Patterned Sensitivity Analysis for IV with Fixed Effects

Patterned sensitivity analysis for instrumental-variables designs with fixed effects or other residualization steps. The package provides uniform Conley-style sensitivity as a baseline, researcher-specified direct-effect patterns, sensitivity paths and tipping points, and optional confirmatory Beyond Plausibly Exogenous diagnostics.

spliv

spliv provides sensitivity analysis for instrumental-variables (IV) designs when exclusion may fail in structured ways. It supports uniform uncertainty intervals, researcher-specified direct-effect patterns, sensitivity paths and tipping points, and confirmatory Beyond Plausibly Exogenous (BPE) designs based on a pre-specified instrument-inactive subset. The package does not search for an unrestricted direct-effect field: patterns and BPE designs must be justified by the researcher.

Installation

Install the released package from CRAN:

install.packages("spliv")

Install the development version from GitHub when you need unreleased changes:

remotes::install_github("koren6684/spliv")

A small synthetic example

The examples below are self-contained and use no empirical or restricted data.

library(spliv)

set.seed(42)
n <- 240
z <- rnorm(n)
w <- rnorm(n)
exposure <- pnorm(w)
inactive <- seq_len(n) <= n / 2
x <- ifelse(inactive, 0, 1) * z + 0.4 * w + rnorm(n)
y <- 1.2 * x + 0.25 * w + 0.15 * exposure * z + rnorm(n)

d <- data.frame(y, x, z, w, exposure, inactive)
f <- y ~ x + w | z + w

Baseline IV estimate

With no method or bound supplied, spliv() uses UCI at delta = 0 and reproduces the conventional IV confidence interval under strict exclusion.

baseline <- spliv(
  f,
  d,
  vcov = "hc1"
)

baseline$estimates

Uniform UCI sensitivity

Union-of-confidence-intervals (UCI) sensitivity allows the excluded instrument's direct effect to vary over a bounded interval. On the default scale, delta is an outcome-unit direct effect for a one-residual-SD shift in the instrument.

uniform <- spliv(
  f,
  d,
  method = "uci",
  delta = 0.20,
  vcov = "hc1",
  grid = list(steps = 11)
)

uniform$estimates

Patterned UCI and LTZ sensitivity

Use a theory-motivated spliv_pattern() to allow the possible direct effect to vary with an observed exposure. The package supports both bounded UCI and local-to-zero (LTZ) sensitivity.

pattern <- spliv_pattern(
  name = "Exposure pattern",
  pattern = ~ exposure,
  rationale = "The alternative channel is expected to be stronger at higher exposure.",
  variables_used = "exposure",
  pattern_type = "theory_defined",
  normalize = "max_abs"
)

patterned_uci <- spliv(
  f,
  d,
  method = "uci",
  delta = 0.20,
  vcov = "hc1",
  violation_pattern = pattern,
  grid = list(steps = 11)
)

patterned_ltz <- spliv(
  f,
  d,
  method = "ltz",
  delta = 0.20,
  vcov = "hc1",
  violation_pattern = pattern
)

patterned_uci$estimates
patterned_ltz$estimates

Sensitivity paths and tipping points

Sensitivity paths report how the estimated interval changes over a pre-specified range of direct-effect magnitudes. The tipping point is the first value on the supplied grid at which the interval includes zero.

path <- spliv_sensitivity_path(
  f,
  d,
  method = "uci",
  delta_grid = seq(0, 0.30, by = 0.05),
  vcov = "hc1",
  violation_pattern = pattern
)

head(path)
spliv_tipping_point(path)
plot(path, term = "x")

Confirmatory BPE

Confirmatory Beyond Plausibly Exogenous (BPE) analysis begins with a pre-specified, outcome-independent instrument-inactive subset and an explicit transportability rationale. The package validates the proposed design and estimates the BPE model only when the eligibility diagnostics pass. The default sampling transport carries the estimated reduced-form sampling covariance; conservative adds a pre-specified covariance inflation.

design <- bpe_design(
  name = "Theory-defined inactive subset",
  subset = ~ inactive,
  rationale = "The treatment channel is absent in the inactive subset.",
  variables_used = "inactive",
  subset_type = "theory_defined",
  pre_specified = TRUE,
  transportability_rationale = "The subset direct effect is informative for the target sample."
)

# This illustrative margin allows a first-stage effect of 0.25 residual
# treatment SD per one-residual-SD instrument shift. In substantive work,
# pre-specify the margin; do not tune it to make BPE pass.
bpe_margin <- 0.25

validation <- bpe_validate_design(
  f,
  d,
  design = design,
  vcov = "hc1",
  bpe_min_n_S = 40,
  bpe_equiv_margin = bpe_margin
)

validation[c(
  "n_S",
  "equivalence_passed",
  "eligibility_passed"
)]

bpe_fit <- spliv(
  f,
  d,
  method = "bpe",
  bpe_design = design,
  vcov = "hc1",
  bpe_min_n_S = 40,
  bpe_equiv_margin = bpe_margin
)

bpe_fit$estimates

bpe_explore_subsets() is an exploratory diagnostic. Searching across subgroups and reporting the first passing rule is not confirmatory BPE; confirmatory BPE requires a pre-specified bpe_design() with a substantive rationale and transportability statement.

Advanced low-level interface

Advanced users needing lower-level controls can consult the online reference documentation. Ordinary analyses should normally use the canonical workflow shown above.

Further resources

• Package website: https://koren6684.github.io/spliv/
• Reproducibility repository: https://github.com/koren6684/spliv-reproducibility
• Citation information: run citation("spliv") after installation.