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1.
This Monte Carlo simulation study investigated methods of forming product indicators for the unconstrained approach for latent variable interaction estimation when the exogenous factors are measured by large and unequal numbers of indicators. Product indicators were created based on multiplying parcels of the larger scale by indicators of the smaller scale, multiplying the three most reliable indicators of each scale matched by reliability, and matching items by reliability to create as many product indicators as the number of indicators of the smallest scale. The unconstrained approach was compared with the latent moderated structural equations (LMS) approach. All methods considered provided unbiased parameter estimates. Unbiased standard errors were obtained in all conditions with the LMS approach and when the sample size was large with the unconstrained approach. Power levels to test the latent interaction and Type I error rates were similar for all methods but slightly better for the LMS approach.  相似文献   

2.
This study examined the efficacy of 4 different parceling methods for modeling categorical data with 2, 3, and 4 categories and with normal, moderately nonnormal, and severely nonnormal distributions. The parceling methods investigated were isolated parceling in which items were parceled with other items sharing the same source of variance, and distributed parceling in which items were parceled with items influenced by different factors. These parceling strategies were crossed with strategies in which items were either parceled with similarly distributed or differently distributed items, to create 4 different parceling methods. Overall, parceling together items influenced by different factors and with different distributions resulted in better model fit, but high levels of parameter estimate bias. Across all parceling methods, parameter estimate bias ranged from 20% to over 130%. Parceling strategies were contrasted with use of the WLSMV estimator for categorical, unparceled data. Results based on this estimator are encouraging, although some bias was found when high levels of nonnormality were present. Values of the chi-square and root mean squared error of approximation based on WLSMV also resulted in Type II error rates for misspecified models when data were severely nonnormally distributed.  相似文献   

3.
Interaction and quadratic effects in latent variable models have to date only rarely been tested in practice. Traditional product indicator approaches need to create product indicators (e.g., x 1 2, x 1 x 4) to serve as indicators of each nonlinear latent construct. These approaches require the use of complex nonlinear constraints and additional model specifications and do not directly address the nonnormal distribution of the product terms. In contrast, recently developed, easy-to-use distribution analytic approaches do not use product indicators, but rather directly model the nonlinear multivariate distribution of the measured indicators. This article outlines the theoretical properties of the distribution analytic Latent Moderated Structural Equations (LMS; Klein & Moosbrugger, 2000) and Quasi-Maximum Likelihood (QML; Klein & Muthén, 2007) estimators. It compares the properties of LMS and QML to those of the product indicator approaches. A small simulation study compares the two approaches and illustrates the advantages of the distribution analytic approaches as multicollinearity increases, particularly in complex models with multiple nonlinear terms. An empirical example from the field of work stress applies LMS and QML to a model with an interaction and 2 quadratic effects. Example syntax for the analyses with both approaches is provided.  相似文献   

4.
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   

5.
Structural equation models with interaction and quadratic effects have become a standard tool for testing nonlinear hypotheses in the social sciences. Most of the current approaches assume normally distributed latent predictor variables. In this article, we describe a nonlinear structural equation mixture approach that integrates the strength of parametric approaches (specification of the nonlinear functional relationship) and the flexibility of semiparametric structural equation mixture approaches for approximating the nonnormality of latent predictor variables. In a comparative simulation study, the advantages of the proposed mixture procedure over contemporary approaches [Latent Moderated Structural Equations approach (LMS) and the extended unconstrained approach] are shown for varying degrees of skewness of the latent predictor variables. Whereas the conventional approaches show either biased parameter estimates or standard errors of the nonlinear effects, the proposed mixture approach provides unbiased estimates and standard errors. We present an empirical example from educational research. Guidelines for applications of the approaches and limitations are discussed.  相似文献   

6.
Little, Bovaird and Widaman (2006) proposed an unconstrained approach with residual centering for estimating latent interaction effects as an alternative to the mean-centered approach proposed by Marsh, Wen, and Hau (2004, 2006). Little et al. also differed from Marsh et al. in the number of indicators used to infer the latent interaction factor and how they were represented, but this issue is separate from the mean versus residual centering distinction that was their primary focus. However, their implementation of the Marsh et al. mean-centered approach failed to incorporate the mean structure that Marsh et al. argued was necessary to obtain unbiased estimates. One might suppose that their new approach would suffer this same problem, an issue not addressed by Little et al. However, we demonstrate here why the Little et al. approach obviates this requirement that heretofore was thought to be necessary for all constrained, partially constrained, and unconstrained approaches. Both the Marsh et al. and Little et al. unconstrained approaches typically result in similar results and are much easier to implement than traditional constrained approaches. They differ primarily in that the Little et al. approach is a 2-step approach involving a potentially large number of separate analyses prior to estimating the structural equation model that apparently does not require the estimation of a mean structure, whereas the Marsh et al. approach is a 1-step approach that includes a mean structure.  相似文献   

7.
This study examined and compared various statistical methods for detecting individual differences in change. Considering 3 issues including test forms (specific vs. generalized), estimation procedures (constrained vs. unconstrained), and nonnormality, we evaluated 4 variance tests including the specific Wald variance test, the generalized Wald variance test, the specific likelihood ratio (LR) variance test, and the generalized LR variance test under both constrained and unconstrained estimation for both normal and nonnormal data. For the constrained estimation procedure, both the mixture distribution approach and the alpha correction approach were evaluated for their performance in dealing with the boundary problem. To deal with the nonnormality issue, we used the sandwich standard error (SE) estimator for the Wald tests and the Satorra–Bentler scaling correction for the LR tests. Simulation results revealed that testing a variance parameter and the associated covariances (generalized) had higher power than testing the variance solely (specific), unless the true covariances were zero. In addition, the variance tests under constrained estimation outperformed those under unconstrained estimation in terms of higher empirical power and better control of Type I error rates. Among all the studied tests, for both normal and nonnormal data, the robust generalized LR and Wald variance tests with the constrained estimation procedure were generally more powerful and had better Type I error rates for testing variance components than the other tests. Results from the comparisons between specific and generalized variance tests and between constrained and unconstrained estimation were discussed.  相似文献   

8.
This study compared 5 scoring methods in terms of their statistical assumptions. They were then used to score the Teacher Observation of Classroom Adaptation Checklist, a measure consisting of 3 subscales and 21 Likert-type items. The 5 methods used were (a) sum/average scores of items, (b) latent factor scores with continuous indicators, (c) latent factor scores with ordered categorical indicators using the mean- and variance-adjusted weighted least squares estimation method, (d) latent factor scores with ordered categorical indicators using the full information maximum likelihood estimation method, and (e) multidimensional graded response model using the Bock-Aitkin expectation-maximization estimation procedure. Measurement invariance between gender groups and between free/reduced-price lunch status groups was evaluated with the second, third, fourth, and fifth methods. Group mean differences based on the 5 methods were calculated and compared.  相似文献   

9.
This article investigates likelihood-based difference statistics for testing nonlinear effects in structural equation modeling using the latent moderated structural equations (LMS) approach. In addition to the standard difference statistic TD, 2 robust statistics have been developed in the literature to ensure valid results under the conditions of nonnormality or small sample sizes: the robust TDR and the “strictly positive” TDRP. These robust statistics have not been examined in combination with LMS yet. In 2 Monte Carlo studies we investigate the performance of these methods for testing quadratic or interaction effects subject to different sources of nonnormality, nonnormality due to the nonlinear terms, and nonnormality due to the distribution of the predictor variables. The results indicate that TD is preferable to both TDR and TDRP. Under the condition of strong nonlinear effects and nonnormal predictors, TDR often produced negative differences and TDRP showed no desirable power.  相似文献   

10.
The purpose of this study was to develop a scale for measuring prospective science teachers’ awareness of waste recycling. The study was conducted with the participation of 382 prospective teachers attending a university located in northern Turkey. The five-point Likert type scale that was developed contained 82 items relating to prospective science teachers’ awareness of waste recycling. The factor analysis conducted showed that five items had factor loadings below 0.30, and five were cross loading items. Factor analysis was repeated after removing these items. A further 24 items were removed from the list at the end of the factor analysis, and the remaining 48 items were grouped under ten dimensions. The reliability coefficient for the factors extracted varied between 0.717 and 0.805, and the internal reliability coefficient for the whole scale was 0.905.  相似文献   

11.
This research introduces, illustrates, and tests a variation of IRT-LR-DIF, called EH-DIF-2, in which the latent density for each group is estimated simultaneously with the item parameters as an empirical histogram (EH). IRT-LR-DIF is used to evaluate the degree to which items have different measurement properties for one group of people versus another, irrespective of mean differences on the construct. Usually, the latent distribution is presumed normal for both groups, but results are biased if this assumption is violated. Simulations show that if the latent densities are nonnormal, Type I error and estimates of the item parameters and focal-group mean and SD are more accurate using EH-DIF-2 than standard methods. Free software for carrying out EH-DIF-2 is available on request.  相似文献   

12.
The hierarchical rater model (HRM) re‐cognizes the hierarchical structure of data that arises when raters score constructed response items. In this approach, raters’ scores are not viewed as being direct indicators of examinee proficiency but rather as indicators of essay quality; the (latent categorical) quality of an examinee's essay in turn serves as an indicator of the examinee's proficiency, thus yielding a hierarchical structure. Here it is shown that a latent class model motivated by signal detection theory (SDT) is a natural candidate for the first level of the HRM, the rater model. The latent class SDT model provides measures of rater precision and various rater effects, above and beyond simply severity or leniency. The HRM‐SDT model is applied to data from a large‐scale assessment and is shown to provide a useful summary of various aspects of the raters’ performance.  相似文献   

13.
This study investigated the extent to which class-specific parameter estimates are biased by the within-class normality assumption in nonnormal growth mixture modeling (GMM). Monte Carlo simulations for nonnormal GMM were conducted to analyze and compare two strategies for obtaining unbiased parameter estimates: relaxing the within-class normality assumption and using data transformation on repeated measures. Based on unconditional GMM with two latent trajectories, data were generated under different sample sizes (300, 800, and 1500), skewness (0.7, 1.2, and 1.6) and kurtosis (2 and 4) of outcomes, numbers of time points (4 and 8), and class proportions (0.5:0.5 and 0.25:0.75). Of the four distributions, it was found that skew-t GMM had the highest accuracy in terms of parameter estimation. In GMM based on data transformations, the adjusted logarithmic method was more effective in obtaining unbiased parameter estimates than the use of van der Waerden quantile normal scores. Even though adjusted logarithmic transformation in nonnormal GMM reduced computation time, skew-t GMM produced much more accurate estimation and was more robust over a range of simulation conditions. This study is significant in that it considers different levels of kurtosis and class proportions, which has not been investigated in depth in previous studies. The present study is also meaningful in that investigated the applicability of data transformation to nonnormal GMM.  相似文献   

14.
Nonlinear factor analysis is a tool commonly used by measurement specialists to identify both the presence and nature of multidimensionality in a set of test items, an important issue given that standard Item Response Theory models assume a unidimensional latent structure. Results from most factor-analytic algorithms include loading matrices, which are used to link items with factors. Interpretation of the loadings typically occurs after they have been rotated in order to amplify the presence of simple structure. The purpose of this simulation study is to compare the ability of two commonly used methods of rotation, Varimax and Promax, in terms of their ability to correctly link items to factors and to identify the presence of simple structure. Results suggest that the two approaches are equally able to recover the underlying factor structure, regardless of the correlations among the factors, though the oblique method is better able to identify the presence of a "simple structure." These results suggest that for identifying which items are associated with which factors, either approach is effective, but that for identifying simple structure when it is present, the oblique method is preferable.  相似文献   

15.
Cross-cultural comparisons of latent variable means demands equivalent loadings and intercepts or thresholds. Although equivalence generally emphasizes items as originally designed, researchers sometimes modify response options in categorical items. For example, substantive research interests drive decisions to reduce the number of item categories. Further, categorical multiple-group confirmatory factor analysis (MG-CFA) methods generally require that the number of indicator categories is equal across groups; however, categories with few observations in at least one group can cause challenges. In the current paper, we examine the impact of collapsing ordinal response categories in MG-CFA. An empirical analysis and a complementary simulation study suggested meaningful impacts on model fit due to collapsing categories. We also found reduced scale reliability, measured as a function of Fisher’s information. Our findings further illustrated artifactual fit improvement, pointing to the possibility of data dredging for improved model-data consistency in challenging invariance contexts with large numbers of groups.  相似文献   

16.
Sometimes, test‐takers may not be able to attempt all items to the best of their ability (with full effort) due to personal factors (e.g., low motivation) or testing conditions (e.g., time limit), resulting in poor performances on certain items, especially those located toward the end of a test. Standard item response theory (IRT) models fail to consider such testing behaviors. In this study, a new class of mixture IRT models was developed to account for such testing behavior in dichotomous and polytomous items, by assuming test‐takers were composed of multiple latent classes and by adding a decrement parameter to each latent class to describe performance decline. Parameter recovery, effect of model misspecification, and robustness of the linearity assumption in performance decline were evaluated using simulations. It was found that the parameters in the new models were recovered fairly well by using the freeware WinBUGS; the failure to account for such behavior by fitting standard IRT models resulted in overestimation of difficulty parameters on items located toward the end of the test and overestimation of test reliability; and the linearity assumption in performance decline was rather robust. An empirical example is provided to illustrate the applications and the implications of the new class of models.  相似文献   

17.
This study represents the first published investigation into the construct validity of goal commitment as it affects the persistence process. Confirmatory factor analyses revealed that goal commitment could be decomposed into multiple indicators of the same latent construct: a special factor called goal commitment that groups items related to goal importance, specificity of goals, and situational influence; a second factor represented by items indicating certainty of purpose; and a third factor consisting of items related to goals in general. The predictive validity of each subcomponent on different outcomes related to student persistence was established. While goal commitment was found to have a significant direct effect on both students' intents to persist and actual persistence behavior, neither of the other two factors were as equally predictive as measures of student retention.  相似文献   

18.
Previous assessments of the reliability of test scores for testlet-composed tests have indicated that item-based estimation methods overestimate reliability. This study was designed to address issues related to the extent to which item-based estimation methods overestimate the reliability of test scores composed of testlets and to compare several estimation methods for different measurement models using simulation techniques. Three types of estimation approach were conceptualized for generalizability theory (GT) and item response theory (IRT): item score approach (ISA), testlet score approach (TSA), and item-nested-testlet approach (INTA). The magnitudes of overestimation when applying item-based methods ranged from 0.02 to 0.06 and were related to the degrees of dependence among within-testlet items. Reliability estimates from TSA were lower than those from INTA due to the loss of information with IRT approaches. However, this could not be applied in GT. Specified methods in IRT produced higher reliability estimates than those in GT using the same approach. Relatively smaller magnitudes of error in reliability estimates were observed for ISA and for methods in IRT. Thus, it seems reasonable to use TSA as well as INTA for both GT and IRT. However, if there is a relatively large dependence among within-testlet items, INTA should be considered for IRT due to nonnegligible loss of information.  相似文献   

19.
In this study, the authors aimed to examine 8 of the different methods for computing confidence intervals around alpha that have been proposed to determine which of these, if any, is the most accurate and precise. Monte Carlo methods were used to simulate samples under known and controlled population conditions wherein the underlying item distribution is nonnormal and when the items’ responses are those of rating scales rather than dichotomous items. Overall, one can conclude that, despite concerns expressed over the use of Fisher's method for coefficient alpha, in general, it actually outperformed the other methods. Larger sample sizes and larger coefficient alphas also resulted in better band coverage, whereas smaller number of items resulted in poorer band coverage.  相似文献   

20.
The present study examined the underlying structure of the variable Institutional Commitment by testing for the convergence, or lack thereof, among different indicators of the construct as represented by three theoretical frameworks (Tinto, 1975, 1987; Bean, 1985; Huselid and Day, 1991). Confirmatory factor analyses revealed that Institutional Commitment could be decomposed into two multiple indicators of the same latent construct: a general factor that groups items related to institutional quality, practical value of an education, utility of an education, fit between student and institution, and loyalty to the institution and another factor represented by items indicating similarity of values (Affinity of Values). Moreover, the study established the predictive validity of each subcomponent on different outcomes related to student persistence. While Institutional Commitment was found to have a significant direct effect on both students' intents to persist and actual persistence behavior, Affinity of Values was not as equally predictive of measures of student retention.Paper presented before the 1991 ASHE Annual Meeting. Boston, Massachusetts.  相似文献   

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