A model for integrating fixed-, random-, and mixed-effects meta-analyses into structural equation modeling.

Abstract

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.Keywords: meta-analysis, structural equation model, fixed-effects model, random-effects model, mixed-effects model It is of methodological importance to see how seemingly unrelated statistical methods can be linked together. Consider the classic example of analysis of variance (ANOVA) and multiple regression. Before the seminal work of Cohen (1968;Cohen & Cohen, 1975), "the textbooks in 'psychological' statistics treat[ed multiple regression, ANOVA, and ANCOVA] quite separately, with wholly different algorithms, nomenclature, output, and examples" (Cohen, 1968, p. 426). Understanding the mathematical equivalence between an ANOVA (and analysis of covariance, or AN-COVA) and a multiple regression helps us to comprehend the details behind the general linear model.Another important example in social statistics has been the development of structural equation modeling (SEM; e.g., Bentler, 2004;Bollen, 1989;Jöreskog & Sörbom, 1996; L. K. Muthén & Muthén, 2007). SEM provides a flexible framework for testing complicated models involving latent and observed variables. It integrates ideas of latent variables in psychometrics, path models in sociology, and structural models in econometrics. The general linear model, path analysis, and confirmatory factor analysis are some special cases of SEM.Recently, it has been shown that many models used in the social and behavioral sciences are related to SEM. Takane and de Leeuw (1987; see also MacIntosh & Hashim, 2003) showed how some item response theory (IRT) models could be analyzed as structural equation models. Several authors (e.g., Bauer, 2003;Curran, 2002; Mehta & Neale, 2005;Rovine & Molenaar, 2000 demonstrated how multilevel models could be formulated as structural equation models. The advantage of integrating these models together is that a unified framework can be used to address complex research questions involving some of these models. There are at least two such general models: Mplus (L. K. Muthén & Muthén, 2007) combines SEM, multilevel models, mixture modeling, survival analysis, latent class ...

Pediatric weight management interventions in primary care settings: A meta-analysis.

“…Mixed-effects models allow for the examination of fixed-effects moderators in the presence of random-effects heterogeneity (Card, 2012). A structural equation modeling approach (using Mplus) was used to estimate mixed-effects models (Cheung, 2008). To do this, a random-effects model was built by transforming the intercept and using it to predict the slope of the transformed effect size; the slope was allowed to vary randomly (Card, 2012).…”

International Comparative Evaluation of Knee Replacement with Fixed or Mobile-Bearing Posterior-Stabilized Prostheses

“…The models estimated the residual covariances precisely as described previously 20 and also implemented a transformation [21][22][23] to ensure that the models could be fitted with existing SAS software (version 9.2; SAS Institute, Cary, North Carolina). Survival probabilities and their standard errors were extracted from each registry for each unique combination of the covariates (e.g., mobility, patellar-resurfacing status, and patient age) at each distinct event time.…”

Coexistence and conflicts between shopping malls and street markets in growing cities: Analysis of shoppers’ behaviour

“…Although correlation matrices are usually preferred in this process, there are cases in which synthesizing covariance matrices is useful, especially when the scales of the measurement are comparable. Thus, SEM is widely used as a statistical framework to test complex models in behavioural and social sciences ( Cheung, 2008 ).…”