Counterfactual law of one unit (abduction, action, prediction)

Computes the per-unit counterfactual of a query coordinate (the outcome) for an observed unit, under a do() intervention – Pearl's third rung on the latent-class structural causal model read off a fitted Gaussian mixture.

Usage

gmm_counterfactual(g, evidence, do, query, ridge_eps = 1e-06)

Arguments

g

A gmm (or gmm_fit) in R^p.

evidence

A length-p numeric vector of the observed unit. Unobserved coordinates are NA; the query coordinate must be observed.

do

A length-p numeric vector. Intervened coordinates take their counterfactual value; the rest are NA. Intervened coordinates must be observed in evidence.

query

A single integer coordinate index in seq_len(p) – the outcome whose counterfactual is sought.

ridge_eps

Tiny ridge added to the conditioning covariances for numerical hygiene.

Value

A gmm_counterfactual_law object carrying the K atoms, their abduction weights, and the identified counterfactual mean.

Details

The three steps are closed form. Abduction recovers the regime posterior \(\pi_k(\text{evidence})\) of the observed unit and, within each component, its structural residual. Action sets the do coordinates. Prediction re-evaluates the query coordinate. For a binary treatment the result is a discrete law on K atoms, $$Y_{t'} \mid (y, t, x) = \sum_k \pi_k(y, t, x)\, \delta\!\big(y + \beta_k^{T}(t' - t)\big),$$ where \(\beta_k^T\) is component k's within-class treatment slope. Only the mean of this law is identified; its spread reflects regime uncertainty, not the (unidentified) cross-world coupling, so the variance and tail accessors refuse to answer (see gmm_cf_variance()).

See also

gmm_intervene(), gmm_cf_variance(), proxy_retrospective_uplift()

Other operators: gmm_affine(), gmm_aggregate(), gmm_convolve(), gmm_filter(), gmm_intervene(), gmm_missing(), gmm_mix(), gmm_observe(), gmm_product(), gmm_reduce()

Other decision: fit_uplift(), gmm_cf_mean(), gmm_cf_tail_prob(), gmm_cf_variance(), gmm_intervene(), proxy_cate(), proxy_confounding_gap(), proxy_decide(), proxy_identification_report(), proxy_overlap(), proxy_policy_value(), proxy_predict(), proxy_regime_segments(), proxy_retrospective_uplift(), proxy_uplift(), uplift_identification(), uplift_model()

Examples

## Observed unit (y = 1.2, t = 0, x = 0.5); imagine t = 1.
g <- gmm(weights = c(0.6, 0.4),
         means = list(c(0, 0, 0), c(2, 1, 1)),
         covariances = list(diag(3), diag(3)))
cf <- gmm_counterfactual(g, evidence = c(1.2, 0, 0.5),
                         do = c(NA, 1, NA), query = 1L)
cf@mean
#> [1] 1.2