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SCM Outer Weights (Joint Optimization of W and V)

Source: R/RcppExports.R
scm_weights_cpp.Rd

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).

Usage

scm_weights_cpp(
  X0,
  X1,
  Z0,
  Z1,
  max_iter = 100L,
  tol = 1e-04,
  t_train = -1L,
  z_rows = NULL,
  multistart = FALSE,
  cheap_face = FALSE
)

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.

z_rows

Optional 1-based row indices of Z defining the evaluation window for the outer V optimisation (the v_window argument of scm_fit()). NULL (default) evaluates on the full Z window. Takes precedence over t_train; the reported loss always uses the full Z window.

multistart

If TRUE, the outer V optimisation runs a deterministic multi-start search (screened start set, coordinate-descent polish, Nelder-Mead refinement) instead of a single coordinate-descent pass from the uniform V. The result is never worse (in outer loss) than the single-start path.

cheap_face

If TRUE, the inner simplex QP solves each active-set face with a cheap bordered-KKT direct solve instead of the scale-robust null-space projection. Valid only for the outcomes-only regime (no user predictors, no predictor rescaling), where it reproduces the null-space solution to round-off while running markedly faster. FALSE (default) keeps the null-space solver required for scale invariance and rank-deficient faces when predictors are supplied.

Value

A list with:

  • W: Donor weight vector (N_co x 1) on the unit simplex

  • V: 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.