Fixed-Effects and Random-Effects Models in Meta-Analysis — misc-models

Books and articles about meta-analysis often describe and discuss the difference between the so-called ‘fixed-effects model’ and the ‘random-effects model’ (e.g., Cooper et al., 2009). The former term is (mostly) avoided throughout the documentation of the metafor package. The term ‘equal-effects model’ is used instead, since it more concretely describes the main assumption underlying this model (i.e., that the underlying true effects/outcomes are homogeneous, or in other words, that they are all equal to each other). The terms ‘common-effect(s) model’ or ‘homogenous-effect(s) model’ have also sometimes been used in the literature to describe this model and are equally descriptive. Moreover, the term ‘fixed-effects model’ creates a bit of a conundrum. When authors use this term, they are really typically referring to the equal-effects model. There is however another type of model, the ‘real’ fixed-effects model, that is different from the equal-effects model, but now we would need to invent (unnecessarily) a different term to refer to this model. Some have done so or tried to make a distinction between the ‘fixed-effect model’ (without the s!) and the ‘fixed-effects model’, but this subtle difference in terminology is easily overlooked/missed. Using the term ‘equal-effects model’ avoids this confusion and is more informative. However, the question then remains what the real fixed-effects model is all about. The purpose of this page is to describe this model and to contrast it with the well-known random-effects model.