The fraction of what is known about \(\mu_\theta\) that comes from
pre-post studies, which is also the factor by which a systematic difference
between their trend distribution and the DiD studies' biases the pooled
effect (see vignette("model-details")).
Arguments
- fit
A
meta_did()fit containing both DiD and pre-post summary studies.
Details
A DiD study supplies an effect estimate and a trend estimate that share its control arm, so the two are correlated, with \(\mathrm{Cov} = -\mathrm{var}(\text{control change})\). Treating them as independent overstates the share by a few percent, so the 2x2 information per study is summed rather than two scalars. Writing \(A\) for the total pre-post precision, $$I = \sum_i \Sigma_i^{-1} + A \mathbf{1}\mathbf{1}^\top, \qquad \omega_{P} = \left(I^{-1} [A, A]^\top\right)_1 .$$
The returned cap is S3's saturation result \(h/(g+h)\): the share cannot
exceed what the DiD studies know about the trend distribution, however many
pre-post studies are added. It uses the scalar (independent) form, so treat
it as the approximation it is.
Computed per posterior draw, since it depends on \(\tau_\theta\) and \(\tau_\beta\). Summary-level data only.