Bootstrap confidence interval for the breakdown point

Computes a non-parametric (or cluster) bootstrap confidence interval for the breakdown point returned by regsen_breakdown() or the scalar $breakdown field of regsen_bounds(). Both a bias-corrected and accelerated (BCa) interval and a percentile interval are returned; type chooses which one $ci reports.

Usage

regsen_boot(
  formula,
  data,
  ...,
  type = c("bca", "perc"),
  R = 999L,
  cluster = NULL,
  level = 0.95,
  seed = NULL,
  ncores = NULL,
  show_progress = interactive()
)

Arguments

formula: Two-sided formula: y ~ x + w1 + w2 + .... The first right-hand-side variable is the primary independent variable; the rest are controls.
data: A data.frame.
...: Additional arguments forwarded to regsen_breakdown() (the analysis to bootstrap).
type: Interval type reported in $ci: "bca" (default) or "perc". Under "bca" both intervals are computed and stored; under "perc" the jackknife BCa needs is skipped and $ci_bca is NA. See Details.
R: Integer. Number of bootstrap replications. Defaults to 999.
cluster: Optional character scalar naming a column of data to resample at the cluster level (e.g. "km_grid_cel_code" for the BFG 2020 application). When NULL the standard non-parametric bootstrap is used.
level: Two-sided confidence level for the percentile CI. Default 0.95.
seed: Optional integer seed for reproducibility. Results are identical for a given seed regardless of ncores: each replicate draws its own seed from a vector generated once up front, so nothing depends on how the work was divided. Passing a seed leaves the session's random stream where it was, so a bootstrap run inside a larger simulation does not disturb that simulation's own draws. With seed = NULL the replicate seeds come from the session stream, which is advanced by that one draw and nothing else.
ncores: Number of cores for the replications and the jackknife. NULL (default) uses the session setting of regsen_cores(), which is 1 unless changed; "auto" uses all but two of the machine's cores. A progress bar is not shown when running in parallel. Capped at R, and at 2 while R CMD check --as-cran is running, which forbids more; results do not depend on the cap. The breakdown computation inside each replicate always runs serially, so cores are not oversubscribed.
show_progress: Logical; print progress bar.

Value

An object of class regsensitivity_boot containing: point, replicates, ci (the interval named by type), ci_bca, ci_perc, z0, acceleration, type, level, R, cluster, na (the number of replicates that could not be computed) and infinite (the number on which the hypothesis survived every value of the sensitivity parameter; these count as +Inf in the intervals rather than being dropped).

Details

For DMP analyses the breakdown point is computed exactly as in regsen_breakdown(); when rxbar, rybar and cbar are all scalar the returned breakdown is the rxbar breakdown for the (scalar) hypothesis on beta. For Oster analyses the breakdown is the |delta| value at which the hypothesis first fails.

The BCa interval takes the percentile interval and shifts the quantiles it reads by two constants: z0, a median-bias correction equal to the normal quantile of the share of replicates below the point estimate, and acceleration, computed from the delete-one jackknife over sampling units – rows, or clusters when cluster is given. The jackknife costs one breakdown computation per unit, which under an i.i.d. bootstrap means one per row and usually dominates the run; both it and the replicates honour ncores, and type = "perc" skips it. When the jackknife is degenerate (every unit gives the same estimate, so the acceleration is undefined) the BCa interval falls back to the percentile interval and acceleration is NA.

Examples

# \donttest{
data(bfg2020)
bfg2020$statea <- factor(bfg2020$statea)
w1 <- c("log_area_2010", "lat", "lon", "temp_mean", "rain_mean",
        "elev_mean", "d_coa", "d_riv", "d_lak", "ave_gyi")
form <- reformulate(c("tye_tfe890_500kNI_100_l6", w1, "statea"),
                    response = "avgrep2000to2016")
set.seed(1)
bb <- regsen_boot(form, bfg2020, compare = w1, cbar = 1,
                   R = 199, cluster = "km_grid_cel_code")
print(bb)
#> Bootstrap confidence interval for the breakdown point
#> ------------------------------------------------------------
#>   R                  : 199
#>   Cluster bootstrap  : km_grid_cel_code
#>   Interval           : BCa
#>   Bias corr. (z0)    : 1.1233
#>   Acceleration       : -0.0008
#>   Confidence level   : 95%
#>   Point estimate     : 0.8036
#>   95% CI            : [0.7465, 0.9025]
#>   (An endpoint is an extreme replicate; raise R)
#>   95% CI (percentile): [0.4997, 0.8612]
# }