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1.
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
2.
Multigroup confirmatory factor analysis (MCFA) is a popular method for the examination of measurement invariance and specifically, factor invariance. Recent research has begun to focus on using MCFA to detect invariance for test items. MCFA requires certain parameters (e.g., factor loadings) to be constrained for model identification, which are assumed to be invariant across groups, and act as referent variables. When this invariance assumption is violated, location of the parameters that actually differ across groups becomes difficult. The factor ratio test and the stepwise partitioning procedure in combination have been suggested as methods to locate invariant referents, and appear to perform favorably with real data examples. However, the procedures have not been evaluated through simulations where the extent and magnitude of a lack of invariance is known. This simulation study examines these methods in terms of accuracy (i.e., true positive and false positive rates) of identifying invariant referent variables. 相似文献
3.
In practice, models always have misfit, and it is not well known in what situations methods that provide point estimates, standard errors (SEs), or confidence intervals (CIs) of standardized structural equation modeling (SEM) parameters are trustworthy. In this article we carried out simulations to evaluate the empirical performance of currently available methods. We studied maximum likelihood point estimates, as well as SE estimators based on the delta method, nonparametric bootstrap (NP-B), and semiparametric bootstrap (SP-B). For CIs we studied Wald CI based on delta, and percentile and BCa intervals based on NP-B and SP-B. We conducted simulation studies using both confirmatory factor analysis and SEM models. Depending on (a) whether point estimate, SE, or CI is of interest; (b) amount of model misfit; (c) sample size; and (d) model complexity, different methods can be the one that renders best performance. Based on the simulation results, we discuss how to choose proper methods in practice. 相似文献
4.
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
5.
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
6.
Evaluating the Comparability of Paper‐ and Computer‐Based Science Tests Across Sex and SES Subgroups
As access and reliance on technology continue to increase, so does the use of computerized testing for admissions, licensure/certification, and accountability exams. Nonetheless, full computer‐based test (CBT) implementation can be difficult due to limited resources. As a result, some testing programs offer both CBT and paper‐based test (PBT) administration formats. In such situations, evidence that scores obtained from different formats are comparable must be gathered. In this study, we illustrate how contemporary statistical methods can be used to provide evidence regarding the comparability of CBT and PBT scores at the total test score and item levels. Specifically, we looked at the invariance of test structure and item functioning across test administration mode across subgroups of students defined by SES and sex. Multiple replications of both confirmatory factor analysis and Rasch differential item functioning analyses were used to assess invariance at the factorial and item levels. Results revealed a unidimensional construct with moderate statistical support for strong factorial‐level invariance across SES subgroups, and moderate support of invariance across sex. Issues involved in applying these analyses to future evaluations of the comparability of scores from different versions of a test are discussed. 相似文献
7.
School climate surveys are central to school improvement and principal evaluation policies. The quality of school climate has been linked both to student achievement and to teacher retention. Oftentimes, policymakers and practitioners are concerned with monitoring change in school climate quality in each academic year. Such applications assume longitudinal factorial invariance—it is presupposed that the surveys are measuring the same things in the same metric at each time point. While there is considerable research examining the validity of inferences based on survey‐derived climate indicators, this research is almost exclusively based on cross‐sectional data. There is little literature describing procedures for gathering evidence of factorial invariance of school climate indicators. This study proposes to adapt existing methods for evaluating factorial invariance in longitudinal designs into multilevel frameworks, and in doing so, articulates a novel method for evaluating longitudinal measurement invariance in school climate research. This technique is illustrated on a widely used school climate survey. 相似文献
8.
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
9.
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
10.
To date, no effective empirical method has been available to identify a truly invariant reference variable (RV) in testing measurement invariance under a multiple-group confirmatory factor analysis. This study proposes a method that, in selecting an RV, uses the smallest modification index (min-mod). The method’s performance is evaluated using 2 models: (a) a full invariance model, and (b) a partial invariance model. Results indicate that for both models the min-mod successfully identifies a truly invariant RV (Study 1). In Study 2, we use the RV found in Study 1 to further evaluate the performance of item-by-item Wald tests at locating a noninvariant variable. The results indicate that Wald tests overall performed better with an RV selected in a partial invariance model than an RV selected in a full invariance model, although in certain conditions their performances were rather similar. Implications and limitations of the study are also discussed. 相似文献
11.
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
12.
Der-Ching Yang 《Educational research; a review for teachers and all concerned with progress in education》2013,55(4):368-388
Background: Number sense is a key topic in mathematics education, and the identification of children’s misconceptions about number is, therefore, important. Information about students’ serious misconceptions can be quite significant for teachers, allowing them to change their teaching plans to help children overcome these misconceptions. In science education, interest in children’s alternative conceptions has led to the development of three- and four-tier tests that not only assess children’s understandings and misconceptions, but also examine children’s confidence in their responses. However, there are few such tests related to mathematical content, especially in studies of number sense.Purpose: The purpose of this study was to investigate children’s performance and misconceptions with respect to number sense via a four-tier diagnostic test (Answer Tier → Confidence rating for Answer Tier → Reason Tier → Confidence rating for Reason Tier).Design and method: A total of 195 fifth graders (10–11 years old) from Taiwan participated in this study. The four-tier test was web-based and contained 40 items across five components of number sense.Findings: The results show that (1) students’ mean confidence rating for the answer tier was significantly higher than for the reason tier; (2) an average of 68% of students tended to have equal confidence ratings in both answer and reason tiers; (3) students who chose correct answers or reasons had higher mean confidence ratings in most items (36 out of 40) than those who did not; and (4) 16 misconceptions were identified and most of them were at a strong level.Conclusion: The four-tier test was able to identify several misconceptions in both the answer and reason tier and provide information about the confidence levels. By using such information, teachers may be better positioned to understand the nature of learners’ misconceptions about number sense and therefore support their pupils’ progress in mathematics. 相似文献
13.
《Structural equation modeling》2013,20(4):579-598
In this article we evaluate the psychometric properties of a scale for a perceptual measure of the extent to which manufacturing organizations develop proprietary equipment. We use a confirmatory factor analysis (CFA) approach to assess unidimensionality and reliability as well as convergent, discriminant and concurrent validity. Convergent and discriminant validity is assessed using CFA of the multitrait-multimethod (MTMM) matrix. In addition, we assess the scale's factorial invariance across industries. Results suggest that although method effects are present, the scale demonstrates internal consistency and validity. Implications of this study in the field of operations strategy and general strategy are discussed. 相似文献
14.
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
15.
Herbert W. Marsh 《Structural equation modeling》2013,20(1):5-34
Typical confirmatory factor analysis studies of factorial invariance test parameter (factor loadings, factor variances/covariances, and uniquenesses) invariance across only two groups (e.g., males and females) or, perhaps, across more than two groups reflecting different levels of a single design facet (e.g., age). The present investigation extends this approach by considering invariance across groups from a two‐facet design. Data consist of multiple dimensions of self‐concept collected from eight groups of students (total N = 4,000) representing a 2 (Gender) × 4 (Age) design. The gender‐stereotypic model posits a particular pattern of gender differences in structure that varies with age. Adopting analysis‐of‐variance terminology, the model posits that structural differences will vary as a function of gender but that this gender effect interacts with age. In testing this model, I consider the lack of invariance in different sets of parameters attributable to gender, age, and their interaction. 相似文献
16.
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
17.
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
18.
刘巧华 《上海大学学报(英文版)》2009,13(3):213-218
This paper proves that the weighting method via modified Gram-Schmidt(MGS) for solving the equality constrained least squares problem in the limit is equivalent to the direct elimination method via MGS(MGS-elimination method). By virtue of this equivalence, the backward and forward roundoff error analysis of the MGS-elimination method is proved. Numerical experiments are provided to verify the results. 相似文献
19.
Laura Trinchera Nicolas Marie George A. Marcoulides 《Structural equation modeling》2018,25(6):876-887
Scales are important tools for obtaining quantitative measures of theoretical constructs. Once a set of measures to be used in a scale is selected, reliability is commonly examined in order to assess their measurement quality. To date, Cronbach’s coefficient alpha is the most commonly reported index of measurement quality for assessing scale reliability. In this paper, an asymptotic distribution of the natural estimator of coefficient alpha is derived. A new interval estimate and a statistical test on the significance of the sample estimate of the coefficient are also presented. The proposed approach is compared to four popular methods commonly used to compute confidence intervals (CI) for alpha using a Monte Carlo simulation study. An R function for implementing the proposed CI approach is also provided. 相似文献
20.
This study investigated the effect of individual differences in state anxiety on tasks tapping the central executive, phonological, and visuo‐spatial components of working memory (WM). It was designed to test Eysenck and Calvo’s processing efficiency theory (PET) which suggests that the phonological and executive components of WM may be important in understanding learning outcomes in anxiety. Typically‐developing children aged 9–10 years were split into high and low state anxiety groups. They performed three WM tasks – forward and backward digit span (assumed to measure phonological and central executive components of WM respectively) and a spatial working memory task (measuring the visuo‐spatial component of WM). Measurements of task accuracy were taken as an indicator of performance outcome or effectiveness. Time taken to complete tasks and a subjective rating of mental effort were taken as measurements of performance efficiency. No differences were found between high and low state anxiety groups in task accuracy for any measure. Children in the high state anxiety group, however, took longer to complete the backward digit span task and reported increased mental effort in the forward digit span task, indicating some effect of anxiety on measures of performance efficiency. 相似文献