scm_design: Experimental Synthetic Control Design
In coresynth: Fast and Unified Synthetic Control Methods

scm_design

R Documentation

Experimental Synthetic Control Design

Description

Selects which units to assign to the treatment arm (and which to the control arm) in a planned experiment, following Abadie and Zhao (2026). Both sets of units are chosen by minimising the distance between their weighted-average predictor vectors and the population-average predictor vector \bar{X}, so the resulting estimates are less susceptible to post-randomisation bias than pure random assignment.

Usage

scm_design(
  data,
  outcome,
  unit,
  time,
  T0,
  T_fit = NULL,
  m_min = 1L,
  m_max = 1L,
  f = NULL,
  predictors = NULL,
  design = c("base", "weakly_targeted", "unit_level"),
  beta = 1,
  xi = 1,
  alpha = 0.05,
  normalize = TRUE,
  max_subsets = 100000L
)

Arguments

`data`	Long-format data frame (one row per unit–time).
`outcome`	Name of the outcome column.
`unit`	Name of the unit identifier column.
`time`	Name of the time identifier column.
`T0`	Last pre-experimental period (a value present in the time column). Periods after `T0` are the experimental periods.
`T_fit`	Number of fitting periods, counted from the start of the pre-experimental phase. Defaults to `NULL`, which uses all pre-experimental periods for fitting (no blank periods; inference disabled). When `T_fit` is smaller than the total number of pre-experimental periods, the remaining periods become blank periods used for inference.
`m_min`	Minimum number of units assigned to treatment (default 1).
`m_max`	Maximum number of units assigned to treatment (default 1).
`f`	Named numeric vector of population weights `f_j`. Defaults to uniform weights `1/J`. Will be normalised to sum to 1.
`predictors`	A `list()` of `pred()` specifications that define the predictor matrix `X_j`. Defaults to `NULL`, which uses all fitting-period outcome values as predictors.
`design`	Design formulation: `"base"` (default), `"weakly_targeted"`, or `"unit_level"`.
`beta`	Trade-off parameter `\beta > 0` for the Weakly targeted design (default 1).
`xi`	Trade-off parameter `\xi > 0` for the Unit-level design (default 1).
`alpha`	Significance level for confidence intervals (default 0.05).
`normalize`	If `TRUE` (default), each row of the predictor matrix is divided by its cross-unit standard deviation before optimisation, so predictors measured on different scales contribute equally.
`max_subsets`	Maximum number of treatment-set candidates to evaluate before switching to random sampling (default 100 000).

Details

Three design formulations are available:

"base" (eq. 7): both the synthetic treated and the synthetic control independently target the population average \bar{X}.
"weakly_targeted" (eq. 9): the treated and control weights jointly minimise the distance of the synthetic treated to \bar{X} plus beta times the distance between the synthetic control and the synthetic treated.
"unit_level" (eq. 10): each treated unit gets its own synthetic control; the treated weights trade off matching \bar{X} against xi times each treated unit's own synthetic-control fit, and the aggregate control weight is the w-weighted combination of the per-unit controls (eq. 11).

Inference uses "blank periods" — pre-experimental periods whose outcomes were not used to estimate the weights. Set T_fit strictly smaller than the number of pre-experimental periods to enable the permutation test and split- conformal confidence intervals from Section 3 of Abadie and Zhao (2026).