Sensitivity of the pooled effect to trend exchangeability

Refits the model across a grid of \(\Delta\), the systematic difference between the pre-post and DiD trend distributions, and reports how the pooled effect responds. This is the exact version of delta_star()'s approximation: it captures the shrinkage and the nonlinearity of the normalised post-only reparameterisation, at the cost of one fit per grid point.

Usage

sensitivity_trend(fit, delta = NULL, probs = c(0.05, 0.95), quiet = FALSE)

Arguments

fit

A meta_did() fit containing pre-post studies.

delta

Numeric vector of shifts to refit at. Defaults to a symmetric grid spanning roughly the population trend, which is the scale on which a plausible exchangeability failure would sit.

probs

Interval probabilities for the reported bounds.

quiet

Suppress the per-refit progress message.

Value

A list with grid (a data frame of delta, estimate, lo, hi, divergences), the fitted slope, omega_empirical (which is -slope, and is what omega_pp() predicts), delta_point, delta_ci, and the fits themselves.

Details

Each refit sets pp_trend_shift = delta, which asserts \(\beta_j \sim N(\mu_\beta + \Delta, \tau_\beta^2)\) for pre-post studies only. Every other setting is taken from the original fit, so a sweep cannot differ from it in a sampler setting or a modelling switch.

Two breakdown values are returned. delta_point is where the posterior mean crosses zero — the SI's \(\Delta^*\). delta_ci is where the interval first includes zero, which is the more useful of the two: it is the shift at which the conclusion, rather than the point estimate, stops holding. Both come from linear interpolation on the grid and are NA when no crossing occurs inside it.

See also

omega_pp(), delta_star()