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1.
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.
The objective was to offer guidelines for applied researchers on how to weigh the consequences of errors made in evaluating measurement invariance (MI) on the assessment of factor mean differences. We conducted a simulation study to supplement the MI literature by focusing on choosing among analysis models with different number of between-group constraints imposed on loadings and intercepts of indicators. Data were generated with varying proportions, patterns, and magnitudes of differences in loadings and intercepts as well as factor mean differences and sample size. Based on the findings, we concluded that researchers who conduct MI analyses should recognize that relaxing as well as imposing constraints can affect Type I error rate, power, and bias of estimates in factor mean differences. In addition, fit indexes can be misleading in making decisions about constraints of loadings and intercepts. We offer suggestions for making MI decisions under uncertainty when assessing factor mean differences.  相似文献   

3.
Measurement invariance with respect to groups is an essential aspect of the fair use of scores of intelligence tests and other psychological measurements. It is widely believed that equal factor loadings are sufficient to establish measurement invariance in confirmatory factor analysis. Here, it is shown why establishing measurement invariance with confirmatory factor analysis requires a statistical test of the equality over groups of measurement intercepts. Without this essential test, measurement bias may be overlooked. A re-analysis of a study by Te Nijenhuis, Tolboom, Resing, and Bleichrodt (2004) on ethnic differences on the RAKIT IQ test illustrates that ignoring intercept differences may lead to the conclusion that bias of IQ tests with respect to minorities is small, while in reality bias is quite severe.  相似文献   

4.
Models of change typically assume longitudinal measurement invariance. Key constructs are often measured by ordered-categorical indicators (e.g., Likert scale items). If tests based on such indicators do not support longitudinal measurement invariance, it would be useful to gauge the practical significance of the detected non-invariance. The authors focus on the commonly used second-order latent growth curve model, proposing a sensitivity analysis that compares the growth parameter estimates from a model assuming the highest achieved level of measurement invariance to those from a model assuming a higher, incorrect level of measurement invariance as a measure of practical significance. A simulation study investigated the practical significance of non-invariance in different locations (loadings, thresholds, uniquenesses) in second-order latent linear growth models. The mean linear slope was affected by non-invariance in the loadings and thresholds, the intercept variance was affected by non-invariance in the uniquenesses, and the linear slope variance and intercept–slope covariance were affected by non-invariance in all three locations.  相似文献   

5.
This study is a methodological-substantive synergy, demonstrating the power and flexibility of exploratory structural equation modeling (ESEM) methods that integrate confirmatory and exploratory factor analyses (CFA and EFA), as applied to substantively important questions based on multidimentional students' evaluations of university teaching (SETs). For these data, there is a well established ESEM structure but typical CFA models do not fit the data and substantially inflate correlations among the nine SET factors (median rs = .34 for ESEM, .72 for CFA) in a way that undermines discriminant validity and usefulness as diagnostic feedback. A 13-model taxonomy of ESEM measurement invariance is proposed, showing complete invariance (factor loadings, factor correlations, item uniquenesses, item intercepts, latent means) over multiple groups based on the SETs collected in the first and second halves of a 13-year period. Fully latent ESEM growth models that unconfounded measurement error from communality showed almost no linear or quadratic effects over this 13-year period. Latent multiple indicators multiple causes models showed that relations with background variables (workload/difficulty, class size, prior subject interest, expected grades) were small in size and varied systematically for different ESEM SET factors, supporting their discriminant validity and a construct validity interpretation of the relations. A new approach to higher order ESEM was demonstrated, but was not fully appropriate for these data. Based on ESEM methodology, substantively important questions were addressed that could not be appropriately addressed with a traditional CFA approach.  相似文献   

6.
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   

7.
Multigroup exploratory factor analysis (EFA) has gained popularity to address measurement invariance for two reasons. Firstly, repeatedly respecifying confirmatory factor analysis (CFA) models strongly capitalizes on chance and using EFA as a precursor works better. Secondly, the fixed zero loadings of CFA are often too restrictive. In multigroup EFA, factor loading invariance is rejected if the fit decreases significantly when fixing the loadings to be equal across groups. To locate the precise factor loading non-invariances by means of hypothesis testing, the factors’ rotational freedom needs to be resolved per group. In the literature, a solution exists for identifying optimal rotations for one group or invariant loadings across groups. Building on this, we present multigroup factor rotation (MGFR) for identifying loading non-invariances. Specifically, MGFR rotates group-specific loadings both to simple structure and between-group agreement, while disentangling loading differences from differences in the structural model (i.e., factor (co)variances).  相似文献   

8.
When modeling latent variables at multiple levels, it is important to consider the meaning of the latent variables at the different levels. If a higher-level common factor represents the aggregated version of a lower-level factor, the associated factor loadings will be equal across levels. However, many researchers do not consider cross-level invariance constraints in their research. Not applying these constraints when in fact they are appropriate leads to overparameterized models, and associated convergence and estimation problems. This simulation study used a two-level mediation model on common factors to show that when factor loadings are equal in the population, not applying cross-level invariance constraints leads to more estimation problems and smaller true positive rates. Some directions for future research on cross-level invariance in MLSEM are discussed.  相似文献   

9.
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   

10.
This Monte Carlo study investigated the impacts of measurement noninvariance across groups on major parameter estimates in latent growth modeling when researchers test group differences in initial status and latent growth. The average initial status and latent growth and the group effects on initial status and latent growth were investigated in terms of Type I error and bias. The location and magnitude of noninvariance across groups was related to the location and magnitude of bias and Type I error in the parameter estimates. That is, noninvariance in factor loadings and intercepts was associated with the Type I error inflation and bias in the parameter estimates of the slope factor (or latent growth) and the intercept factor (or initial status), respectively. As noninvariance became large, the degree of Type I error and bias also increased. On the other hand, a correctly specified second-order latent growth model yielded unbiased parameter estimates and correct statistical inferences. Other findings and implications on future studies were discussed.  相似文献   

11.
This study examined the measurement structure, cross-year stability of achievement goals, and mediating effects of achievement goals between self-efficacy and math grades in a national sample of Taiwan middle school students. The measurement model with factorial structure showed good fit to the data. In the panel data (N?=?343), four achievement goals showed strong measurement invariance, suggesting factor loadings and intercepts of the items remained invariant across a year. Though mean scores of the four latent achievement goals held quite stable, the rank order of students across two time-points changed more profoundly in the two avoidance goals than in the approached goals. In the cross-sectional data (N?=?748), we found approach-based goals were positive mediators between self-efficacy and math grades while avoidance-based goals were negative mediators. This result could be relevant for middle-school students in learning mathematics. Some instructional implications are provided.  相似文献   

12.
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   

13.
Structural Equation Modeling (SEM) was used in this study to determine the extent to which teachers, principals, and superintendents perceive the leadership construct in the same way. The researchers found that the two-factor model fits the principal group and particularly the superintendent group better than does the four-factor model. The principals and particularly the superintendents appear to have a more tightly focused mental model of leadership than teachers. The test of structural invariance across the three groups indicated that there was configural and weak invariance, but not strong or strict invariance. It appears that the item-loading patterns and item loadings are invariant, but the intercepts are different, which suggests that the groups put different emphases on the importance of the factors. The study affirms the importance of determining and reporting the extent to which comparison groups share the same mental model for leadership.   相似文献   

14.
We present a test for cluster bias, which can be used to detect violations of measurement invariance across clusters in 2-level data. We show how measurement invariance assumptions across clusters imply measurement invariance across levels in a 2-level factor model. Cluster bias is investigated by testing whether the within-level factor loadings are equal to the between-level factor loadings, and whether the between-level residual variances are zero. The test is illustrated with an example from school research. In a simulation study, we show that the cluster bias test has sufficient power, and the proportions of false positives are close to the chosen levels of significance.  相似文献   

15.
A brief 15-item version of the California School Climate Scale (Brief-CSCS) is presented to fill a need for a measure that could be used for periodic monitoring of school personnel's general perception of the climate of their school campus. From a sample of 81,261 California school personnel, random subsamples of 2,400 teachers and 2,400 administrators were used in the analyses. Confirmatory factor analyses supported a model in which general school climate was a second-order latent factor composed of 2 first-order latent traits, organizational supports and relational supports. Measurement invariance of factor loadings for teachers and administrators was found. Additional analyses revealed that administrators held more positive perceptions of school climate than teachers, with this difference increasing from primary through high school. The implications for these findings for educational research and policy reform are outlined.  相似文献   

16.
The purposes of this study were to (a) test the hypothesized factor structure of the Student-Teacher Relationship Scale (STRS; Pianta, 2001) for 308 African American (AA) and European American (EA) children using confirmatory factor analysis (CFA) and (b) examine the measurement invariance of the factor structure across AA and EA children. CFA of the hypothesized three-factor model with correlated latent factors did not yield an optimal model fit. Parameter estimates obtained from CFA identified items with low factor loadings and R2 values, suggesting that content revision is required for those items on the STRS. Deletion of two items from the scale yielded a good model fit, suggesting that the remaining 26 items reliably and validly measure the constructs for the whole sample. Tests for configural invariance, however, revealed that the underlying constructs may differ for AA and EA groups. Subsequent exploratory factor analyses (EFAs) for AA and EA children were carried out to investigate the comparability of the measurement model of the STRS across the groups. The results of EFAs provided evidence suggesting differential factor models of the STRS across AA and EA groups. This study provides implications for construct validity research and substantive research using the STRS given that the STRS is extensively used in intervention and research in early childhood education.  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.
Chinese University of Hong Kong students (N = 844) selected a “good” and a “poor” teacher, and rated each using a Chinese translation of the Students' Evaluations of Educational Quality (SEEQ) instrument. Multigroup confirmatory factor analysis (CFA) models, based on a 3 × 2 design, were constructed to test the invariance of the SEEQ factor structure across 3 discipline groups (a between‐group comparison of ratings by students in arts, social sciences, and education; in business administration; and in engineering, medicine, and science) and across ratings of good and poor teachers (via within‐subjects comparison). The selected model imposed between‐group invariance constraints on factor loadings, factor correlations, and factor variances across the 3 discipline groups and within‐subjects invariance constraints on factor loadings across ratings of good and poor teachers. The results support the use of SEEQ in this Chinese setting, demonstrating the generality of North American research findings and the usefulness of CFA in this research area.  相似文献   

19.
We estimated the invariance of educational achievement (EA) and learning attitudes (LA) measures across nations. A multi-group confirmatory factor analysis was used to estimate the invariance of educational achievement and learning attitudes across 55 nations (Programme for International Student Assessment [PISA] 2006 data, N?=?354,203). The constructs had the same meaning (factor loadings) but different scales (intercepts). Our conclusion is that comparisons of the relationships between educational achievement and learning attitudes across countries need to take into consideration two sources of variability: individual differences of students and group differences of educational systems. The lack of scalar invariance in EA and LA measures means that the relationships between EA and LA may have a different meaning at the level of nations and at the student level within countries. In other words, as PISA measures are not invariant in scalar sense, the comparisons across countries with nationally aggregated scores are not justified.  相似文献   

20.
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   

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