TROP estimate on matrix input

A thin, matrix-in wrapper around the TROP working model, written independently from the paper. The matrix-in form is convenient for numerically comparing trop() against other matrix-based implementations on identical inputs. For data-frame input, cross-validated penalty selection, inference and the multi-estimator comparison, use trop() and panel_compare() instead.

Usage

trop_matrix(
  Y,
  W,
  treated_units = NULL,
  lambda_unit,
  lambda_time,
  lambda_nn,
  treated_periods = NULL,
  control = trop_control()
)

Arguments

Y: N x T outcome matrix.
W: N x T 0/1 treatment matrix (1 = actively treated cell).
treated_units: Integer row indices of the treated units, used to anchor the unit weights. Defaults to NULL, in which case the treated rows are inferred from W as the rows with at least one treated cell.
lambda_unit, lambda_time: Non-negative decay parameters for the unit and time weights.
lambda_nn: Nuclear-norm penalty; use Inf to drop the low-rank term. As in trop(), the solver adds the small scale-relative stabilising floor nn_floor (see trop_control()) to a finite lambda_nn; Inf is never affected, so the weighted-TWFE special case used for the exact numerical-agreement checks is unchanged. For like-for-like comparisons against other implementations at identical finite penalty values, pass control = trop_control(nn_floor = 0) so lambda_nn is applied exactly as supplied.
treated_periods: Number of final columns treated as the post block, used to build the pre-period mask and the time-distance centre. Defaults to NULL, in which case it is inferred from W as the number of periods in which any treated unit is active.
control: A list of solver controls from trop_control().

Value

A single numeric ATT estimate.

Details

The untreated outcome model is fitted on the control cells with the supplied weights, and the returned effect is the average over treated cells of Y - alpha - beta - L, exactly as in the paper's eq. (2). With lambda_nn = Inf the low-rank term is dropped and the fit is weighted two-way fixed effects, matching the reference to numerical tolerance. With a finite lambda_nn the nuclear-norm term is solved by this package's proximal-gradient / soft-impute routine, which targets the same convex program as eq. (2) (loss sum_js w (Y - alpha - beta - L)^2, with no 1/2 factor); lambda_nn is therefore on the same scale as the official Python and Stata packages, and finite-penalty results agree with them to solver tolerance.

trop_matrix() always uses the pooled weighting scheme anchored to the centre of the treated block: it takes no anchor argument and has no per-cell mode. It therefore computes the same pooled, block-centre estimator as the official Python package's TROP_TWFE_average (implemented independently), and exists as a like-for-like matrix-in cross-check against that pooled reference. trop(..., anchor = "pooled") uses the same convention (unit distances to the average treated trajectory, time distances to the centre of the treated block), so on a trailing-block design the two agree to solver tolerance for the same penalties. For the per-cell estimator (the paper's eq. (12) / Algorithm 2), use trop(..., anchor = "per_cell"), which shares the data-frame core .trop_att().

References

Athey, S., Imbens, G. W., Qu, Z., & Viviano, D. (2026). Triply Robust Panel Estimators. Journal of Applied Econometrics. doi:10.1002/jae.70061 .

Examples

df <- sim_panel(N = 14, T = 9, n_treated = 3, t0 = 6, att = 2, seed = 1)
Y <- matrix(0, max(df$id), max(df$t)); W <- Y
for (k in seq_len(nrow(df))) { Y[df$id[k], df$t[k]] <- df$y[k]
  W[df$id[k], df$t[k]] <- df$w[k] }
tu <- which(rowSums(W) > 0)
trop_matrix(Y, W, tu, 0.1, 0.1, Inf, treated_periods = 4)
#> [1] 1.419739

# treated_units and treated_periods are inferred from W when omitted, so the
# matrices produced by panel_matrices() can be fed in directly.
pm <- panel_matrices(df, "y", "w", "id", "t")
trop_matrix(pm$Y, pm$W, lambda_unit = 0.1, lambda_time = 0.1, lambda_nn = Inf)
#> [1] 1.419739