Simulate counterfactual paths under tvhte + feedback fits

Implements Algorithm 1 of Botosaru and Liu (2026): given fits of the outcome model (tvhte) and feedback model (fit_feedback), simulate counterfactual joint trajectories {Y_i^{T,*}, X_i^{T,*}} under alternative treatment timing or initial conditions.

Usage

simulate_counterfactual(
  fit,
  fit_fb,
  t0_star,
  N_star = 500,
  Y0_star = NULL,
  X0_star = NULL,
  seed = NULL
)

Arguments

fit

A tvhte object.

fit_fb

A tvhte_feedback object.

t0_star

Counterfactual treatment timing (scalar applied to all simulated units, or length-N_star vector). Use Inf for never- treated counterfactuals.

N_star

Number of counterfactual units to simulate.

Y0_star, X0_star

Counterfactual baseline values (length-N_star each). Default draws standard normals.

seed

Optional RNG seed.

Value

A list with Y (N_star x T matrix of counterfactual outcomes), X (N_star x T x 1 array), and lambda (N_star x 2 matrix of drawn latent effects).

Details

Latent lambda_i = (alpha_i, delta_{i0}) is drawn from the estimated Gaussian prior; event-time effects evolve via the AR(1) on delta_{ij}; covariates evolve via the estimated feedback process; outcomes accumulate the direct effect (delta_{ij}) plus the indirect effect (X_it' beta).

Examples

# Fit the model, fit the feedback, then simulate counterfactual paths
# under shifted treatment timing.
sim <- simulate_tvhte(N = 300, T = 6, t0 = 3, J = 2, beta = 0.4,
                      feedback_gamma = c(0.2, 0.3, 0.5, 0.4), seed = 1)
fit <- tvhte(sim$Y, sim$Y0, t0 = sim$t0, J = sim$J, X = sim$X,
             compute_se = FALSE)
fb  <- fit_feedback(sim$Y, sim$Y0, sim$X, sim$X0)

# Counterfactual: treatment delayed from t=3 to t=5
cf <- simulate_counterfactual(fit, fb, t0_star = 5,
                               N_star = 200, seed = 99)
colMeans(cf$Y)   # average counterfactual outcome path
#> [1] 0.1401096 0.2805138 0.3674985 0.3779429 1.6185435 1.9285446