Skip to contents

Optimize cLHS Sample Size Using KL Divergence

Source: R/kl_optimization.R
ss_kl_optimize.Rd

Determines the sample size at which a conditioned Latin hypercube sample (cLHS) best represents the population distribution, following the KL-divergence-based approach of Malone et al. (2019). Runs cLHS at a range of sample sizes, fits an exponential decay curve to the mean KL divergence, and reports the smallest sample size that reaches a target proportion of the maximum achievable improvement.

Usage

ss_kl_optimize(
  population_data,
  min_samples = 10,
  max_samples = 500,
  step_size = 10,
  n_replicates = 10,
  n_bins = 25,
  probability_threshold = 0.95
)

Arguments

population_data

Data frame of population ancillary data (one row per population unit, one column per covariate).

min_samples

Integer, minimum sample size to test. Default 10.

max_samples

Integer, maximum sample size to test. Default 500.

step_size

Integer, increment between tested sample sizes. Default 10.

n_replicates

Integer, number of cLHS replicates per sample size. Default 10.

n_bins

Integer, number of histogram bins used by ss_kl_divergence(). Default 25.

probability_threshold

Numeric in (0, 1], CDF threshold used to pick the optimal sample size. Default 0.95.

Value

A list with:

raw_results

Data frame, one row per replicate.

summary_results

Data frame, mean/sd KL divergence per sample size.

fitted_model

The fitted nls exponential decay model, or NULL.

fitted_curve

Data frame of fitted KL divergence per sample size.

optimal_sample_size

Integer, the recommended sample size.

plot_kl

A ggplot of KL divergence vs. sample size.

plot_cdf

A ggplot of the CDF used to pick the optimal size.

Details

The relationship between sample size \(n\) and KL divergence is modeled as \(KL(n) = b_1 e^{-kn} + b_0\). The optimal sample size is the smallest \(n\) for which the cumulative proportion of improvement, \((max(KL) - KL(n)) / (max(KL) - min(KL))\), reaches probability_threshold.

See also

ss_kl_divergence()

Examples

if (FALSE) { # \dontrun{
pop <- data.frame(a = rnorm(2000), b = runif(2000))
res <- ss_kl_optimize(pop, min_samples = 10, max_samples = 60,
  step_size = 10, n_replicates = 3)
res$optimal_sample_size
} # }