Iteratively adjust intercept to achieve target proportion in binomial simulation

This function uses an iterative approach to find the appropriate intercept value that produces a desired proportion of 1s in binomial response simulation. It works by adjusting the intercept on the log-odds scale using adaptive damping to prevent overshooting due to the nonlinear logistic transformation.

Usage

adjust_proportion(
  target_prop,
  functional_effects,
  max_iter = 15,
  tolerance = 0.03,
  verbose = FALSE
)

Arguments

target_prop

Desired proportion of 1s in the response. Must be between 0 and 1 (exclusive).

functional_effects

Numeric vector of functional effects (e.g., from 2D integration of surfaces). These represent the variability around the baseline intercept.

max_iter

Maximum number of iterations for adjustment. Default is 15.

tolerance

Convergence tolerance for the difference between target and achieved proportion. Default is 0.03.

verbose

Logical indicating whether to print iteration progress. Default is FALSE.

Value

A list containing:

• y: Binary response vector of length equal to functional_effects

• intercept: Final adjusted intercept value

• final_prop: Achieved proportion of 1s in the response

• iterations: Number of iterations used

• converged: Logical indicating whether convergence was achieved

• final_error: Final absolute error between target and achieved proportion

Details

The function works by:

1. Starting with an initial intercept based on qlogis(target_prop)

2. Computing probabilities using plogis(intercept + functional_effects)

3. Generating binary outcomes using rbinom()

4. Adjusting the intercept based on the error between target and achieved proportions

5. Using adaptive damping (0.3 for large errors, 0.5 for medium, 0.7 for small)

The adjustment formula is: adjustment = (qlogis(target_prop) - qlogis(achieved_prop)) * damping_factor

This approach works in log-odds space to prevent probabilities from exceeding the unit interval and provides robust control over response proportions in functional regression simulation studies.

See also

data_generator_po_2d for using this function in 2D functional data simulation.

Examples

# Basic usage with simulated functional effects
set.seed(123)
effects <- rnorm(100, mean = 0, sd = 0.5)
result <- adjust_proportion(target_prop = 0.3, functional_effects = effects)
cat("Achieved proportion:", result$final_prop, "\n")
#> Achieved proportion: 0.27 
cat("Converged in", result$iterations, "iterations\n")
#> Converged in 1 iterations

# Usage with 2D functional regression effects
# Assuming you have computed 2D integral effects from surfaces
# integral_effects <- compute_2d_integrals(surfaces, beta_surface)
# result <- adjust_proportion(0.4, integral_effects, tolerance = 0.01)

# Check for convergence issues
if (!result$converged) {
  warning("Adjustment did not converge. Final error: ", result$final_error)
}