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

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.

scholarly journals Meta-Analytic Structural Equation Modeling

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.

scholarly journals Meta-Analytic Structural Equation Modeling

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.

scholarly journals PERBANDINGAN ANTARA UNWEIGHTED LEAST SQUARES (ULS) DAN PARTIAL LEAST SQUARES (PLS) DALAM PEMODELAN PERSAMAAN STRUKTURAL (STUDI KASUS MODEL ANALISIS PRESTASI BELAJAR MAHASISWA TAHUN PERTAMA PROGRAM STUDI S1 MATEMATIKA FMIPA-INSTUTUT PERTANIAN BOGOR)

2017 ◽  
Vol 2 (1) ◽  
pp. 21
Author(s):  
Muhammad Amin Paris
Keyword(s):  
Least Squares ◽  
Student Learning ◽  
Partial Least Squares ◽  
Structural Equation ◽  
Weighted Least Squares ◽  
Generalized Least Squares ◽  
Primary Data ◽  
Equation Modeling ◽  
Multivariate Techniques ◽  
Mathematics Students

Structural Equation Modeling (SEM) is one of multivariate techniques  that can estimates a series of interrelated dependence relationships from a number of endogenous and exogenous variables, as well as latent (unobserved) variables simultaneously. Estimation of Parameter methods that is often applied in SEM are Maximum Likelihood (ML), Weighted Least Squares (WLS), Unweighted Least Squares (ULS), Generalized Least Squares (GLS) and Partial Least Squares (PLS). This research aims to compare ULS method and PLS method in estimating parameter model of achievement of student learning in first year undergraduate Mathematics students, FMIPA, Bogor  Agricultural University ( IPB). This research use secondary and primary data which amounts to 112. The result of this research indicates that ULS method is more accurate than PLS methods. The analysis done with ULS method shows that motivation, capability and environmental had an effect to achievement of student learning.

scholarly journals Comparative Analysis of Some Structural Equation Model Estimation Methods with Application to Coronary Heart Disease Risk

2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
David Adedia ◽  
Atinuke O. Adebanji ◽  
Simon Kojo Appiah
Keyword(s):  
Coronary Heart Disease ◽  
Maximum Likelihood ◽  
Least Squares ◽  
Asymptotic Distribution ◽  
Structural Equation ◽  
Generalized Least Squares ◽  
Least Squares Estimator ◽  
Coronary Risk ◽  
Distribution Free ◽  
Better Than

This study compared a ridge maximum likelihood estimator to Yuan and Chan (2008) ridge maximum likelihood, maximum likelihood, unweighted least squares, generalized least squares, and asymptotic distribution-free estimators in fitting six models that show relationships in some noncommunicable diseases. Uncontrolled hypertension has been shown to be a leading cause of coronary heart disease, kidney dysfunction, and other negative health outcomes. It poses equal danger when asymptomatic and undetected. Research has also shown that it tends to coexist with diabetes mellitus (DM), with the presence of DM doubling the risk of hypertension. The study assessed the effect of obesity, type II diabetes, and hypertension on coronary risk and also the existence of converse relationship with structural equation modelling (SEM). The results showed that the two ridge estimators did better than other estimators. Nonconvergence occurred for most of the models for asymptotic distribution-free estimator and unweighted least squares estimator whilst generalized least squares estimator had one nonconvergence of results. Other estimators provided competing outputs, but unweighted least squares estimator reported unreliable parameter estimates such as large chi-square test statistic and root mean square error of approximation for Model 3. The maximum likelihood family of estimators did better than others like asymptotic distribution-free estimator in terms of overall model fit and parameter estimation. Also, the study found that increase in obesity could result in a significant increase in both hypertension and coronary risk. Diastolic blood pressure and diabetes have significant converse effects on each other. This implies those who are hypertensive can develop diabetes and vice versa.

scholarly journals PEMANTAUAN PERSAMAAN MODEL STRUKTURAL DALAM DATA ORDINAL

2009 ◽  
Vol 8 (1) ◽  
pp. 21
Author(s):  
B. SUHARJO ◽  
LA MBAU ◽  
N. K. K. ARDANA
Keyword(s):  
Least Squares ◽  
Structural Equation ◽  
Weighted Least Squares ◽  
Generalized Least Squares ◽  
The Other ◽  
Estimation Methods ◽  
Equation Modeling ◽  
Multivariate Techniques ◽  
Exogenous Variables ◽  
Design Data

Structural equation modeling (SEM) is one of multivariate techniques  that can estimates a series of interrelated dependence relationships from a number of endogenous and exogenous variables, as well as latent (unobserved) variables simultaneously. To estimates their parameters, SEM based on structure covariance matrix, there are severals methods can be used as estimation methods, namely maximum likelihood (ML), weighted least squares (WLS), generalized least squares (GLS) and unweighted least squares (ULS). The purpose of this paper are to learn these methods in estimating SEM parameters and to compare their consistency, accuracy and sensitivity based on sample size and multinormality assumption of observed variables.  Using a fully crossed design, data were generated for 2 conditions of normality  and 5 different sample sizes. The result showed that when data are normally distributed, ML and GLS more consistent and accurate then the  other methods

scholarly journals Synthesizing Indirect Effects in Mediation Models with Meta-Analytic Methods

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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