Depicting estimates using the intercept in meta-regression models: The moving constant technique.

In any scientific discipline, the ability to portray research patterns graphically often aids greatly in interpreting a phenomenon. In part to depict phenomena, the statistics and capabilities of meta-analytic models have grown increasingly sophisticated. Accordingly, this article details how to move the constant in weighted meta-analysis regression models (viz. "meta-regression") to illuminate the patterns in such models across a range of complexities. Although it is commonly ignored in practice, the constant (or intercept) in such models can be indispensible when it is not relegated to its usual static role. The moving constant technique makes possible estimates and confidence intervals at moderator levels of interest as well as continuous confidence bands around the meta-regression line itself. Such estimates, in turn, can be highly informative to interpret the nature of the phenomenon being studied in the meta-analysis, especially when a comparison with an absolute or a practical criterion is the goal. Knowing the point at which effect size estimates reach statistical significance or other practical criteria of effect size magnitude can be quite important. Examples ranging from simple to complex models illustrate these principles. Limitations and extensions of the strategy are discussed.