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Pin the true AIE of a moderated DGP (inversion step)

Source: R/aie.R
set_aie.Rd

For a DGP with a moderator, solves all three effect coefficients from targets in effect-size units: the two main effects from their conditional-at-reference APEs (the APE of each variable with the other held at its reference value – 0 for binary, the mean for continuous), and the interaction coefficient from the target average interaction effect (AIE), holding the mains fixed. The AIE is ginteff's estimand: the double difference for binary-by-binary, the difference of average derivatives for mixed pairs, and the average cross-partial for continuous-by-continuous.

Usage

set_aie(dgp, target, main_focal, main_moderator)

Arguments

dgp

A powerape_dgp from ape_dgp() or ape_dgp_panel(), with a moderator.

target

Assumed true AIE (the planning value), in APE units.

main_focal, main_moderator

Conditional-at-reference APEs anchoring the two main effects.

Value

The dgp with beta_focal, beta_mod, beta_int, and target_est filled in; estimand becomes "aie".

Details

All three anchors are explicit – there are no silent defaults. Errors report the attainable range when a target is infeasible (for binary-by-binary, the four counterfactual cell rates must stay in (0,1); otherwise the AIE plateaus in the interaction coefficient).

For panel DGPs (ape_dgp_panel() with a moderator; binary x binary), all anchors are defined on the average structural function: unit effects are integrated out and the Mundlak means held fixed, so the panel AIE is the same population quantity a cross-sectional AIE design targets.

Examples

d <- ape_dgp(focal = pa_var("treat", "binary", p = 0.5),
             moderator = pa_var("female", "binary", p = 0.55),
             baseline = 0.30)
d <- set_aie(d, target = 0.04, main_focal = 0.10, main_moderator = 0.05)
d
#> powerape DGP -- probit
#>   focal: treat (binary, p = 0.50)
#>   moderator: female (binary, p = 0.55) (focal-by-moderator interaction included)
#>   covariates: none
#>   baseline P(Y=1 | reference) = 0.300, nuisance signal (latent pseudo-R2) = 0.000
#>   true AIE pinned at +0.0400 (beta_int = 0.0892)
#>   main APEs at reference: treat +0.100 (beta = 0.2711), female +0.050 (beta = 0.1391)