Placebo (randomisation) test for a TROP ATT

Assesses whether a fitted trop() ATT is distinguishable from zero by comparing it to a placebo null distribution. Control units are repeatedly relabelled as pseudo-treated — using the same number of treated units and the same treatment timing as the real design, so block, staggered and non-absorbing patterns are all reproduced faithfully — and the estimator is refit at the fit's cross-validated penalties (the true effect is zero by construction). The observed ATT is then placed against that null.

Usage

trop_placebo_test(
  object,
  B = 500L,
  alternative = c("two.sided", "greater", "less"),
  control = NULL
)

# S3 method for class 'trop_placebo_test'
print(x, digits = 4, ...)

Arguments

object

A trop fit from trop().

B

Number of placebo assignments to draw.

alternative

Direction of the test: "two.sided" (default), "greater" or "less".

control

A trop_control() list for the placebo refits (penalties are held fixed at the fit's values; this mainly sets seed and workers). Defaults to trop_control(); set seed here for reproducible draws.

x

A trop_placebo_test object.

digits

Number of significant digits to print.

...

Unused.

Value

An object of class trop_placebo_test (a list) with the observed ATT, the vector of placebo ATTs, the p.value, the placebo-null mean and sd, a central null interval null.low/null.high, alternative, B, and n_treated_units. It has print() and autoplot() methods.

Details

This is a randomisation/permutation test, not a standard error: it answers "could a TROP design like mine produce an effect this large when there is none?" For interval estimates use the bootstrap or jackknife (see trop() and compare_se_modes()).

See also

trop(), compare_se_modes()

Examples

# \donttest{
df  <- sim_panel(N = 16, T = 9, n_treated = 3, t0 = 6, att = 3, seed = 1)
# fixed penalties keep the example fast; omit `lambda` to cross-validate
fit <- trop(df, "y", "w", "id", "t", se = "none",
            lambda = list(time = 0.1, unit = 0.5, nn = 2))
pt  <- trop_placebo_test(fit, B = 30)
pt
#> TROP placebo test
#>   observed ATT : 3.464
#>   placebo null : mean -0.07527, sd 0.3276  (30 draws, 3 pseudo-treated units)
#>   null 95% range: [-0.6849, 0.5333]
#>   two.sided p-value : 0.0000
# }