\(\Delta^* = \hat\mu_\theta / \omega_P\): the systematic difference between the pre-post and DiD trend distributions that would be needed to move the pooled effect to zero. A large value relative to plausible secular trends indicates robustness; a small one flags dependence on the assumption.
Arguments
- fit
A
meta_did()fit containing both DiD and pre-post summary studies.
Details
\(\Delta^*\) is a ratio of two posterior quantities, so its tails are heavy when \(\omega_P\) is near zero — which is the robust case, since a vanishing share means no shift can explain the effect away. Read the median and the interval, not the mean.
Units are those of the fitted effect, per study interval: on the normalised scale a \(\Delta^*\) of \(-0.5\) means pre-post trends would have to run 50 percentage points of baseline below DiD trends over each study's own pre-to-post interval. It is not an annual rate, since interval lengths differ across studies.