Jointly optimises donor weights W (on the simplex) and the diagonal metric matrix V via coordinate descent on the pre-treatment prediction MSPE, following Abadie, Diamond & Hainmueller (2010).
Arguments
- X0
Covariate matrix for control units (k x N_co, typically pre-treatment outcomes)
- X1
Covariate vector for the treated unit (k x 1)
- Z0
Outcome matrix for control units in the pre-treatment window (T_pre x N_co)
- Z1
Outcome vector for the treated unit in the pre-treatment window (T_pre x 1)
- max_iter
Maximum coordinate-descent iterations (default 100)
- tol
Convergence tolerance on MSPE improvement (default 1e-4)
- t_train
Validation-window split for V selection. -1 (default): V selected on the full Z window (in-sample). Positive: rows t_train..(T_pre-1) of Z form the validation window used to select V (W is fitted on the full X throughout); after selecting V*, W is refit and the reported loss uses the full Z window.
Value
A list with:
W: Donor weight vector (N_co x 1) on the unit simplexV: Optimal metric diagonal (k x 1, normalised to sum to 1)loss: Final pre-treatment prediction loss (full pre-treatment window)
Details
When t_train > 0, V is selected by minimising MSPE on a validation
window (rows t_train..T_pre-1 of Z) while W is fitted on the full
predictor matrix X. This is appropriate when X is a fixed predictor
matrix that contains no validation-period outcome information (the
user-supplied predictors case). For the outcomes-only case the proper
Abadie (2021) S.3.2 train/validation split is implemented in R
(.scm_oos_outcomes()): candidate W(V) are fitted on training-half
outcomes only, by passing the training rows as X and the validation
rows as Z to this function with t_train = -1.