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Breakdown frontier for a regression coefficient hypothesis

Source: R/api.R
regsen_breakdown.Rd

Find the smallest sensitivity-parameter value at which a given hypothesis about the long-regression coefficient first fails. For DMP, this is rxbar as a function of (cbar, rybar, beta) or – with direction = "rybar" – rybar as a function of (rxbar, cbar, beta). For Oster, this is |delta| as a function of R-squared(long), beta and (optionally) maxovb.

Usage

regsen_breakdown(
  formula,
  data,
  analysis = c("dmp", "oster"),
  compare = NULL,
  nocompare = NULL,
  cbar = 1,
  clow = 0,
  rybar = Inf,
  rybar_expr = NULL,
  direction = c("rxbar", "rybar"),
  rxbar = NULL,
  r2long = 1,
  maxovb = NA,
  r2long_type = c("eq", "relative"),
  maxovb_type = c("bound", "relative"),
  beta = "sign",
  subset = NULL,
  ncores = NULL
)

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.

analysis

Which sensitivity analysis to run: "dmp" (default) or "oster".

compare

Optional character vector of variables to use as the comparison set. Defaults to all controls if neither compare nor nocompare is given.

nocompare

Optional character vector of controls to exclude from the comparison set.

cbar, clow, rybar, rybar_expr

(DMP) Same as in regsen_bounds().

direction

(DMP) Which sensitivity parameter the breakdown point is reported in: "rxbar" (default) sweeps cbar or beta and solves for rxbar; "rybar" sweeps rxbar and solves for rybar, the frontier rybar_bf(rxbar) of DMP (2026) Theorem 4. The two trace the same frontier, but only the rybar direction can describe its horizontal arm, where the conclusion survives every rxbar and the rxbar breakdown point is +Inf.

rxbar

(DMP, direction = "rybar") Numeric vector of rxbar values at which to evaluate the frontier. Defaults to an 11-point grid over [0, 2 * rmax(cbar)].

r2long, maxovb

(Oster) Same as in regsen_bounds().

r2long_type

One of "eq" (the default) or "relative". When "relative", values are multiplied by R-squared(medium).

maxovb_type

One of "bound" (default) or "relative". When "relative", values are multiplied by |Beta(medium)|.

beta

Hypothesis spec. One of:

  • "sign" – the hypothesis that sign(beta_long) = sign(beta_med).

  • a numeric scalar or vector. Use the helpers bnd_lb(), bnd_ub(), bnd_eq() to set the direction, e.g. beta = bnd_lb(0) for the hypothesis beta > 0.

subset

Optional logical or integer vector indicating which rows of data to include in the estimation.

ncores

Number of cores to spread the frontier's values over. NULL (default) uses the session setting of regsen_cores(); "auto" uses all but two of the machine's cores. Only frontiers that need the optimizer (finite rybar, rybar_expr, or direction = "rybar") are costly enough to benefit. Results are identical for any number of cores.

Value

A regsensitivity object. results$index holds the swept parameter and results$breakdown the breakdown point at each value.

Details

For analysis = "oster" the hypothesis selects between two quantities that Masten and Poirier (2026) distinguish. An equality hypothesis (beta = bnd_eq(0)) returns the explain away breakdown point: the signed delta at which beta_long equals the hypothesized value, the number psacalc reports. An inequality or sign hypothesis (the default) returns the sign change breakdown point: the smallest |delta| at which some value on the wrong side of the hypothesis enters the identified set. The two can differ by an order of magnitude and the second is the one that bears on whether the conclusion could be wrong.

Their Theorem 2 shows the sign change breakdown point can never exceed one, so without maxovb the reported value is capped at 1: a printed 1 means the sign survives every |delta| below the conventional cutoff, not that a solution was found there. Supplying maxovb adds the assumption that lifts the cap.

Examples

data(bfg2020)
bk <- regsen_breakdown(
  avgrep2000to2016 ~ tye_tfe890_500kNI_100_l6 +
    log_area_2010 + lat + lon + temp_mean + rain_mean + elev_mean +
    d_coa + d_riv + d_lak + ave_gyi,
  data = bfg2020,
  cbar = seq(0, 1, 0.1)
)
print(bk)
#> 
#> Regression Sensitivity Analysis ----- Breakdown Frontier
#> ------------------------------------------------------------------------
#> Analysis:          DMP (2026)
#> Treatment:         tye_tfe890_500kNI_100_l6
#> Outcome:           avgrep2000to2016
#> N (obs):           2036
#> Hypothesis:        Beta > 0
#> 
#> --- Summary statistics ----------------------------------
#>   Beta (short)                  1.7078
#>   Beta (medium)                 1.5864
#>   R2 (short)                    0.0269
#>   R2 (medium)                   0.1345
#>   Var(Y)                      136.3204
#>   Var(X)                        1.2574
#>   Var(X_Residual)               1.0903
#> 
#> --- Results ---------------------------------------------
#>   index breakdown
#>       0   0.38508
#>     0.1    0.3726
#>     0.2   0.36438
#>     0.3   0.36007
#>     0.4   0.35936
#>     0.5   0.35936
#>     0.6   0.35936
#>     0.7   0.35936
#>     0.8   0.35936
#>     0.9   0.35936
#>       1   0.35936