The random-effects model allows for the possibility that studies in a meta-analysis have heterogeneous effects. That is, observed study estimates vary not only due to random sampling error but also due to inherent differences in the way studies have been designed and conducted. In this chapter, we consider methods to estimate the heterogeneity variance parameter in a random-effects model, consider in more detail what this parameter represents and how the possible explanations for heterogeneity can be explored through statistical methods. Toward the end of this chapter, publication bias is discussed as an alternative explanation for why observed effect estimates might form some distribution other than what we might come to expect.
Keywords: DerSimonian-Laird; Funnel plot asymmetry; Heterogeneity; Paule-Mandel; Publication bias; REML; Random-effects.
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