Abstract

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

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.
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Evaluated the comparability of 7 sets of factor structures reported in previous research (e.g., L. O. Ruch [see PA, Vol 72:1306]) with the Bem Sex-Role Inventory. Results indicate that the inventory's primary factors were reproduced in the studies, although the Masculine scale was somewhat less invariant than its Feminine counterpart. Results support the validity of this androgyny measure across several variations in sample types. The present study represents a heuristic example of a methodology for the meta-analysis of factor structure studies. (PsycINFO Database Record (c) 2002 APA, all rights reserved)
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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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Abstract

Research on methods of meta-analysis (the synthesis of related study results) has dealt with many simple study indices, but less attention has been paid to the issue of summarizing regression slopes. In part this is because of the many complications that arise when real sets of regression models are accumulated. We outline the complexities involved in synthesizing slopes, describe existing methods of analysis and present a multivariate generalized least squares approach to the synthesis of regression slopes.
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Abstract

This article outlines analyses for the results of a series of studies examining intercorrelations among a set of p + 1 variables. A test of whether a common population correlation matrix underlies the set of empirical results is given. Methods are presented for estimating either a pooled or average correlation matrix, depending, on whether the studies appear to arise from a single population. A random effects model provides the basis for estimation and testing when the series of correlation matrices may not share a common population matrix. Finally, I show how a pooled correlation matrix (or average matrix) can be used to estimate the standardized coefficients of a regression model for variables measured in the series of studies. Data from a synthesis of relationships among mathematical, verbal, and spatial ability measures illustrate the procedures.
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Abstract

Reports an error in the original article by B. J. Becker (Journal of Educational Statistics, 1992[Win], Vol 17[4], 341-362). Corrected numerical values are provided for part of the example used to illustrate the analysis of a set of correlation matrices. (The following abstract of this article originally appeared in PA, Vol 80:16071.) Treats the problem of combining information to estimate standardized partial regression coefficients in a linear model. The following procedures are illustrative: analyses for the results of studies examining intercorrelations among a set of p + 1 variables, a test of whether a common population correlation matrix underlies the set of empirical results, and methods for estimating either a pooled or average correlation matrix, depending on whether the studies appear to arise from a single population. Other illustrative procedures include a random effects model as the basis for estimation and testing when the series of correlation matrices may not share a common population matrix, and a pooled correlation matrix (or average matrix) to estimate the standardized coefficients of a regression model for variables measured in the series of studies. Data from a synthesis of relationships among mathematical, verbal, and spatial ability measures are used. (PsycINFO Database Record (c) 2002 APA, all rights reserved)
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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-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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