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Second language (L2) listening comprehension is a function of many variables. We focused on metacognitive awareness, which we measured using the Metacognitive Awareness Listening Questionnaire (MALQ; Vandergrift et al., 2006), and meta-analyzed (a) the factor structure of the MALQ and (b) the relationship between metacognitive awareness and L2 listening comprehension. We used meta-analytic structural equation modeling to synthesize 29 studies that provided Pearson's product-moment correlation matrices from 4,574 learners. Results showed (a) that the MALQ measured metacognitive awareness as a single factor with five subcomponents (their interrelationship and relative contribution to metacognitive awareness varied) and (b) that metacognitive awareness explained listening comprehension (b* = .306). The results were moderated by publication type, the response format of listening comprehension tests, and participant type. The findings can help researchers to better conceptualize the construct of metacognitive awareness in relation to listening comprehension as well as to score metacognitive awareness.

Meta-analytic structural equation modeling (MASEM) refers to fitting structural equation models (SEMs) (such as path models or factor models) to meta-analytic data. Currently, fitting MASEMs may be challenging for researchers that are not accustomed to working with R software and packages. Therefore, we developed webMASEM; a web application for MASEM. This app implements the one-stage MASEM approach, and allows users to apply MASEM in a user-friendly way. The aim of this article is to provide a tutorial on one-stage MASEM and a practical guide to webMASEM. We will pay specific attention to how the data should be structured and prepared for webMASEM, because mistakes in this step may lead to faulty results without receiving an error message. The use of webMASEM is illustrated with an analysis of a meta-analytic path model in which the path coefficients are moderated by a study-level variable, a meta-analytic factor model in which the factor loadings are moderated by a study-level variable, and a meta-analytic panel model in which the effects are moderated by a study-level variable. All used datafiles and R scripts are available online.

The current study examines the relationship between bilingual children's dual language experience (i.e. language input, language output and vocabulary proficiency), and their social-emotional and behavioral skills. Data were analysed from 805 Singaporean bilingual preschoolers (ages 4; 1-5; 8 years), who are learning English and either Mandarin (n = 551), Malay (n = 105), or Tamil, (n = 149). A parent questionnaire and standardized vocabulary tests were used to assess children's bilingual language environment and vocabulary knowledge. Children's social-emotional and behavioral skills were evaluated by teachers using the Strengths and Difficulties Questionnaire. A series of variables which might influence social-emotional and behavioral skills (e.g. gender, non-verbal IQ, SES, and emotion recognition) were controlled and mixed-effects models were used to conduct data analysis. Results demonstrated that children who had larger bilingual receptive vocabulary and had frequently spoken both languages for a longer time had better social-emotional and behavioral skills. Gender and emotion recognition ability were also found to be significantly related to children's social-emotional and behavioral skills. Such findings held true for children across different Mother Tongue language backgrounds. This suggests that a good language environment for bilingual children should be promoted not only for the sake of their early language development, but also because of the potential benefits to their social-emotional and behavioral skills.

Meta-analysis and structural equation modeling (SEM) are 2 of the most prominent statistical techniques employed in the behavioral, medical, and social sciences. They each have their own well-established research communities, terminologies, statistical models, software packages, and journals ("Research Synthesis Methods" and "Structural Equation Modeling: A Multidisciplinary Journal"). In this paper, I will provide some personal reflections on combining meta-analysis and SEM in the forms of meta-analytic SEM and SEM-based meta-analysis. The critical contributions of Becker (1992), Shadish (1992), and Viswesvaran and Ones (1995) in the early development of meta-analytic SEM are highlighted. Another goal of the paper is to illustrate how meta-analysis can be extended and integrated with other techniques to address new research questions such as the analysis of Big Data. I hope that this paper may stimulate more research development in the area of combining meta-analysis and SEM.

Meta-analytic structural equation modeling (MASEM) combines the techniques of meta-analysis and structural equation modeling for the purpose of synthesizing correlation or covariance matrices and fitting structural equation models on the pooled correlation or covariance matrix. Both fixed-effects and random-effects models can be defined in MASEM. Random-effects models are well known in conventional meta-analysis but are less studied in MASEM. The primary objective of this paper was to address issues related to random-effects models in MASEM. Specifically, we compared two different random-effects models in MASEM--correlation-based MASEM and parameter-based MASEM--and explored their strengths and limitations. Two examples were used to illustrate the similarities and differences between these models. We offered some practical guidelines for choosing between these two models. Future directions for research on random-effects models in MASEM were also discussed.

Principal component regression (PCR) is a popular technique in data analysis and machine learning. However, the technique has two limitations. First, the principal components (PCs) with the largest variances may not be relevant to the outcome variables. Second, the lack of standard error estimates for the unstandardized regression coefficients makes it hard to interpret the results. To address these two limitations, we propose a model‐based approach that includes two mean and covariance structure models defined for multivariate PCR. By estimating the defined models, we can obtain inferential information that will allow us to test the explanatory power of individual PCs and compute the standard error estimates for the unstandardized regression coefficients. A real example is used to illustrate our approach, and simulation studies under normality and nonnormality conditions are presented to validate the standard error estimates for the unstandardized regression coefficients. Finally, future research topics are discussed. [ABSTRACT FROM AUTHOR]

Redundancy analysis (RA) is a multivariate method that maximizes the mean variance of a set of criterion variables explained by a small number of redundancy variates (i.e., linear combinations of a set of predictor variables). However, two challenges exist in RA. First, inferential information for the RA estimates might not be readily available. Second, the existing methods addressing the dimensionality problem in RA are limited for various reasons. To aid the applications of RA, we propose a direct covariance structure modeling approach to RA. The proposed approach (1) provides inferential information for the RA estimates, and (2) allows the researcher to use a simple yet practical criterion to address the dimensionality problem in RA. We illustrate our approach with an artificial example, validate some standard error estimates by simulations, and demonstrate our new criterion in a real example. Finally, we conclude with future research topics. [ABSTRACT FROM AUTHOR]

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. (Contains 1 footnote.)

Meta-analysis is the statistical analysis of a collection of analysis results from individual studies, conducted for the purpose of integrating the findings. Structural equation modeling (SEM), on the other hand, is a multivariate technique for testing hypothetical models with latent and observed variables. This article shows that fixed-effects meta-analyses with the following characteristics can be modeled in the SEM framework: (a) using any type of effect size; (b) including categorical and continuous moderators; and (c) including multivariate effect sizes. Empirical examples in LISREL syntax are used to demonstrate the equivalence between the meta-analytic and SEM approaches. Future directions for and extensions to this approach are discussed. (Contains 3 figures, 3 tables and 8 footnotes.)

Confidence intervals (CIs) for parameters are usually constructed based on the estimated standard errors. These are known as Wald CIs. This article argues that likelihood-based CIs (CIs based on likelihood ratio statistics) are often preferred to Wald CIs. It shows how the likelihood-based CIs and the Wald CIs for many statistics and psychometric indexes can be constructed with the use of phantom variables (Rindskopf, 1984) in some of the current structural equation modeling (SEM) packages. The procedures to form CIs for the differences in correlation coefficients, squared multiple correlations, indirect effects, coefficient alphas, and reliability estimates are illustrated. A simulation study on the Pearson correlation is used to demonstrate the advantages of the likelihood-based CI over the Wald CI. Issues arising from this SEM approach and extensions of this approach are discussed. (Contains 1 table, 5 figures and 7 footnotes.)

Structural equation modeling (SEM) is widely used as a statistical framework to test complex models in behavioral and social sciences. When the number of publications increases, there is a need to systematically synthesize them. Methodology of synthesizing findings in the context of SEM is known as meta-analytic SEM (MASEM). Although correlation matrices are usually preferred in MASEM, there are cases in which synthesizing covariance matrices is useful, especially when the scales of the measurement are comparable. This study extends the 2-stage SEM (TSSEM) approach proposed by M. W. L. Cheung and Chan (2005b) to synthesizing covariance matrices in MASEM. A simulation study was conducted to compare the TSSEM approach with several approximate methods. An empirical example is used to illustrate the procedures and future directions for MASEM are discussed. (Contains 5 tables and 3 footnotes.)

Meta-analysis and structural equation modeling (SEM) are two important statistical methods in the behavioral, social, and medical sciences. They are generally treated as two unrelated topics in the literature. The present article proposes a model to integrate fixed-, random-, and mixed-effects meta-analyses into the SEM framework. By applying an appropriate transformation on the data, studies in a meta-analysis can be analyzed as subjects in a structural equation model. This article also highlights some practical benefits of using the SEM approach to conduct a meta-analysis. Specifically, the SEM-based meta-analysis can be used to handle missing covariates, to quantify the heterogeneity of effect sizes, and to address the heterogeneity of effect sizes with mixture models. Examples are used to illustrate the equivalence between the conventional meta-analysis and the SEM-based meta-analysis. Future directions on and issues related to the SEM-based meta-analysis are discussed. (Contains 1 table, 5 figures, and 10 footnotes.)

Mediators are variables that explain the association between an independent variable and a dependent variable. Structural equation modeling (SEM) is widely used to test models with mediating effects. This article illustrates how to construct confidence intervals (CIs) of the mediating effects for a variety of models in SEM. Specifically, mediating models with 1 mediator, 2 intermediate mediators, 2 specific mediators, and 1 mediator in 2 independent groups are illustrated. By using phantom variables (Rindskopf, 1984), a Wald CI, percentile bootstrap CI, bias-corrected bootstrap CI, and a likelihood-based CI on the mediating effect are easily constructed with some existing SEM packages, such as LISREL, M plus, and Mx. Monte Carlo simulation studies are used to compare the coverage probabilities of these CIs. The results show that the coverage probabilities of these CIs are comparable when the mediating effect is large or when the sample size is large. However, when the mediating effect and the sample size are both small, the bootstrap CI and likelihood-based CI are preferred over the Wald CI. Extensions of this SEM approach for future research are discussed.

Response bias has long been recognized as an issue in the behavioral and social sciences, especially in cross-cultural research. Transforming raw data into ipsatized data, individual scores subject to a constant sum constraint, is proposed to be an effective measure to minimize response bias. One major problem of applying ipsatized data is that scores are incomparable across individuals. By assuming that the ipsatized data are transformed from a preipsative confirmatory factor analytic model, factor scores based on the ipsatized data are proposed to serve as proxy variables for the preipsative information in this study. The ipsative factor scores can be used for further data analysis. Simulation results reveal that the proposed method works reasonably well. A real example is used to illustrate how this method can be applied to real data sets. (Contains 6 tables.)

To synthesize studies that use structural equation modeling (SEM), researchers usually use Pearson correlations (univariate r), Fisher z scores (univariate z), or generalized least squares (GLS) to combine the correlation matrices. The pooled correlation matrix is then analyzed by the use of SEM. Questionable inferences may occur for these ad hoc procedures. A 2-stage structural equation modeling (TSSEM) method is proposed to incorporate meta-analytic techniques and SEM into a unified framework. Simulation results reveal that the univariate-r, univariate-z, and TSSEM methods perform well in testing the homogeneity of correlation matrices and estimating the pooled correlation matrix. When fitting SEM, only TSSEM works well. The GLS method performed poorly in small to medium samples.

Researchers are becoming interested in combining meta-analytic techniques and structural equation modeling to test theoretical models from a pool of studies. Most existing procedures are based on the assumption that all correlation matrices are homogeneous. Few studies have addressed what the next step should be when studies being analyzed are heterogeneous and the search for moderator variables for homogeneous subgroup analysis fails. Cluster analysis is proposed and evaluated in this article as an exploratory tool to classify studies into relatively homogeneous groups. Simulation studies indicate that using Euclidean distance on raw correlation coefficients or U-transformed scores with the complete linkage or Wards minimum-variance methods will provide satisfactory results.

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 Muthn'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.

Ipsative data (individual scores subject to a constant-sum constraint), suggested to minimize response bias, are sometimes observed in behavioral sciences. Chan and Bentler (1993, 1996) proposed a method to analyze ipsative data in a single-group case. Cheung and Chan (2002) extended the method to multiple-group analysis. However, these methods require tedious procedures on formulating within- and between-group constraints and recovering the parameter estimates and their standard errors. A direct estimation method, which is equivalent to Chan and Bentler's method with an alternative model specification, is proposed in this article. The 1st-order factor-analytic ipsative model in Chan and Bentler's method is reparameterized as a restricted 2nd-order factor-analytic model with fixed factor loading matrix reflecting the ipsative properties in the direct estimation method. The direct estimation method can be easily extended to test measurement invariance properties in multiple-group analysis. Issues related to ipsative models are also addressed.

Defines a mathematical model of uniform response bias (URB) and proposes ipsative measures to minimize the effect of URB in multigroup confirmatory factor analysis. Illustrates the method using real data from the Chinese Personality Assessment Inventory for 2 groups of sample sizes 793 and 792 adults. (SLD)