Sensitivity analysis for equivalence testing

Test how sensitive equivalence conclusions are to the choice of tolerance and number of grid points.

Usage

sensitivity_analysis(
  pair,
  y,
  tol_range = c(1e-08, 1e-06, 1e-04, 0.01),
  n_points_range = c(20, 50, 100),
  method = c("grid", "optimization"),
  progress = interactive()
)

Arguments

pair

An equivalence_pair object

y

Numeric vector of observed data

tol_range

Numeric vector of tolerance values to test

n_points_range

Integer vector of n_points values to test

method

Comparison method: "grid" or "optimization"

progress

Logical; show progress bar

Value

An S3 object of class sensitivity_result containing:

results

Data frame with columns: tol, n_points, equivalent, max_discrepancy

pair

The equivalence pair tested

stable

Logical; whether conclusion is stable across all settings

critical_tol

Smallest tolerance at which models appear equivalent

Examples

exp_spec <- model_spec(
  loglik_fn = function(y, lambda) sum(dexp(y, rate = lambda, log = TRUE)),
  par_names = "lambda",
  par_bounds = list(lambda = c(1e-6, 100)),
  name = "Exponential"
)

gamma_spec <- model_spec(
  loglik_fn = function(y, rate) sum(dgamma(y, shape = 1, rate = rate, log = TRUE)),
  par_names = "rate",
  par_bounds = list(rate = c(1e-6, 100)),
  name = "Gamma(1)"
)

pair <- equivalence_pair(exp_spec, gamma_spec)
set.seed(123)
y <- rexp(50, rate = 2)

# Test sensitivity to tolerance and grid size
sens <- sensitivity_analysis(pair, y,
  tol_range = c(1e-8, 1e-6, 1e-4),
  n_points_range = c(20, 50))
print(sens)