A Parsimonious Weight Function for Modeling Publication Bias

Quantitative research literature is often biased because studies that fail to find a significant effect (or that demonstrate effects in an undesired or unexpected direction) are less likely to be published. This phenomenon, termed publication bias, can cause problems when researchers attempt to synthesize results using metaanalytic methods. Various techniques exist that attempt to estimate and correct meta-analyses for publication bias. However, there is no single method that can (a) account for continuous moderators by including them within the model, (b) allow for substantial data heterogeneity, (c) produce an adjusted mean effect size, (d) include a formal test for publication bias, and (e) allow for correction when only a small number of effects is included in the analysis. This article describes a method that we believe helps fill that gap. The model uses the beta density as a weight function that represents the selection process and provides adjusted parameter estimates that account for publication bias. Use of the beta density allows us to represent selection using fewer parameters than similar models so that the proposed model is suitable for meta-analyses that include relatively few studies. We explain the model and its rationale, illustrate its use with a real data set, and describe the results of a simulation study that shows the model's utility.