Meta-Analysis of Correlations, Correlation Matrices, and Their Functions

Meta-analysis of panel data is uniquely suited to uncovering phenomena that develop over time, but extant approaches are limited. There is no straightforward means of aggregating findings of primary panel studies that use different time lags and different numbers of waves. We introduce continuous time meta-analysis (CoTiMA) as a parameter-based approach to meta-analysis of cross-lagged panel correlation matrices. CoTiMA enables aggregation of studies using two or more waves even if there are varying time lags within and between studies. CoTiMA thus provides meta-analytic estimates of cross-lagged effects for a given time lag regardless of the frequency with which that time lag is used in primary studies. We describe the continuous time underpinnings of CoTiMA, its advantages over discrete-time, correlation-based meta-analysis of structural equation models (MASEM), and how CoTiMA would be applied to meta-analysis of panel studies. An example is then used to illustrate the approach. We also conducted Monte Carlo simulations demonstrating that bias is larger for time category–based MASEM than for CoTiMA under various conditions. Finally, we discuss data requirements, open questions, and possible future extensions.

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Meta-Analytic Structural Equation Modeling

Oxford Research Encyclopedia of Business and Management ◽

10.1093/acrefore/9780190224851.013.225 ◽

2021 ◽

Author(s):

Mike W.-L. Cheung

Keyword(s):

Structural Equation Modeling ◽

Correlation Matrix ◽

Structural Equation ◽

Structural Equation Models ◽

Meta Analysis ◽

Equation Modeling ◽

Average Correlation ◽

Correlation Matrices ◽

Factor Analytic Model ◽

Special Cases

Meta-analysis and structural equation modeling (SEM) are two popular statistical models in the social, behavioral, and management sciences. Meta-analysis summarizes research findings to provide an estimate of the average effect and its heterogeneity. When there is moderate to high heterogeneity, moderators such as study characteristics may be used to explain the heterogeneity in the data. On the other hand, SEM includes several special cases, including the general linear model, path model, and confirmatory factor analytic model. SEM allows researchers to test hypothetical models with empirical data. Meta-analytic structural equation modeling (MASEM) is a statistical approach combining the advantages of both meta-analysis and SEM for fitting structural equation models on a pool of correlation matrices. There are usually two stages in the analyses. In the first stage of analysis, a pool of correlation matrices is combined to form an average correlation matrix. In the second stage of analysis, proposed structural equation models are tested against the average correlation matrix. MASEM enables researchers to synthesize researching findings using SEM as the research tool in primary studies. There are several popular approaches to conduct MASEM, including the univariate-r, generalized least squares, two-stage SEM (TSSEM), and one-stage MASEM (OSMASEM). MASEM helps to answer the following key research questions: (a) Are the correlation matrices homogeneous? (b) Do the proposed models fit the data? (c) Are there moderators that can be used to explain the heterogeneity of the correlation matrices? The MASEM framework has also been expanded to analyze large datasets or big data with or without the raw data.

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Allowing for correlations between correlations in random-effects meta-analysis of correlation matrices.

Psychological Methods ◽

10.1037/1082-989x.12.4.434 ◽

2007 ◽

Vol 12 (4) ◽

pp. 434-450 ◽

Cited By ~ 9

Author(s):

A. Toby Prevost ◽

Dan Mason ◽

Simon Griffin ◽

Ann-Louise Kinmonth ◽

Stephen Sutton ◽

...

Keyword(s):

Random Effects ◽

Meta Analysis ◽

Correlation Matrices

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The meta-analysis of factor analyses: An illustration based on the cumulation of correlation matrices.

Psychological Methods ◽

10.1037/1082-989x.1.4.341 ◽

1996 ◽

Vol 1 (4) ◽

pp. 341-353 ◽

Cited By ~ 42

Author(s):

Gilbert Becker

Keyword(s):

Meta Analysis ◽

Factor Analyses ◽

Correlation Matrices

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Meta-Analytical SEM: Equivalence Between Maximum Likelihood and Generalized Least Squares

Journal of Educational and Behavioral Statistics ◽

10.3102/1076998618787799 ◽

2018 ◽

Vol 43 (6) ◽

pp. 693-720

Author(s):

Ke-Hai Yuan ◽

Yutaka Kano

Keyword(s):

Maximum Likelihood ◽

Least Squares ◽

Correlation Matrix ◽

Structural Equation ◽

Structural Model ◽

Meta Analysis ◽

Generalized Least Squares ◽

Equation Modeling ◽

Correlation Matrices ◽

Latent Constructs

Meta-analysis plays a key role in combining studies to obtain more reliable results. In social, behavioral, and health sciences, measurement units are typically not well defined. More meaningful results can be obtained by standardizing the variables and via the analysis of the correlation matrix. Structural equation modeling (SEM) with the combined correlations, called meta-analytical SEM (MASEM), is a powerful tool for examining the relationship among latent constructs as well as those between the latent constructs and the manifest variables. Three classes of methods have been proposed for MASEM: (1) generalized least squares (GLS) in combining correlations and in estimating the structural model, (2) normal-distribution-based maximum likelihood (ML) in combining the correlations and then GLS in estimating the structural model (ML-GLS), and (3) ML in combining correlations and in estimating the structural model (ML). The current article shows that these three methods are equivalent. In particular, (a) the GLS method for combining correlation matrices in meta-analysis is asymptotically equivalent to ML, (b) the three methods (GLS, ML-GLS, ML) for MASEM with correlation matrices are asymptotically equivalent, (c) they also perform equally well empirically, and (d) the GLS method for SEM with the sample correlation matrix in a single study is asymptotically equivalent to ML, which has being discussed extensively in the SEM literature regarding whether the analysis of a correlation matrix yields consistent standard errors and asymptotically valid test statistics. The results and analysis suggest that a sample-size weighted GLS method is preferred for combining correlations and for MASEM.

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Multivariate Bayesian meta-analysis: joint modelling of multiple cancer types using summary statistics

International Journal of Health Geographics ◽

10.1186/s12942-020-00234-0 ◽

2020 ◽

Vol 19 (1) ◽

Author(s):

Farzana Jahan ◽

Earl W. Duncan ◽

Susana M. Cramb ◽

Peter D. Baade ◽

Kerrie L. Mengersen

Keyword(s):

Cancer Incidence ◽

Meta Analysis ◽

Multiple Cancer ◽

Correlation Matrices ◽

Small Areas ◽

Remote Areas ◽

Multiple Cancers ◽

Record Data ◽

Cancer Types ◽

Analysis Models

Abstract Background Cancer atlases often provide estimates of cancer incidence, mortality or survival across small areas of a region or country. A recent example of a cancer atlas is the Australian cancer atlas (ACA), that provides interactive maps to visualise spatially smoothed estimates of cancer incidence and survival for 20 different cancer types over 2148 small areas across Australia. Methods The present study proposes a multivariate Bayesian meta-analysis model, which can model multiple cancers jointly using summary measures without requiring access to the unit record data. This new approach is illustrated by modelling the publicly available spatially smoothed standardised incidence ratios for multiple cancers in the ACA divided into three groups: common, rare/less common and smoking-related. The multivariate Bayesian meta-analysis models are fitted to each group in order to explore any possible association between the cancers in three remoteness regions: major cities, regional and remote areas across Australia. The correlation between the pairs of cancers included in each multivariate model for a group was examined by computing the posterior correlation matrix for each cancer group in each region. The posterior correlation matrices in different remoteness regions were compared using Jennrich’s test of equality of correlation matrices (Jennrich in J Am Stat Assoc. 1970;65(330):904–12. 10.1080/01621459.1970.10481133). Results Substantive correlation was observed among some cancer types. There was evidence that the magnitude of this correlation varied according to remoteness of a region. For example, there has been significant negative correlation between prostate and lung cancer in major cities, but zero correlation found in regional and remote areas for the same pair of cancer types. High risk areas for specific combinations of cancer types were identified and visualised from the proposed model. Conclusions Publicly available spatially smoothed disease estimates can be used to explore additional research questions by modelling multiple cancer types jointly. These proposed multivariate meta-analysis models could be useful when unit record data are unavailable because of privacy and confidentiality requirements.

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Meta-Analytic Structural Equation Modeling

10.31234/osf.io/epsqt ◽

2020 ◽

Author(s):

Mike W.-L. Cheung

Keyword(s):

Structural Equation Modeling ◽

Correlation Matrix ◽

Structural Equation ◽

Structural Equation Models ◽

Meta Analysis ◽

Equation Modeling ◽

Average Correlation ◽

Correlation Matrices ◽

Factor Analytic Model ◽

Special Cases

Meta-analysis and structural equation modeling (SEM) are two popular statistical models in the social, behavioral, and management sciences. Meta-analysis summarizes research findings to provide an estimate of the average effect and its heterogeneity. When there is non-trial heterogeneity, moderators such as study characteristics may be used to explain the heterogeneity in the data. On the other hand, SEM includes several special cases, including the general linear model, path model, and confirmatory factor analytic model. SEM allows researchers to test hypothetical models with empirical data. Meta-analytic structural equation modeling (MASEM) is a statistical approach combining the advantages of both meta-analysis and SEM for fitting structural equation models on a pool of correlation matrices. There are usually two stages in the analyses. In the first stage of analysis, a pool of correlation matrices is combined to form an average correlation matrix. In the second stage of analysis, proposed structural equation models are tested against the average correlation matrix. MASEM enables researchers to synthesize researching findings using SEM as the research tool in primary studies. There are several popular approaches to conduct MASEM, including the univariate-r, generalized least squares, two-stage SEM (TSSEM), and one-stage MASEM (OSMASEM). MASEM helps to answer the following key research questions: (1) Are the correlation matrices homogeneous? (2) Do the proposed models fit the data? (3) Are there moderators that can be used to explain the heterogeneity of the correlation matrices? The MASEM framework has also been expanded to analyze large datasets or big data with or without the raw data.

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Synthesizing Indirect Effects in Mediation Models with Meta-Analytic Methods

10.31234/osf.io/df6jp ◽

2020 ◽

Author(s):

Mike W.-L. Cheung

Keyword(s):

Indirect Effects ◽

Structural Equation ◽

Meta Analysis ◽

Underlying Mechanism ◽

Equation Modeling ◽

Outcome Variable ◽

Correlation Matrices ◽

Independent Variable ◽

Research Questions ◽

Mediation Models

A mediator is a variable that explains the underlying mechanism between an independent variable and a dependent variable. The indirect effect indicates the effect from the predictor to the outcome variable via the mediator. In contrast, the direct effect represents the effect of the predictor on the outcome variable after controlling for the mediator. A single study rarely provides enough evidence to answer research questions in a particular domain. Replications are generally recommended as the gold standard to conduct scientific research. When a sufficient number of studies have been conducted addressing similar research questions, a meta-analysis can be used to synthesize the findings of those studies. The main objective of this paper is to introduce two approaches to integrating studies using mediation analysis. The first approach involves calculating standardized indirect effects and direct effects and conducting a multivariate meta-analysis on those effect sizes. The second approach uses meta-analytic structural equation modeling to synthesize correlation matrices and fit mediation models on the average correlation matrix. We illustrate these procedures on a real dataset using the R statistical platform. This paper closes with some further directions for future studies.ind

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FIRO–B: Factors and Facets

Psychological Reports ◽

10.2466/pr0.2000.86.1.311 ◽

2000 ◽

Vol 86 (1) ◽

pp. 311-320 ◽

Cited By ~ 6

Author(s):

W. D. K. Macrosson

Keyword(s):

Meta Analysis ◽

The Other ◽

Correlation Matrices

10 FIRO–B intercorrelation matrices were factor analysed; one matrix was derived from new FIRO–B data, all the other matrices were found in the literature. The correlation matrices were also subjected to meta-analysis. The findings suggested that the four FIRO–B scales associated with Inclusion and Affection are facets of the ubiquitous interpersonal superfactor, Nurturance, but the two FIRO–B Control scales each express an orthogonal construct both of which relate to the superfactor, Dominance.

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