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1.
A 2-stage robust procedure as well as an R package, rsem, were recently developed for structural equation modeling with nonnormal missing data by Yuan and Zhang (2012). Several test statistics that have been used for complete data analysis are employed to evaluate model fit in the 2-stage robust method. However, properties of these statistics under robust procedures for incomplete nonnormal data analysis have never been studied. This study aims to systematically evaluate and compare 5 test statistics, including a test statistic derived from normal-distribution-based maximum likelihood, a rescaled chi-square statistic, an adjusted chi-square statistic, a corrected residual-based asymptotical distribution-free chi-square statistic, and a residual-based F statistic. These statistics are evaluated under a linear growth curve model by varying 8 factors: population distribution, missing data mechanism, missing data rate, sample size, number of measurement occasions, covariance between the latent intercept and slope, variance of measurement errors, and downweighting rate of the 2-stage robust method. The performance of the test statistics varies and the one derived from the 2-stage normal-distribution-based maximum likelihood performs much worse than the other four. Application of the 2-stage robust method and of the test statistics is illustrated through growth curve analysis of mathematical ability development, using data on the Peabody Individual Achievement Test mathematics assessment from the National Longitudinal Survey of Youth 1997 Cohort.  相似文献   

2.
This simulation study focused on the power for detecting group differences in linear growth trajectory parameters within the framework of structural equation modeling (SEM) and compared the latent growth modeling (LGM) approach to the more traditional repeated-measures analysis of variance (ANOVA) approach. Several patterns of group differences in linear growth trajectories were considered. SEM growth modeling consistently showed higher statistical power for detecting group differences in the linear growth slope than repeated-measures ANOVA. For small group differences in the growth trajectories, large sample size (e.g., N > 500) would be required for adequate statistical power. For medium or large group differences, moderate or small sample size would be sufficient for adequate power. Some future research directions are discussed.  相似文献   

3.
The latent growth curve modeling (LGCM) approach has been increasingly utilized to investigate longitudinal mediation. However, little is known about the accuracy of the estimates and statistical power when mediation is evaluated in the LGCM framework. A simulation study was conducted to address these issues under various conditions including sample size, effect size of mediated effect, number of measurement occasions, and R 2 of measured variables. In general, the results showed that relatively large samples were needed to accurately estimate the mediated effects and to have adequate statistical power, when testing mediation in the LGCM framework. Guidelines for designing studies to examine longitudinal mediation and ways to improve the accuracy of the estimates and statistical power were discussed.  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.
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   

6.
Latent growth modeling (LGM) is a popular and flexible technique that may be used when data are collected across several different measurement occasions. Modeling the appropriate growth trajectory has important implications with respect to the accurate interpretation of parameter estimates of interest in a latent growth model that may impact educational policy decisions. A Monte Carlo simulation study was conducted to examine the accuracy of six information-based criteria (i.e., AIC, CAIC, AICC, BIC, nBIC, and HQIC) when selecting among various growth trajectories modeled using LGM under different sample size, number of time points, and growth trajectory scenarios. The accuracy of the information criteria generally improved as sample size increased. The cubic and linear growth models were distinguished most accurately by the information criteria. All of the nonlinear models were more easily distinguished as the number of time points increased. The comparative performance of the six information criteria was dependent upon the manipulated conditions. Implications of the findings are discussed.  相似文献   

7.
Popular longitudinal models allow for prediction of growth trajectories in alternative ways. In latent class growth models (LCGMs), person-level covariates predict membership in discrete latent classes that each holistically define an entire trajectory of change (e.g., a high-stable class vs. late-onset class vs. moderate-desisting class). In random coefficient growth models (RCGMs, also known as latent curve models), however, person-level covariates separately predict continuously distributed latent growth factors (e.g., an intercept vs. slope factor). This article first explains how complex and nonlinear interactions between predictors and time are recovered in different ways via LCGM versus RCGM specifications. Then a simulation comparison illustrates that, aside from some modest efficiency differences, such predictor relationships can be recovered approximately equally well by either model—regardless of which model generated the data. Our results also provide an empirical rationale for integrating findings about prediction of individual change across LCGMs and RCGMs in practice.  相似文献   

8.
Cognitive diagnosis models (CDMs) have been developed to evaluate the mastery status of individuals with respect to a set of defined attributes or skills that are measured through testing. When individuals are repeatedly administered a cognitive diagnosis test, a new class of multilevel CDMs is required to assess the changes in their attributes and simultaneously estimate the model parameters from the different measurements. In this study, the most general CDM of the generalized deterministic input, noisy “and” gate (G‐DINA) model was extended to a multilevel higher order CDM by embedding a multilevel structure into higher order latent traits. A series of simulations based on diverse factors was conducted to assess the quality of the parameter estimation. The results demonstrate that the model parameters can be recovered fairly well and attribute mastery can be precisely estimated if the sample size is large and the test is sufficiently long. The range of the location parameters had opposing effects on the recovery of the item and person parameters. Ignoring the multilevel structure in the data by fitting a single‐level G‐DINA model decreased the attribute classification accuracy and the precision of latent trait estimation. The number of measurement occasions had a substantial impact on latent trait estimation. Satisfactory model and person parameter recoveries could be achieved even when assumptions of the measurement invariance of the model parameters over time were violated. A longitudinal basic ability assessment is outlined to demonstrate the application of the new models.  相似文献   

9.
This study examined the effect of sample size ratio and model misfit on the Type I error rates and power of the Difficulty Parameter Differences procedure using Winsteps. A unidimensional 30-item test with responses from 130,000 examinees was simulated and four independent variables were manipulated: sample size ratio (20/100/250/500/1000); model fit/misfit (1 PL and 3PLc =. 15 models); impact (no difference/mean differences/variance differences/mean and variance differences); and percentage of items with uniform and nonuniform DIF (0%/10%/20%). In general, the results indicate the importance of ensuring model fit to achieve greater control of Type I error and adequate statistical power. The manipulated variables produced inflated Type I error rates, which were well controlled when a measure of DIF magnitude was applied. Sample size ratio also had an effect on the power of the procedure. The paper discusses the practical implications of these results.  相似文献   

10.
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   

11.
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   

12.
The authors investigated 2 issues concerning the power of latent growth modeling (LGM) in detecting linear growth: the effect of the number of repeated measurements on LGM's power in detecting linear growth and the comparison between LGM and some other approaches in terms of power for detecting linear growth. A Monte Carlo simulation design was used, with 3 crossed factors (growth magnitude, number of repeated measurements, and sample size) and 1,000 replications within each cell condition. The major findings were as follows: For 3 repeated measurements, a substantial proportion of samples failed to converge in structural equation modeling; the number of repeated measurements did not show any effect on the statistical power of LGM in detecting linear growth; and the LGM approach outperformed both the dependent t test and repeated-measures analysis of variance (ANOVA) in terms of statistical power for detecting growth under the conditions of small growth magnitude and small to moderate sample size conditions. The multivariate repeated-measures ANOVA approach consistently underperformed the other tests.  相似文献   

13.
A linear latent growth curve mixture model with regime switching is extended in 2 ways. Previously, the matrix of first-order Markov switching probabilities was specified to be time-invariant, regardless of the pair of occasions being considered. The first extension, time-varying transitions, specifies different Markov transition matrices between each pair of occasions. The second extension is second-order time-invariant Markov transition probabilities, such that the probability of switching depends on the states at the 2 previous occasions. The models are implemented using the R package OpenMx, which facilitates data handling, parallel computation, and further model development. It also enables the extraction and display of relative likelihoods for every individual in the sample. The models are illustrated with previously published data on alcohol use observed on 4 occasions as part of the National Longitudinal Survey of Youth, and demonstrate improved fit to the data.  相似文献   

14.
Calls for accountability, coupled with a desire to improve teaching and learning, have prompted many colleges and universities to consider ways of assessing the effects of postsecondary education on student growth and development. Despite widespread support for the concept of assessing student change, relatively few institutions have implemented this type of assessment, in part because of a concern about the best method of measuring change. This article describes the use of structural equation models with latent variables to assess the effects of education on change. Advantages of using structural equation models with latent variables include error-free measurement of change, direct tests of the assumptions underlying change research, along with the power and flexibility of maximum likelihood estimation. An analysis of data on freshman-to-senior gains provides evidence of the advantages of latent variable structural equation modeling and also suggests that the group differences identified by traditional analysis of variance and covariance techniques may be an artifact of measurement error.  相似文献   

15.
When conducting longitudinal research, the investigation of between-individual differences in patterns of within-individual change can provide important insights. In this article, we use simulation methods to investigate the performance of a model-based exploratory data mining technique—structural equation model trees (SEM trees; Brandmaier, Oertzen, McArdle, & Lindenberger, 2013)—as a tool for detecting population heterogeneity. We use a latent-change score model as a data generation model and manipulate the precision of the information provided by a covariate about the true latent profile as well as other factors, including sample size, under the possible influences of model misspecifications. Simulation results show that, compared with latent growth curve mixture models, SEM trees might be very sensitive to model misspecification in estimating the number of classes. This can be attributed to the lower statistical power in identifying classes, resulting from smaller differences of parameters prescribed by the template model between classes.  相似文献   

16.
This study examined the performance of 4 correlation-based fit indexes (marginal and conditional pseudo R 2s; average and conditional concordance correlations) in detecting misspecification in mean structures in growth curve models. Their performance was also compared to that of 4 traditional SEM fit indexes. We found that the marginal pseudo R 2 and average concordance correlation were able to detect misspecification in the marginal mean structure (average change trajectory). The conditional pseudo R 2 and concordance correlation could detect misspecification when it occurred in the conditional mean structure (individual change trajectory) or in both mean structures. Compared to the SEM fit indexes, the correlation-based fit indexes were more robust to sample size but were less robust to data properties such as magnitude of population mean and measurement error. Theoretical and practical implications of the results and directions for future research are discussed.  相似文献   

17.
Applying item response theory models to repeated observations has demonstrated great promise in developmental research. By allowing the researcher to take account of the characteristics of both item response and measurement error in longitudinal trajectory analysis, it improves the reliability and validity of latent growth curve analysis. This has enabled the study, to differentially weigh individual items and examine developmental stability and change over time, to propose a comprehensive modeling framework, combining a measurement model with a structural model. Despite a large number of components requiring attention, this study focuses on model formulation, evaluates the performance of the estimators of model parameters, incorporates prior knowledge from Bayesian analysis, and applies the model using an illustrative example. It is hoped that this fundamental study can demonstrate the breadth of this unified latent growth curve model.  相似文献   

18.
This research focuses on the problem of model selection between the latent change score (LCS) model and the autoregressive cross-lagged (ARCL) model when the goal is to infer the longitudinal relationship between variables. We conducted a large-scale simulation study to (a) investigate the conditions under which these models return statistically (and substantively) different results concerning the presence of bivariate longitudinal relationships, and (b) ascertain the relative performance of an array of model selection procedures when such different results arise. The simulation results show that the primary sources of differences in parameter estimates across models are model parameters related to the slope factor scores in the LCS model (specifically, the correlation between the intercept factor and the slope factor scores) as well as the size of the data (specifically, the number of time points and sample size). Among several model selection procedures, correct selection rates were higher when using model fit indexes (i.e., comparative fit index, root mean square error of approximation) than when using a likelihood ratio test or any of several information criteria (i.e., Akaike’s information criterion, Bayesian information criterion, consistent AIC, and sample-size-adjusted BIC).  相似文献   

19.
Little research has examined factors influencing statistical power to detect the correct number of latent classes using latent profile analysis (LPA). This simulation study examined power related to interclass distance between latent classes given true number of classes, sample size, and number of indicators. Seven model selection methods were evaluated. None had adequate power to select the correct number of classes with a small (Cohen's d = .2) or medium (d = .5) degree of separation. With a very large degree of separation (d = 1.5), the Lo–Mendell–Rubin test (LMR), adjusted LMR, bootstrap likelihood ratio test, Bayesian Information Criterion (BIC), and sample-size-adjusted BIC were good at selecting the correct number of classes. However, with a large degree of separation (d = .8), power depended on number of indicators and sample size. Akaike's Information Criterion and entropy poorly selected the correct number of classes, regardless of degree of separation, number of indicators, or sample size.  相似文献   

20.
All Year 2 children in six randomly selected primary schools within one Local Education Authority (LEA) comprised the sample to which the Lawseq self‐esteem questionnaire was administered. Four years later, when they were Year 6, they completed the Lawseq again. A two‐way analysis of variance with Sex and Occasions was carried out on the 12 individual items of the instrument and the total. There were no significant differences between occasions or sexes on the overall score, but there were significant differences between occasions on seven of the 12 items and between sexes on two items. On only one item was there a significant interaction between sexes and occasions. The mean for the total fell over the 4 years. The means for both occasions were considerably below the mean of 19.00 obtained when Lawrence standardised the test in 1981. Discussion centred on possible reasons for this, such as appropriacy of the instrument for the age‐groups under study, stability of administration and changes within society and school.  相似文献   

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