# Chapter 5Multivariate meta-analysis

This chapter extends univariate meta-analysis to a multivariate meta-analysis that allows researchers to analyze more than one effect size per study. We begin the chapter by discussing different types of dependence in the effect sizes and the need for a multivariate meta-analysis to handle multiple effect sizes. Several conventional approaches to conducting multivariate meta-analysis are briefly mentioned. The structural equation modeling (SEM) approach to conducting fixed-, random-, and mixed-effects multivariate meta-analyses is introduced. We then extend the multivariate meta-analysis to mediation and moderation models among the *true* effect sizes. Several examples are used to illustrate the procedures in the R statistical environment.

## 5.1 Introduction

Most meta-analytic procedures assume independence among the effect sizes. Because of the research design of the primary studies, many effect sizes reported in publications are not independent. The assumption of independence among the effect sizes may not be tenable in many research settings. Moreover, many research questions are multivariate in nature. A single effect size may not be sufficient to summarize the outcome effect. Multivariate meta-analysis is required to address the complexity of the research questions.

### 5.1.1 Types of dependence

There are several types of dependence in a meta-analysis (e.g., Hedges et al., 2010). The first type is the dependence owing to sampling error. This ...