DiP (Difference-in-Predictions) Estimator — msd

DiP estimator for ATE using paired predictions. DiP (Difference-in-Predictions) Estimator

Computes the Difference-in-Predictions (DiP) estimator for the average treatment effect (ATE). This estimator uses both treatment and control predictions for each unlabeled unit, computing the contrast S^(1) - S^(0) at the unit level.

Usage

msd_dip(
  formula_or_data,
  data = NULL,
  observed = NULL,
  unobserved = NULL,
  conf_level = 0.95
)

Arguments

formula_or_data: Either an msd_data object created by msd_data, or a formula of the form outcome ~ treatment | pred_treated + pred_control.
data: If formula_or_data is a formula, this should be either: an msd_data object, a combined dataframe, or NULL (if using observed/unobserved).
observed: If using formula with separate dataframes, the observed data.
unobserved: If using formula with separate dataframes, the unobserved data.
conf_level: Confidence level for the confidence interval (default 0.95)

Value

An msd_result object containing:

estimate: Point estimate of the ATE
variance: Estimated variance
se: Standard error
ci_lower, ci_upper: Confidence interval bounds
method: Name of the estimation method
lambda: Tuning parameter (always 1 for DiP)

Details

The DiP estimator is: $$\hat{\tau}^{DiP} = \frac{1}{|\mathcal{U}|}\sum_{i \in \mathcal{U}} (S_i^{(1)} - S_i^{(0)}) + \frac{1}{n_1}\sum_{i \in \mathcal{O}_1} (Y_i - S_i^{(1)}) - \frac{1}{n_0}\sum_{i \in \mathcal{O}_0}(Y_i - S_i^{(0)})$$

Note

DiP requires BOTH S0 and S1 predictions for ALL units. The key advantage of DiP over GREG is that when S^(1) and S^(0) are positively correlated, the variance of their difference is smaller.

Examples

# Using msd_data object
obs_df <- data.frame(
  Y = c(1.2, 1.4, 0.8, 0.6),
  S0 = c(1.0, 1.2, 0.7, 0.5),
  S1 = c(1.1, 1.3, 0.9, 0.7),
  D = c(1, 1, 0, 0)
)
unobs_df <- data.frame(
  S0 = c(1.1, 0.9, 1.0, 0.8),
  S1 = c(1.2, 1.0, 1.1, 0.9),
  D = c(1, 1, 0, 0)
)
msd <- msd_data(observed = obs_df, unobserved = unobs_df)
result <- msd_dip(msd)

# Using formula interface
result2 <- msd_dip(Y ~ D | S1 + S0, observed = obs_df, unobserved = unobs_df)