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1.
Fang Fang Chen 《Structural equation modeling》2013,20(3):464-504
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
2.
With the increasing use of international survey data especially in cross-cultural and multinational studies, establishing measurement invariance (MI) across a large number of groups in a study is essential. Testing MI over many groups is methodologically challenging, however. We identified 5 methods for MI testing across many groups (multiple group confirmatory factor analysis, multilevel confirmatory factor analysis, multilevel factor mixture modeling, Bayesian approximate MI testing, and alignment optimization) and explicated the similarities and differences of these approaches in terms of their conceptual models and statistical procedures. A Monte Carlo study was conducted to investigate the efficacy of the 5 methods in detecting measurement noninvariance across many groups using various fit criteria. Generally, the 5 methods showed reasonable performance in identifying the level of invariance if an appropriate fit criterion was used (e.g., Bayesian information criteron with multilevel factor mixture modeling). Finally, general guidelines in selecting an appropriate method are provided. 相似文献
3.
In testing the factorial invariance of a measure across groups, the groups are often of different sizes. Large imbalances in group size might affect the results of factorial invariance studies and lead to incorrect conclusions of invariance because the fit function in multiple-group factor analysis includes a weighting by group sample size. The implication is that violations of invariance might not be detected if the sample sizes of the 2 groups are severely unbalanced. In this study, we examined the effects of group size differences on results of factorial invariance tests, proposed a subsampling method to address unbalanced sample size issue in factorial invariance studies, and evaluated the proposed approach in various simulation conditions. Our findings confirm that violations of invariance might be masked in the case of severely unbalanced group size conditions and support the use of the proposed subsampling method to obtain accurate results for invariance studies. 相似文献
4.
In spite of the challenges inherent in making dozens of comparisons across heterogeneous populations, a relatively recent interest in scale-score equivalence for non-achievement measures in an international context has emerged. Until recently, operational procedures for establishing measurement invariance using multiple-groups analyses were typically supported with research that was limited in scope to few groups and relatively small sample sizes. Recent research that examined situations more representative of international surveys recommended some revisions to typically used fit measures. The current study extends this research and evaluates the performance of several fit measures when data are assumed to have an ordered categorical, rather than the typically assumed continuous, scale. Using a simulation study based on empirical results, findings indicated that classic measures and associated criteria were either unsuitable in a large-group and varied sample-size context or should be adjusted, particularly when observed variables were not normally distributed. We provide specific recommendations for revising currently used criteria for evaluating overall and relative fit based on the chi-square test, root mean-squared error of approximation, and comparative fit index (CFI). 相似文献
5.
Eun Sook Kim Seang-Hwane Joo Philseok Lee Yan Wang Stephen Stark 《Structural equation modeling》2016,23(6):870-887
This simulation study examines the efficacy of multilevel factor mixture modeling (ML FMM) for measurement invariance testing across unobserved groups when the groups are at the between level of multilevel data. To this end, latent classes are generated with class-specific item parameters (i.e., factor loading and intercept) across the between-level classes. The efficacy of ML FMM is evaluated in terms of class enumeration, class assignment, and the detection of noninvariance. Various classification criteria such as Akaike’s information criterion, Bayesian information criterion, and bootstrap likelihood ratio tests are examined for the correct enumeration of between-level latent classes. For the detection of measurement noninvariance, free and constrained baseline approaches are compared with respect to true positive and false positive rates. This study evidences the adequacy of ML FMM. However, its performance heavily depends on the simulation factors such as the classification criteria, sample size, and the magnitude of noninvariance. Practical guidelines for applied researchers are provided. 相似文献
6.
Subscore added value analyses assume invariance across test taking populations; however, this assumption may be untenable in practice as differential subdomain relationships may be present among subgroups. The purpose of this simulation study was to understand the conditions associated with subscore added value noninvariance when manipulating: (a) subdomain test length, (b) differences in subgroup mean ability, and (c) subgroup differences in intersubdomain correlations. Results demonstrated that subscore added value was noninvariant for 24–100% of replications (depending on subdomain test length) when the subgroup difference in intersubdomain correlation was equal to .30. To examine if this condition was met in practice, applied invariance analyses of three operational testing programs were conducted. Across these datasets, noninvariant subscore added value was present for some subdomains across sex and ethnic subgroups. Overall, these results indicate that subscore added value noninvariance is largely driven by differential intersubdomain correlations among subgroups, which may be present in some operational testing programs. 相似文献
7.
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
8.
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
9.
In latent growth modeling, measurement invariance across groups has received little attention. Considering that a group difference is commonly of interest in social science, a Monte Carlo study explored the performance of multigroup second-order latent growth modeling (MSLGM) in testing measurement invariance. True positive and false positive rates in detecting noninvariance across groups in addition to bias estimates of major MSLGM parameters were investigated. Simulation results support the suitability of MSLGM for measurement invariance testing when either forward or iterative likelihood ratio procedure is applied. 相似文献
10.
《Structural equation modeling》2013,20(2):233-255
Measurement invariance is usually tested using Multigroup Confirmatory Factor Analysis, which examines the change in the goodness-of-fit index (GFI) when cross-group constraints are imposed on a measurement model. Although many studies have examined the properties of GFI as indicators of overall model fit for single-group data, there have been none to date that examine how GFIs change when between-group constraints are added to a measurement model. The lack of a consensus about what constitutes significant GFI differences places limits on measurement invariance testing. We examine 20 GFIs based on the minimum fit function. A simulation under the two-group situation was used to examine changes in the GFIs (ΔGFIs) when invariance constraints were added. Based on the results, we recommend using Δcomparative fit index, ΔGamma hat, and ΔMcDonald's Noncentrality Index to evaluate measurement invariance. These three ΔGFIs are independent of both model complexity and sample size, and are not correlated with the overall fit measures. We propose critical values of these ΔGFIs that indicate measurement invariance. 相似文献
11.
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
12.
Tiffany A. Whittaker 《Structural equation modeling》2013,20(1):108-130
Latent means methods such as multiple-indicator multiple-cause (MIMIC) and structured means modeling (SMM) allow researchers to determine whether or not a significant difference exists between groups' factor means. Strong invariance is typically recommended when interpreting latent mean differences. The extent of the impact of noninvariant intercepts on conclusions made when implementing both MIMIC and SMM methods was the main purpose of this study. The impact of intercept noninvariance on Type I error rates, power, and two model fit indices when using MIMIC and SMM approaches under various conditions were examined. Type I error and power were adversely affected by intercept noninvariance. Although the fit indices did not detect small misspecifications in the form of noninvariant intercepts, one did perform more optimally. 相似文献
13.
Testing for factorial invariance of the Modified Leadership Scale for Sports: using a Japanese version 总被引：1，自引：1，他引：0
The objective of this study was to provide empirical evidence to support psychometric properties of a modified four-dimensional model of the Leadership Scale for Sports (LSS). The study tested invariance of all parameters (i.e., factor loadings, error variances, and factor variances–covariances) in the four-dimensional measurement model between two groups of student-athletes. For testing multi-group invariance of the proposed scale, 335 middle school and 320 high school student-athletes in Japan participated in this study. The modified version of the LSS consists of 35 items representing training instruction, democratic behaviour, positive feedback, and social support. A chi-square difference test was employed for model comparisons. The results supported configural, metric, scalar and factor variance–covariance invariance in the modified LSS across the two student-athlete groups. 相似文献
14.
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
15.
Tihomir Asparouhov 《Structural equation modeling》2013,20(4):495-508
This article presents a new method for multiple-group confirmatory factor analysis (CFA), referred to as the alignment method. The alignment method can be used to estimate group-specific factor means and variances without requiring exact measurement invariance. A strength of the method is the ability to conveniently estimate models for many groups. The method is a valuable alternative to the currently used multiple-group CFA methods for studying measurement invariance that require multiple manual model adjustments guided by modification indexes. Multiple-group CFA is not practical with many groups due to poor model fit of the scalar model and too many large modification indexes. In contrast, the alignment method is based on the configural model and essentially automates and greatly simplifies measurement invariance analysis. The method also provides a detailed account of parameter invariance for every model parameter in every group. 相似文献
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Socioeconomic status (SES) is often used as control variable when relations between academic outcomes and students' migrational background are investigated. When measuring SES, indicators used must have the same meaning across groups. This study aims to examine the measurement invariance of SES, using data from TIMSS, 2003. The study shows that a latent SES variable has the same meaning across sub-populations with Swedish and non-Swedish background. However, the assumption of scalar invariance was rejected, which is essential for estimation of differences in latent means between groups. Comparisons between models assuming different degrees of scalar invariance indicated that models allowing partial scalar invariance should not be used when comparing latent variable means across groups of students with different migrational backgrounds. 相似文献
18.
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
19.
《Structural equation modeling》2013,20(2):257-274
This study investigated the factorial invariance of scores from a 7th-grade state reading assessment across general education students and selected groups of students with disabilities. Confirmatory factor analysis was used to assess the fit of a 2-factor model to each of the 4 groups. In addition to overall fit of this model, 5 levels of constraint, including equal factor loadings, intercepts, error variances, factor variances, and factor covariances, were investigated. Invariance across the factor loadings and intercepts was supported across the groups of students with disabilities and general education students. Invariance for these groups was not supported for the error variances. For the students with mental retardation, the lack of fit of the 2-factor model and the observed score results suggested a mismatch between the difficulty level of this test and the ability level of these students. Although the results generally supported the score comparability of the reading assessment across these groups, further research is needed into the nature of the larger error variances for the student with disabilities groups and into accommodations and modifications for the students with mental retardation. 相似文献
20.
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