Causal conformal normal curvature (CCNC) and its block decomposition
Source:R/curvature.R
bic_curvature.RdBuilds the causal Delta matrix (Theorem 3.2 of Ospina, 2026) by moving
each unit's observed response between its two potential-outcome
log-densities, and from it the conformal normal curvature in the
treatment direction, B_dT, and its exact additive split into a
discrete-component part and a continuous-component part (Theorem 3.5),
which holds because the Fisher information of the BIc model is block
diagonal (Lemma 2.1). The observed information is a numerical Hessian
of the fitted log-likelihood, the same construction used for the
real-data results in Ospina (2026), Section 8, so this does not depend
on a closed-form score for a particular link function.
Arguments
- fit
A fitted model from
bic_fit().- treat
Character, the name of the treatment variable.
- data
The data frame the effect is averaged over (by default, the data
fitwas fitted on).- eps
Step size passed to
numDeriv::jacobian()/numDeriv::hessian()for the numerical derivatives.
Value
A list of class "bic_curvature" with elements BdT (the
scalar curvature), BdT_discrete, BdT_continuous (its two
components, summing to BdT), Delta (the p x n causal Delta
matrix), Iinv (the p x p inverse observed information),
cross_term (the numerically-vanishing cross term between the two
blocks, a diagnostic for Lemma 2.1 holding on this fit), and trm
(internal design/index information reused by bic_icim() and
bic_sensitivity()).
Details
This answers a different question from bic_gcomp(). bic_gcomp()
says how big the effect is and through which component; BdT says how
much the fitted model itself depends on the treatment assignment of
the sample at hand, a sensitivity/leverage reading, not an effect size,
and in particular not something that should be expected to equal, or
even track closely, the share each component contributes to tau
(one is a share of an average effect, the other a share of a
curvature). A large gap between the two shares is itself informative:
it can mean a submodel affects the curvature, e.g. through a treatment
effect on precision, without affecting tau at all, since the mixture
mean does not depend on precision.
Examples
dat <- simulate_bic(400, seed = 1)
fit <- bic_fit(y ~ T + W2, nu.formula = ~ T + W1, data = dat)
cv <- bic_curvature(fit, "T", dat)
cv$BdT; cv$BdT_discrete + cv$BdT_continuous # match cv$BdT
#> [1] 0.08341132
#> [1] 0.08341132