get_simpsons_paradox_c: Simpson's Paradox Transformation with Copula and Simulated...

In covalchemy: Constructing Joint Distributions with Control Over Statistical Properties

Simpson's Paradox Transformation with Copula and Simulated Annealing

Description

This function simulates the Simpson's Paradox phenomenon by transforming data using Gaussian copulas, optimizing the transformation with simulated annealing, and comparing the results.

Usage

get_simpsons_paradox_c(
  x,
  y,
  z,
  corr_vector,
  inv_cdf_type = "quantile_7",
  sd_x = 0.05,
  sd_y = 0.05,
  lambda1 = 1,
  lambda2 = 1,
  lambda3 = 1,
  lambda4 = 1,
  max_iter = 1000,
  initial_temp = 1,
  cooling_rate = 0.99,
  order_vec = NA,
  degree = 5
)

Arguments

x	A numeric vector of data points for variable X.
y	A numeric vector of data points for variable Y.
z	A categorical variable representing groups (e.g., factor or character vector).
corr_vector	A vector of correlations for each category of z.
inv_cdf_type	Type of inverse CDF transformation ("quantile_1", "quantile_4", "quantile_7", "quantile_8", "linear", "akima", "poly"). Default is "quantile_7".
sd_x	Standard deviation for perturbations on X (default is 0.05).
sd_y	Standard deviation for perturbations on Y (default is 0.05).
lambda1	Regularization parameter for simulated annealing (default is 1).
lambda2	Regularization parameter for simulated annealing (default is 1).
lambda3	Regularization parameter for simulated annealing (default is 1).
lambda4	Regularization parameter for simulated annealing (default is 1).
max_iter	Maximum iterations for simulated annealing (default is 1000).
initial_temp	Initial temperature for simulated annealing (default is 1.0).
cooling_rate	Cooling rate for simulated annealing (default is 0.99).
order_vec	Manual ordering of grids (default is NA, calculated automatically if not specified).
degree	Degree of polynomial used for polynomial inverse CDF (default is 5).

Value

A list containing:

df_all	The final dataset with original, transformed, and annealed data.
df_res	A simplified version with only the optimized data.

Examples

set.seed(123)
n <- 300
z <- sample(c("A", "B", "C"), prob = c(0.3, 0.4, 0.3), size = n, replace = TRUE)
x <- rnorm(n, 10, sd = 5) + 5 * rbeta(n, 5, 3)
y <- 2 * x + rnorm(n, 5, sd = 4)
t <- c(-0.8, 0.8, -0.8)
res <- get_simpsons_paradox_c(x, y, z, t, sd_x = 0.07, sd_y = 0.07, lambda4 = 5)

covalchemy documentation built on April 12, 2025, 2:15 a.m.