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1.
This article provides a brief overview of confirmatory tetrad analysis (CTA) and presents a new set of Stata commands for conducting CTA. The tetrad command allows researchers to use model-implied vanishing tetrads to test the overall fit of structural equation models (SEMs) and the relative fit of two SEMs that are tetrad-nested. An extension of the command, tetrad_matrix, allows researchers to conduct CTA using a sample covariance matrix as input rather than relying on raw data. Researchers can also use the tetrad_matrix command to input a polychoric correlation matrix and conduct CTA for SEMs involving dichotomous, ordinal, or censored outcomes. Another extension of the command, tetrad_bootstrap, provides a bootstrapped p value for the chi-square test statistic. With Stata’s recently developed commands for structural equation modeling, researchers can integrate CTA with data preparation, likelihood ratio tests for model fit, and the estimation of model parameters in a single statistical software package.  相似文献   

2.
This article considers the implications for other noncentrality parameter-based statistics from Steiger's (1998) multiple sample adjustment to the root mean square error of approximation (RMSEA) measure. When a structural equation model is fitted simultaneously in more than 1 sample, it is shown that the calculation of the noncentrality parameter used in tests of approximate fit and in point and interval estimators of other noncentral fit statistics (except the expected cross-validation index) also requires a likeminded adjustment. Furthermore, it is shown that an adjustment is needed in multiple sample models for correctly calculating MacCallum, Browne, and Sugawara's (1996) approach to power analysis. The accuracy of these proposals is investigated and demonstrated in a small Monte Carlo study in which particular attention is paid to using appropriately constructed covariance matrices that give specified nonzero population discrepancy values under maximum likelihood estimation.  相似文献   

3.
This study investigated the performance of fit indexes in selecting a covariance structure for longitudinal data. Data were simulated to follow a compound symmetry, first-order autoregressive, first-order moving average, or random-coefficients covariance structure. We examined the ability of the likelihood ratio test (LRT), root mean square error of approximation (RMSEA), comparative fit index (CFI), and Tucker–Lewis Index (TLI) to reject misspecified models with varying degrees of misspecification. With a sample size of 20, RMSEA, CFI, and TLI are high in both Type I and Type II error rates, whereas LRT has a high Type II error rate. With a sample size of 100, these indexes generally have satisfactory performance, but CFI and TLI are affected by a confounding effect of their baseline model. Akaike's Information Criterion (AIC) and Bayesian Information Criterion (BIC) have high success rates in identifying the true model when sample size is 100. A comparison with the mixed model approach indicates that separately modeling the means and covariance structures in structural equation modeling dramatically improves the success rate of AIC and BIC.  相似文献   

4.
Analysis of variance is one of the most frequently used statistical analyses in the behavioral, educational, and social sciences, and special attention has been paid to the selection and use of an appropriate effect size measure of association in analysis of variance. This article presents the sample size procedures for precise interval estimation of eta-squared and partial eta-squared in fixed-effects analysis of variance designs. The desired precision of a confidence interval is assessed with respect to (a) the control of expected width and (b) the tolerance probability of interval width within a designated value. In addition, sample size calculations for standardized contrasts of treatment effects and corresponding partial strength of association effect sizes are also considered.  相似文献   

5.
In order to analyze intensive longitudinal data collected across multiple individuals, researchers frequently have to decide between aggregating all individuals or analyzing each individual separately. This paper presents an R package, gimme, which allows for the automatic specification of individual-level structural equation models that combine group-, subgroup-, and individual-level information. This R package is a complement of the GIMME program currently available via a combination of MATLAB and LISREL. By capitalizing on the flexibility of R and the capabilities of the existing structural equation modeling package lavaan, gimme allows for the automated specification and estimation of group-, subgroup-, and individual-level relations in time series data from within a structural equation modeling framework. Applications include daily diary data as well as functional magnetic resonance imaging data.  相似文献   

6.
A problem central to structural equation modeling is measurement model specification error and its propagation into the structural part of nonrecursive latent variable models. Full-information estimation techniques such as maximum likelihood are consistent when the model is correctly specified and the sample size large enough; however, any misspecification within the model can affect parameter estimates in other parts of the model. The goals of this study included comparing the bias, efficiency, and accuracy of hypothesis tests in nonrecursive latent variable models with indirect and direct feedback loops. We compare the performance of maximum likelihood, two-stage least-squares and Bayesian estimators in nonrecursive latent variable models with indirect and direct feedback loops under various degrees of misspecification in small to moderate sample size conditions.  相似文献   

7.
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8.
The relation among fit indexes, power, and sample size in structural equation modeling is examined. The noncentrality parameter is required to compute power. The 2 existing methods of computing power have estimated the noncentrality parameter by specifying an alternative hypothesis or alternative fit. These methods cannot be implemented easily and reliably. In this study, 4 fit indexes (RMSEA, CFI, McDonald's Fit Index, and Steiger's gamma) were used to compute the noncentrality parameter and sample size to achieve certain level of power. The resulting power and sample size varied as a function of (a) choice of fit index, (b) number of variables/degrees of freedom, (c) relation among the variables, and (d) value of the fit index. However, if the level of misspecification were held constant, then the resulting power and sample size would be identical.  相似文献   

9.
The aim of this article is to introduce the R package semds for structural equation multidimensional scaling. This methodology combines multidimensional scaling with latent variable features from structural equation modeling and is applicable to asymmetric and three-way input dissimilarity data. This key idea of this approach is that the input data are assumed to be imperfect measurements of a latent symmetric dissimilarity matrix. The parameter estimation is performed via an alternating least squares multidimensional scaling procedure that minimizes the stress. The latent dissimilarities are estimated as factor scores within a structural equation modeling framework. Applications shown in the article involve data associated with the banking crisis and data from avalanche research. The models fitted with the semds package are compared to related methods from multidimensional scaling. The R code to reproduce all the computations is provided in the supplementary materials.  相似文献   

10.
Yuan and Hayashi (2010) Yuan, K.-H. and Hayashi, K. 2010. Fitting data to model: Structural equation modeling diagnosis using two scatter plots. Psychological Methods, 15: 335–351. [Crossref], [Web of Science ®] , [Google Scholar] introduced 2 scatter plots for model and data diagnostics in structural equation modeling (SEM). However, the generation of the plots requires in-depth understanding of their underlying technical details. This article develops and introduces an R package semdiag for easily drawing the 2 plots. With a model specified in EQS syntax, one only needs to supply as few as 2 parameters to generate the 2 plots using the semdiag package. Two examples are provided to illustrate the use of the package. Multiple figures are used to explain the elements of data and model diagnostics. Advice on selecting proper estimation methods following the diagnostics is also given.  相似文献   

11.
Multiple-group analysis in covariance-based structural equation modeling (SEM) is an important technique to ensure the invariance of latent construct measurements and the validity of theoretical models across different subpopulations. However, not all SEM software packages provide multiple-group analysis capabilities. The sem package for the R system, which holds an important position as the only open-source SEM software, does not currently offer multigroup analysis. This article offers an alternative to true multigroup modeling that is easy to understand and apply in the R software. It is limited, however, by the constraint that groups require equal sample size.  相似文献   

12.
Though the common default maximum likelihood estimator used in structural equation modeling is predicated on the assumption of multivariate normality, applied researchers often find themselves with data clearly violating this assumption and without sufficient sample size to utilize distribution-free estimation methods. Fortunately, promising alternatives are being integrated into popular software packages. Bootstrap resampling, which is offered in AMOS (Arbuckle, 1997), is one potential solution for estimating model test statistic p values and parameter standard errors under nonnormal data conditions. This study is an evaluation of the bootstrap method under varied conditions of nonnormality, sample size, model specification, and number of bootstrap samples drawn from the resampling space. Accuracy of the test statistic p values is evaluated in terms of model rejection rates, whereas accuracy of bootstrap standard error estimates takes the form of bias and variability of the standard error estimates themselves.  相似文献   

13.
Multilevel structural equation modeling (MSEM) has been proposed as an extension to structural equation modeling for analyzing data with nested structure. We have begun to see a few applications in cross-cultural research in which MSEM fits well as the statistical model. However, given that cross-cultural studies can only afford collecting data from a relatively small number of countries, the appropriateness of MSEM has been questioned. Using the data from the International Social Survey Program (1997; N = 15,244 from 27 countries), we first showed how Muth?n's MSEM procedure could be applied to a real data set on cross-cultural research. Given a small country-level sample size (27 countries) we then demonstrated that results on the individual level were quite stable even when using small individual-level sample sizes, whereas the group-level parameter estimates and their standard errors were affected unsystematically by varying individual-level sample sizes. Use of the findings for cross-cultural research and other areas with limited numbers of groups are discussed.  相似文献   

14.
Meta-analytic structural equation modeling (MASEM) refers to a set of meta-analysis techniques for combining and comparing structural equation modeling (SEM) results from multiple studies. Existing approaches to MASEM cannot appropriately model between-studies heterogeneity in structural parameters because of missing correlations, lack model fit assessment, and suffer from several theoretical limitations. In this study, we address the major shortcomings of existing approaches by proposing a novel Bayesian multilevel SEM approach. Simulation results showed that the proposed approach performed satisfactorily in terms of parameter estimation and model fit evaluation when the number of studies and the within-study sample size were sufficiently large and when correlations were missing completely at random. An empirical example about the structure of personality based on a subset of data was provided. Results favored the third factor structure over the hierarchical structure. We end the article with discussions and future directions.  相似文献   

15.
Structural equation modeling (SEM) is now a generic modeling framework for many multivariate techniques applied in the social and behavioral sciences. Many statistical models can be considered either as special cases of SEM or as part of the latent variable modeling framework. One popular extension is the use of SEM to conduct linear mixed-effects modeling (LMM) such as cross-sectional multilevel modeling and latent growth modeling. It is well known that LMM can be formulated as structural equation models. However, one main difference between the implementations in SEM and LMM is that maximum likelihood (ML) estimation is usually used in SEM, whereas restricted (or residual) maximum likelihood (REML) estimation is the default method in most LMM packages. This article shows how REML estimation can be implemented in SEM. Two empirical examples on latent growth model and meta-analysis are used to illustrate the procedures implemented in OpenMx. Issues related to implementing REML in SEM are discussed.  相似文献   

16.
When using the popular structural equation modeling (SEM) methodology, the issues of sample size, method of parameter estimation, assessment of model fit, and capitalization on chance are of great importance in the process of evaluating the results of an empirical study. We focus first on implications of the large‐sample theory underlying applications of the methodology. The utility for applied contexts of the asymptotically distribution‐free parameter estimation and model testing method is discussed next. We then argue for wider use of a recently developed, non conventional model‐fit assessment strategy in SEM. We conclude by discussing the issue of capitalization on chance, primarily in situations in which exploratory and confirmatory analyses are conducted on the same data set.  相似文献   

17.
This article compares two structural equation modeling fit indexes—Bentler's ( 1990; Bentler & Bonett, 1980) Confirmatory Fit Index (CFI) and Steiger and Lind's (1980; Browne & Cudeck, 1993) Root Mean Square Error of Approximation (RMSEA). These two fit indexes are both conceptually linked to the noncentral chi‐square distribution, but CFI has seen much wider use in applied research, whereas RMSEA has only recently been gaining attention. The article suggests that use of CFI is problematic because of its baseline model. CFI seems to be appropriate in more exploratory contexts, whereas RMSEA is appropriate in more confirmatory contexts. On the other hand, CFI does have an established parsimony adjustment, although the adjustment included in RMSEA may be inadequate.  相似文献   

18.
A Monte Carlo simulation study was conducted to investigate the effects on structural equation modeling (SEM) fit indexes of sample size, estimation method, and model specification. Based on a balanced experimental design, samples were generated from a prespecified population covariance matrix and fitted to structural equation models with different degrees of model misspecification. Ten SEM fit indexes were studied. Two primary conclusions were suggested: (a) some fit indexes appear to be noncomparable in terms of the information they provide about model fit for misspecified models and (b) estimation method strongly influenced almost all the fit indexes examined, especially for misspecified models. These 2 issues do not seem to have drawn enough attention from SEM practitioners. Future research should study not only different models vis‐à‐vis model complexity, but a wider range of model specification conditions, including correctly specified models and models specified incorrectly to varying degrees.  相似文献   

19.
Teachers’ professional development (PD) receives a great deal of attention in current educational settings. However, research has shown that many teachers hesitate to attend PD programs. In this study, data were collected from 270 elementary school teachers and were subjected to confirmatory factor analysis and structural equation modeling to examine their intention to attend the weekly PD programs on Wednesday afternoons (PDWAP). The results revealed that the participants value the acquisition of pedagogical content knowledge (PCK) more than they value pedagogical knowledge (PK) and content knowledge (CK) because of the expected usefulness of each for teaching. Moreover, the results of this study have implications for PD program design, and call for a stronger focus on PCK.

AbbreviationAdjusted Goodness of Fit Index (AGFI); Analysis of Moment Structures(AMOS); average variance (AVE); Chi-square(); content knowledge (CK); continuing professional development (CPD); Comparative Fit Index (CFI); degree of freedom (df); expectancy-value theory (EVT); Goodness of Fit Index (GFI); Incremental Fit Index (IFI); Mean(M); Parsimonious Goodness of Fit Index (PGFI); Parsimonious Normed Fit Index (PNFI); Parsimonious comparative-fit-index (PCFI); pedagogical content knowledge (PCK); pedagogical knowledge (PK); professional development (PD); professional development programs on Wednesday afternoons (PDWAP); Root Mean Square Error of Approximation (RMSEA); standard deviation (SD); structural equation modeling (SEM); square of multiple correlation coefficients (R2); Teaching Beliefs Survey (TBS); theory of planned behavior (TPB); Tucker-Lewis Index (TLI); United Kingdom (UK)  相似文献   


20.
Conventional null hypothesis testing (NHT) is a very important tool if the ultimate goal is to find a difference or to reject a model. However, the purpose of structural equation modeling (SEM) is to identify a model and use it to account for the relationship among substantive variables. With the setup of NHT, a nonsignificant test statistic does not necessarily imply that the model is correctly specified or the size of misspecification is properly controlled. To overcome this problem, this article proposes to replace NHT by equivalence testing, the goal of which is to endorse a model under a null hypothesis rather than to reject it. Differences and similarities between equivalence testing and NHT are discussed, and new “T-size” terminology is introduced to convey the goodness of the current model under equivalence testing. Adjusted cutoff values of root mean square error of approximation (RMSEA) and comparative fit index (CFI) corresponding to those conventionally used in the literature are obtained to facilitate the understanding of T-size RMSEA and CFI. The single most notable property of equivalence testing is that it allows a researcher to confidently claim that the size of misspecification in the current model is below the T-size RMSEA or CFI, which gives SEM a desirable property to be a scientific methodology. R code for conducting equivalence testing is provided in an appendix.  相似文献   

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