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Bigsimr

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A Julia package for simulating high-dimensional multivariate data with a target correlation and arbitrary marginal distributions via Gaussian copula. Bigsimr works with any univariate distribution implemented in Distributions.jl or any user-defined distribution derived from Distributions univariate classes. Additionally, Bigsimr accounts for different target correlations:

  • Pearson: employs a matching algorithm (Xiao and Zhou 2019) to account for the non-linear transformation in the Normal-to-Anything (NORTA) step
  • Spearman and Kendall: Use explicit transformations (Lebrun and Dutfoy 2009)

Other Features

  • Nearest Correlation Matrix - Calculate the nearest positive [semi]definite correlation matrix (Qi and Sun 2006)
  • Fast Approximate Correlation Matrix - Calculate an approximation to the nearest positive definite correlation matrix
  • Random Correlation Matrix - Generate random positive [semi]definite correlation matrices
  • Fast Multivariate Normal Generation - Utilize multithreading to generate multivariate normal samples in parallel

Examples

Pearson matching

using Bigsimr
using Distributions

target_corr = cor_randPD(3)
margins = [Binomial(20, 0.2), Beta(2, 3), LogNormal(3, 1)]

adjusted_corr = pearson_match(target_corr, margins)

x = rvec(100_000, adjusted_corr, margins)
cor(Pearson, x)

Spearman/Kendall matching

spearman_corr = cor_randPD(3)
adjusted_corr = cor_convert(spearman_corr, Spearman, Pearson)

x = rvec(100_000, adjusted_corr, margins)
cor(Spearman, x)

Nearest correlation matrix

import LinearAlgebra: isposdef

s = cor_randPSD(200)
r = cor_convert(s, Spearman, Pearson)
isposdef(r)

p = cor_nearPD(r)
isposdef(p)

Fast approximate nearest correlation matrix

s = cor_randPSD(2000)
r = cor_convert(s, Spearman, Pearson)
isposdef(r)

p = cor_fastPD(r)
isposdef(p)

References

  • Xiao, Q., & Zhou, S. (2019). Matching a correlation coefficient by a Gaussian copula. Communications in Statistics-Theory and Methods, 48(7), 1728-1747.
  • Lebrun, R., & Dutfoy, A. (2009). An innovating analysis of the Nataf transformation from the copula viewpoint. Probabilistic Engineering Mechanics, 24(3), 312-320.
  • Qi, H., & Sun, D. (2006). A quadratically convergent Newton method for computing the nearest correlation matrix. SIAM journal on matrix analysis and applications, 28(2), 360-385.
  • amoeba (https://stats.stackexchange.com/users/28666/amoeba), How to generate a large full-rank random correlation matrix with some strong correlations present?, URL (version: 2017-04-13): https://stats.stackexchange.com/q/125020