This is an evolving blog post.
I am starting to think that Simpson’s Paradox and the Aggregation Paradox (which elsewhere I term “multilevel structure”), are variations of the same phenomenon.
Consider a simple regression equation.
\[y_{ij} = \beta_0 + \beta_1 x_{ij} + \beta_2 z_{ij} + u_{0j} + e_{ij}\]
- Simpson’s Paradox could possibly occur if we omit \(z_{ij}\) from the regression equation.
- The Aggregation Paradox could possibly occur if we omit \(u_{0j}\) from the regression equation.