Meta-Regression
Explaining Heterogeneity
Why Effect Sizes Vary
In the previous module, we found a pooled effect size. But usually, the most interesting finding is Heterogeneity (\(I^2\)). Why does the treatment work wonderfully in Study A but fail in Study B?
Meta-Regression allows us to predict effect size differences using study characteristics (Moderators).
Interactive Lab: The Grief Data (Part 2)
We will use the same grief dataset, but this time we have added Moderators:
risk: Participant Risk Level (Normal, At-Risk, Complicated)n.sess: Number of Therapy Sessions (Continuous)female: Percentage of female participants
1. Categorical Moderator: Risk Level
Does the intervention work better for “At-Risk” populations?
Visualizing Categories
Instead of base R boxplots, we use ggplot2 to visualize the moderator effect, weighting the points by precision (Inverse Variance).
2. Continuous Moderator: Dose-Response
Does more therapy (Number of Sessions) lead to better outcomes?
Visualizing Slope
The “Bubble Plot” of Meta-Analysis.
3. Multi-Predictor Model (Advanced Visualization)
Real life is multivariate. Let’s control for multiple factors at once.
\[ ES_i = \beta_0 + \beta_1(Risk) + \beta_2(Sessions) + \beta_3(\%Female) + \epsilon_i + \zeta_i \]