first step in locating the source of violation(s) might be to pursue partial factorial invariance (PFI). Two commonly used methods for PFI are sequential use of the modification index (backward MI method) and the factor-ratio test. In this study, we propose a simple forward method using the confidence interval (forward CI method). We compare the performances of the aforementioned 3 methods under various simulated PFI conditions. Results indicate that the forward CI method using 99% CIs has the highest perfect recovery rates and the lowest Type I error rates. A performance that is competitive with this is that produced by the backward method with the more conservative criterion (MI = 6.635). Consistently delivering the poorest performance, regardless of the chosen confidence level, was the factor-ratio test. Also discussed are the work’s contribution, implications, and limitations. 相似文献
9.
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
10.
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
11.
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
12.
Esther Ulitzsch Jana Holtmann Martin Schultze Michael Eid 《Structural equation modeling》2017,24(1):80-103
This simulation study assesses the statistical performance of two mathematically equivalent parameterizations for multitrait–multimethod data with interchangeable raters—a multilevel confirmatory factor analysis (CFA) and a classical CFA parameterization. The sample sizes of targets and raters, the factorial structure of the trait factors, and rater missingness are varied. The classical CFA approach yields a high proportion of improper solutions under conditions with small sample sizes and indicator-specific trait factors. In general, trait factor related parameters are more sensitive to bias than other types of parameters. For multilevel CFAs, there is a drastic bias in fit statistics under conditions with unidimensional trait factors on the between level, where root mean square error of approximation (RMSEA) and χ2 distributions reveal a downward bias, whereas the between standardized root mean square residual is biased upwards. In contrast, RMSEA and χ2 for classical CFA models are severely upwardly biased in conditions with a high number of raters and a small number of targets. 相似文献
13.
Charles R. Greenwood Jay BuzhardtDale Walker Luke McCuneWaylon Howard 《Early childhood research quarterly》2013
The Early Communication Indicator (ECI) is a measure for universal screening, intervention decision-making, progress monitoring for infants and toddlers needing higher levels of support, and program accountability. In the context of the ECI's long-term wide-scale use for these purposes, we examined the invariance of ECI measurement in two samples of the same Early Head Start (EHS) population differing in the years data were collected. Invariance or equivalence across samples is an important step in measurement validation because making inferences assumes that the measurements are factorially invariant. A number of time-covarying factors (e.g., assessors, children, etc.) can be hypothesized as threats to measurement invariance. Results of latent growth curve analyses indicated similarity in the functional forms (velocity and shape) of the ECIs four key skill trajectories between groups of children and ECI vocalizations, single, and multiple words trajectories met strong factorial and structural invariance. Gestures met only weak factorial invariance. ECI total communications, a weighted composite of the four scales, also met both strong factorial and structural invariance. With one exception, results indicated that the ECI produced comparable growth estimates over different conditions of programs, assessors, and children over time, strengthening the construct validity of the ECI. Implications are discussed. 相似文献
14.
This study examined the effect of district and school size on principal teacher allocation decisions. The study tested the invariance of a personnel allocation decision making model for elementary school principals from three categories of school and district size. The sample consisted of elementary school principals from small, medium, and large schools and districts. The results confirmed the fit of the model across schools of all sizes and across small and medium size districts. For large school districts the proposed decision-making model did not fit the data. This result implies that district size has an effect on the personnel allocation decisions made by elementary school principals. 相似文献
15.
Kok-Mun Ng Chuang Wang Carlos P. Zalaquett Nancy Bodenhorn 《International journal for the advancement of counseling》2007,29(3-4):173-185
There is the need for a reliable and valid measure to facilitate emotional intelligence (EI) research on international college
students (ICSs). The present study examined the factorial invariance of the Wong and Law Emotional Intelligence Scale (WLEIS),
a trait EI measure, in a sample of 628 ICSs. A web-based survey was developed to facilitate data collection across the country.
Results of a confirmatory factor analysis support the factorial invariance of the WLEIS in ICSs. Reliabilities and scale correlations
further supported the psychometric properties of the measure for international students. Additional findings indicate possible
country-of-origin difference on trait EI among different national groups.
An erratum to this article can be found at 相似文献
16.
Factorial invariance assessment is central in the development of educational and psychological assessments. Establishing invariance of factor structures is key for building a strong score and inference validity argument and assists in establishing the fairness of score use. Fit indices and guidelines for judging a lack of invariance is an ongoing line of research. In this study, the authors examined the performance of the root mean squared error of approximation equivalence testing approach described by Yuan and Chan in the context of measurement invariance assessment. This investigation was completed through a simulation study in which several factors were varied, including sample size, type of invariance tested, and magnitude and percent of a lack of invariance. The findings generally support the use of equivalence testing for situations in which the indicator variables were normally distributed, particularly for total sample sizes of 200 or more. 相似文献
17.
This study presents a new approach to synthesizing differential item functioning (DIF) effect size: First, using correlation matrices from each study, we perform a multigroup confirmatory factor analysis (MGCFA) that examines measurement invariance of a test item between two subgroups (i.e., focal and reference groups). Then we synthesize, across the studies, the differences in the estimated factor loadings between the two subgroups, resulting in a meta-analytic summary of the MGCFA effect sizes (MGCFA-ES). The performance of this new approach was examined using a Monte Carlo simulation, where we created 108 conditions by four factors: (1) three levels of item difficulty, (2) four magnitudes of DIF, (3) three levels of sample size, and (4) three types of correlation matrix (tetrachoric, adjusted Pearson, and Pearson). Results indicate that when MGCFA is fitted to tetrachoric correlation matrices, the meta-analytic summary of the MGCFA-ES performed best in terms of bias and mean square error values, 95% confidence interval coverages, empirical standard errors, Type I error rates, and statistical power; and reasonably well with adjusted Pearson correlation matrices. In addition, when tetrachoric correlation matrices are used, a meta-analytic summary of the MGCFA-ES performed well, particularly, under the condition that a high difficulty item with a large DIF was administered to a large sample size. Our result offers an option for synthesizing the magnitude of DIF on a flagged item across studies in practice. 相似文献
18.
We present a multigroup multilevel confirmatory factor analysis (CFA) model and a procedure for testing multilevel factorial invariance in n-level structural equation modeling (nSEM). Multigroup multilevel CFA introduces a complexity when the group membership at the lower level intersects the clustered structure, because the observations in different groups but in the same cluster are not independent of one another. nSEM provides a framework in which the multigroup multilevel data structure is represented with the dependency between groups at the lower level properly taken into account. The procedure for testing multilevel factorial invariance is illustrated with an empirical example using an R package xxm2. 相似文献
19.
The alignment method (Asparouhov & Muthén, 2014) is an alternative to multiple-group factor analysis for estimating measurement models and testing for measurement invariance across groups. Simulation studies evaluating the performance of the alignment for estimating measurement models across groups show promising results for continuous indicators. This simulation study builds on previous research by investigating the performance of the alignment method’s measurement models estimates with polytomous indicators under conditions of systematically increasing, partial measurement invariance. We also present an evaluation of the testing procedure, which has not been the focus of previous simulation studies. Results indicate that the alignment adequately recovers parameter estimates under small and moderate amounts of noninvariance, with issues only arising in extreme conditions. In addition, the statistical tests of invariance were fairly conservative, and had less power for items with more extreme skew. We include recommendations for using the alignment method based on these results. 相似文献
20.
The study assesses the psychometric properties of the Italian version of the Norwegian Teacher Self-Efficacy Scale – NTSES. Multiple group confirmatory factor analysis was used to explore the measurement invariance of the scale across two countries. Analyses performed on Italian and Norwegian samples confirmed a six-factor structure of the scale with a strong factorial invariance. The analyses conducted on the Italian sample supported good internal consistency and test-retest reliability. The Italian version of the NTSES showed expected correlations with measures of job-related well-being. These results confirm the good psychometric properties of the Italian version of the NTSES. 相似文献