Meta-Analysis: A Structural Equation Modeling Approach

Chapter 8Advanced topics in SEM-based meta-analysis

This chapter discusses two advanced topics in the structural equation modeling (SEM)-based meta-analysis. The first topic is the restricted (or residual) maximum likelihood (REML) estimation. We compare the pros and cons of the maximum likelihood (ML) estimation against the REML estimation. A graphical model is proposed to represent the transformation of the REML estimation. How to implement the REML estimation in SEM to conduct the SEM-based meta-analyses is introduced. The next topic is how to handle missing values in the moderators in a mixed-effects meta-analysis. Problems of and common methods on handling missing values in the moderators in meta-analysis are reviewed. ML estimation is proposed as a preferred method to handle the missing values. Examples are used to illustrate these procedures in the R statistical environment.

8.1 Restricted (or residual) maximum likelihood estimation

There are several estimation methods available in SEM, for example, two-stage least squares, unweighted least squares, generalized least squares, ML estimation, and weighted least squares (see Bentler, 2006; Jöreskog and Sörbom, 1996; Muthén and Muthén, 2012). In the previous chapters, we mainly focus on the ML estimation method. Under some regularity conditions (e.g., Millar, 2011), ML estimators have many desirable properties. For instance, they are consistent, asymptotically unbiased, asymptotically efficient, and asymptotically normally ...