Abstract

Meta-analytic structural equation modeling (MASEM) combines the ideas 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. Cheung and Chan (Psychological Methods 10:40–64, 2005b, Structural Equation Modeling 16:28–53, 2009) proposed a two-stage structural equation modeling (TSSEM) approach to conducting MASEM that was based on a fixed-effects model by assuming that all studies have the same population correlation or covariance matrices. The main objective of this article is to extend the TSSEM approach to a random-effects model by the inclusion of study-specific random effects. Another objective is to demonstrate the procedures with two examples using the metaSEM package implemented in the R statistical environment. Issues related to and future directions for MASEM are discussed.
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Abstract

Cheung and Chan (2005) proposed a two-stage method to conduct meta analytic structural equation modelling (MASEM). MASEM refers to the technique of fitting structural equation models to pooled correlation or covariance matrices from several studies. Unfortunately, researchers do not always report all correlations between the variables of interest. In this paper, we propose a method to deal with missing correlations in the two-stage approach. We illustrate the proposed model with a meta-analysis of teacher child relationships variables from 99 studies. In addition, using simulated data, we show that our method leads to more precise parameter estimates than the existing approach.
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Abstract

Regression methods are widely used by researchers in many fields, yet methods for synthesizing regression results are scarce. This study proposes using a factored likelihood method, originally developed to handle missing data, to appropriately synthesize regression models involving different predictors. This method uses the correlations reported in the regression studies to calculate synthesized standardized slopes. It uses available correlations to estimate missing ones through a series of regressions, allowing us to synthesize correlations among variables as if each included study contained all the same variables. Great accuracy and stability of this method under fixed-effects models were found through Monte Carlo simulation. An example was provided to demonstrate the steps for calculating the synthesized slopes through sweep operators. By rearranging the predictors in the included regression models or omitting a relatively small number of correlations from those models, we can easily apply the factored likelihood method to many situations involving synthesis of linear models. Limitations and other possible methods for synthesizing more complicated models are discussed. Copyright © 2012 John Wiley & Sons, Ltd.
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Abstract

Practical meta-analysis of correlation matrices generally ignores covariances (and hence correlations) between correlation estimates. The authors consider various methods for allowing for covariances, including generalized least squares, maximum marginal likelihood, and Bayesian approaches, illustrated using a 6-dimensional response in a series of psychological studies concerning prediction of exercise behavior change. Quantities of interest include the overall population mean correlation matrix, the contrast between the mean correlations, the predicted correlation matrix in a new study, and the conflict between the existing studies and a new correlation matrix. The authors conclude that accounting for correlations between correlations is unnecessary when interested in individual correlations but potentially important if concerned with a composite measure involving 2 or more correlations. A simulation study indicates the asymptotic normal assumption appears reasonable. Because of potential instability in the generalized least squares methods, they recommend a model-based approach, either the maximum marginal likelihood approach or a full Bayesian analysis. Copyright (c) 2008 APA.
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This article introduces and illustrates a procedure for aggregating data from several factor analyses in a meta-analysis. The central idea is to combine the correlation matrices first and then perform a new factor analysis. Special attention is given to the handling of general factors in data sets and to the use of correlations corrected for attenuation. (PsycINFO Database Record (c) 2002 APA, all rights reserved) (journal abstract)
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Abstract

The partial correlation and the semi-partial correlation can be seen as measures of partial effect sizes for the correlational family. Thus, both indices have been used in the meta-analysis literature to represent the relationship between an outcome and a predictor of interest, controlling for the effect of other variables in the model. This article evaluates the accuracy of synthesizing these two indices under different situations. Both partial correlation and the semi-partial correlation appear to behave as expected with respect to bias and root mean squared error (RMSE). However, the partial correlation seems to outperform the semi-partial correlation regarding Type I error of the homogeneity test (Q statistic). Although further investigation is needed to fully understand the impact of meta-analyzing partial effect sizes, the current study demonstrates the accuracy of both indices.
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Abstract

During the past two decades, organizational researchers have combined the techniques of meta-analysis (MA) and structural equation modeling (SEM) with the intention of building on the strengths of these approaches to address unique research questions. Though these integrative analyses can involve the use of SEM to conduct MA, the focus of the current article is on those situations in which meta-analytic correlations are used as input for testing structural models not previously evaluated in any single, primary study. The purpose of this paper is to provide a summary of the salient choices that must be made by researchers interested in integrating these methods and offering several recommendations for those undertaking such analytic strategies. Overall, the combination of MA and SEM offers researchers unique opportunities, but caution must be exercised when drawing inferences from results.
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Abstract

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.
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Abstract

Monte Carlo studies of several fixed-effects methods for combining and comparing correlation matrices have shown that two refinements improve estimation and inference substantially. With rare exception, however, these simulations have involved homogeneous data analyzed using conditional meta-analytic procedures. The present study builds on previous evidence about these methods' relative performance by examining their behavior under heterogeneity, which is more realistic in practice. Results based on both conditional and unconditional estimands indicate that of the two refinements, using estimated correlations in conditional (co) variances improves point and interval estimates of mean correlations more than analyzing Fisher Z correlations, despite the latter's superiority for testing homogeneity. Recommended choices among methods are offered.
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Abstract

Examines a procedure proposed by H. F. Kaiser et al (1969) that has been used to integrate the results from different factor analyses and that compares factor solutions from 2 samples of Ss. After giving a geometrical description of the procedure, its use is illustrated with 21 factor analytic studies of the Buss-Durkee Hostility-Guilt Inventory (BDHGI). The results show that the 7 subscales of the BDHGI measure 2 dimensions of aggressiveness, one that can be called overt and one that can be called covert. (PsycINFO Database Record (c) 2002 APA, all rights reserved)
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Abstract

Numerical approaches to developing accurate and efficient approximations to combined likelihoods of population correlation matrices in meta-analysis under normality assumptions for the data are studied. The likelihood is expressed as a multiple integral over the unit cube in (p-1)-dimensional space, where p is the row and column dimensionality of the correlation matrix. Three types of computation are proposed as ways to calculate the likelihood for any population correlation matrix P. As an application, inference is explored concerning intercorrelations among math, spatial and verbal scores in a SAT exam. Comparisons are made with conventional methods.
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Abstract

Combining multiple regression estimates with meta-analysis has continued to be a difficult task. A variety of methods have been proposed and used to combine multiple regression slope estimates with meta-analysis, however, most of these methods have serious methodological and practical limitations. The purpose of this study was to explore the use of robust variance estimation for combining commonly specified multiple regression models and for combining sample-dependent focal slope estimates from diversely specified models. A series of Monte-Carlo simulations were conducted to investigate the performance of a robust variance estimator for each of these approaches. Key meta-analytic parameters were varied throughout the process. Also, two small scale, examples were conducted to illustrate the use of the robust variance estimator in each of these two approaches. In general, the robust variance estimator performed well. Robust confidence interval parameter recovery was close to the specified 95% under almost all conditions. Only when there were a larger number of slope estimates and a small number of study samples did the robust standard errors noticeably lose efficiency. Combining sample-dependent focal slope estimates provides biased point estimates, however, the results of this paper suggest that the robust standard errors are still accurate.
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Abstract

The potential of structural equation models for combining information from different studies in environmental epidemiology is explored. For illustration, we synthesize data from two birth cohorts assessing the effects of prenatal exposure to methylmercury (MeHg) on childhood cognitive performance. One cohort was the largest by far, but a smaller cohort included superior assessment of the PCB exposure which has been considered an important confounder when estimating the mercury effect. The data were analyzed by specification of a structural equation model for each cohort. Information was then pooled based on a joint likelihood function with key parameters constrained to be equal in the different models. Modeling assumptions were chosen to obtain a meaningful biological interpretation of the joint effect parameters. Measurement errors in mercury variables were taken into account by viewing observed variables as indicators of latent variables. Adjustments for measurement error were also included for confounder variables. In particular, this example illustrates how to properly utilize that one study provided superior information about a confounder. A final more advanced model pooled information across different outcomes to gain power and to avoid multiple testing problems. In this model, the mercury effect remained statistically significant, while the effect of PCB was less certain. Copyright © 2009 John Wiley & Sons, Ltd.
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Abstract

A simulation study was used to evaluate multiple imputation (MI) to handle MCAR correlations in the first step of meta-analytic structural equation modeling: the synthesis of the correlation matrix and the test of homogeneity. No substantial parameter bias resulted from using MI. Although some SE bias was found for meta-analyses involving smaller numbers of studies, the homogeneity test was never rejected when using MI.
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Abstract

Structural equation modeling (SEM) is a useful technique in the behavioral sciences, where latent variables and measurement errors are hypothesized to exist. To investigate a certain phenomenon of interest, different researchers may carry out different SEM studies and report (seemingly or not) different results. It is meaningful to synthesize their findings, so as to explain how and why a set of relationships differs in different situations and better understand the phenomenon of interest. The method to synthesize SEM studies is commonly referred to as meta-analytic SEM (MASEM). Currently, methods to perform MASEM are all limited to the fixed-effects context, where the assumption is made that all the SEM studies included in a meta-analysis have exactly the same population covariance matrix. However, this is an unrealistic assumption because different studies usually have their own characteristics and a set of relationships usually behave differently in different situations. A more reasonable method is one that acknowledges and models the heterogeneity among the SEM studies. In this dissertation, I propose an MASEM method that allows the meta-analyst to include categorical study-level moderators in the meta-analysis, so as to account for the systematic heterogeneity among the SEM studies.
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Abstract

When conducting a meta-analysis, it is common to find many collected studies that report regression analyses, because multiple regression analysis is widely used in many fields. Meta-analysis uses effect sizes drawn from individual studies as a means of synthesizing a collection of results. However, indices of effect size from regression analyses have not been studied extensively. Standardized regression coefficients from multiple regression analysis are scale free estimates of the effect of a predictor on a single outcome. Thus these coefficients can be used as effect-size indices for combining studies of the effect of a focal predictor on a target outcome. I begin with a discussion of the statistical properties of standardized regression coefficients when used as measures of effect size in meta-analysis. The main purpose of this dissertation is the presentation of methods for obtaining standardized regression coefficients and their standard errors from reported regression results. An example of this method is demonstrated using selected studies from a published meta-analysis on teacher verbal ability and school outcomes (Aloe & Becker, 2009). Last, a simulation is conducted to examine the effect of multicollinearity (intercorrelation among predictors), as well as the number of predictors on the distributions of the estimated standardized regression slopes and their variance estimates. This is followed by an examination of the empirical distribution of estimated standardized regression slopes and their variances from simulated data for different conditions. The estimated standardized regression slopes have larger variance and get close to zero when predictors are highly correlated via the simulation study.
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Abstract

Meta-analytic Structural Equation Modeling (MASEM) has drawn interest from many researchers recently. In doing MASEM, researchers usually first synthesize correlation matrices across studies using meta-analysis techniques and then analyze the pooled correlation matrix using structural equation modeling techniques. Several multivariate methods of MASEM have been proposed by the researchers. In this dissertation, I compared the commonly used multivariate methods for meta-analytic path modeling. Specifically, I examined the Generalized Least Squares (GLS) method (Becker, 1992; Becker & Schram, 1994) and the Two-Stage Structural Equation Modeling (TSSEM) method (Cheung, 2002; Cheung & Chan, 2005) using both simulation studies and real data analyses. Both the traditional GLS approach (Becker, 1992) and the modified GLS approaches (Becker & Fahrbach, 1994) were applied and compared with the TSSEM approach. Fixed-effects data and random-effects data were generated to see how these approaches differ at the first and second stages of MASEM. The results shows that the modified GLS approach performs as well as or better than the TSSEM approach in both the first step of synthesizing correlation matrices and the second step estimation of the parameters and standard errors, using both fixed-effects data and random-effects data. The original GLS approach only performs well when the within-study sample size is large enough (of the simulation situations in this dissertation, n = 100). Both the modified GLS approach and the TSSEM approach produce equivalent parameter estimates across all conditions. However, the standard errors from the TSSEM approach seem to be over-estimates under certain conditions. Overall, both the modified GLS and TSSEM approaches are appropriate for conducting meta-analytic path modeling and the difference in parameter estimates is minimal.
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journal abstract: Meta-analytic structural equation modeling (MA-SEM) is increasingly being used to assess model-fit for variables' interrelations synthesized across studies. MA-SEM researchers have analyzed synthesized correlation matrices using structural equation modeling (SEM) estimation that is designed for covariance matrices. This can produce incorrect model-fit chi-square statistics, standard error estimates (Cudeck, 1989), or both for parameters that are not scale free or that describe a scale-noninvariant model unless corrected SEM estimation is used to analyze the correlations. This study introduced univariate and multivariate approximate methods for synthesizing covariance matrices for use in MA-SEM. A simulation study assessed the approximate methods by estimating parameters in a scale-noninvariant model using synthesized covariances versus synthesized correlations with and without the appropriate corrections. Standard error bias was noted only for uncorrected analyses of pooled correlations. Chi-square model-fit statistics were overly conservative except when covariance matrices were analyzed. Benefits and limitations of this approximate method are presented and discussed. (PsycINFO Database Record (c) 2007 APA, all rights reserved)
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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 Ward's minimum-variance methods will provide satisfactory results. (PsycINFO Database Record (c) 2007 APA, all rights reserved)
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Abstract

Greater understanding of the mechanisms (mediators) by which behavioral-change interventions work is critical to developing theory and refining interventions. Although systematic reviews have been advocated as a method for exploring mediators, this is rarely done. One challenge is that intervention researchers typically test only two paths of the mediational model: the effect of the intervention on mediators and on outcomes. The authors addressed this challenge by drawing information not only from intervention studies but also from observational studies that provide data on associations between potential mediators and outcomes. They also reviewed qualitative studies of participants' perceptions of why and how interventions worked. Using data from intervention (n = 37) and quantitative observational studies (n = 55), the authors conducted a meta-analysis of the mediation effects of eight variables. Qualitative findings (n = 6) contributed to more in-depth explanations for findings. The methods used have potential to contribute to understanding of core mechanisms of behavioral-change interventions.
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This paper presents an overview of a useful approach for theory testing in the social sciences that combines the principles of psychometric meta-analysis and structural equations modeling. In this approach to theory testing, the estimated true score correlations between the constructs of interest are established through the application of meta-analysis (Hunter & Schmidt, 1990), and structural equations modeling is then applied to the matrix of estimated true score correlations. The potential advantages and limitations of this approach are presented. The approach enables researchers to test complex theories involving several constructs that cannot all be measured in a single study. Decision points are identified, the options available to a researcher are enumerated, and the potential problems as well as the prospects of each are discussed.
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Abstract

Meta-analytic structural equations modeling is increasingly used in theory testing. There has been much debate when meta-analyzed correlation matrices are used in structural equations modeling on whether to use mean observed correlations (i.e., corrected only for sampling error) or correlations corrected for study artifacts such as unreliability in measures. This paper investigates whether the fit indices are affected by the corrections and if the stability of the paths (i.e., changes in significance, magnitude, and relative strengths or rank order) is affected by the corrections. Results suggest that substantive model conclusions are generally unaffected by study artifacts and related statistical corrections as long as the variables included in the path analyses had typical levels of reliability as found in the psychological literature. More specifically, all models examined exhibited similar model fit and pathway stability. Copyright © 2011 John Wiley & Sons, Ltd.
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Abstract

Meta-analysis has mostly been used to summarize the size of an effect averaged over multiple studies, but meta-analysis has not been much applied to the study of causal mediating processes through which an effect is produced. This lacuna has limited the contribution of meta-analysis to the explanatory theories that play such a key role in science. Fortunately, meta-analysts can explore causal processes. This article reviews several examples of how this has been done in past meta-analyses, using these examples to introduce the methodological, statistical, and conceptual problems that are raised when meta-analysis is applied to the task. Meta-analysts are encouraged to adapt such methods to their work to improve the capacity of their work to contribute to scientific theory, and statisticians are encouraged to solve the remaining statistical problems that current meta-analytic mediational analyses incur. (PsycINFO Database Record (c) 2008 APA, all rights reserved)
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