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Generate Correlated Random Variables Using Halton or Scrambled Halton Draws

corr_haltons.Rd

This function generates N correlated random variables using Halton or scrambled Halton draws. The function supports normal and truncated normal distributions.

Usage

corr_haltons(
  means,
  cholesky = NULL,
  stdev = NULL,
  correlations = NULL,
  hdraws = NULL,
  ndraws = 500,
  scrambled = FALSE,
  dist = "normal",
  lower = -Inf,
  upper = Inf
)

Arguments

means

A numeric vector of means for each variable.

cholesky

A Cholesky decomposition matrix to introduce correlation.

stdev

A numeric vector of standard deviations for each variable. If provided, the function will use these values instead of the Cholesky decomposition matrix (must also provide a correlation matrix if providing standard deviations). Default is NULL.

correlations

A correlation matrix to introduce correlation. If provided, the function will use these values instead of the Cholesky decomposition matrix (must also provide standard deviations). Default is NULL.

hdraws

A matrix of Halton or scrambled Halton draws. If provided, the function will use these draws instead of generating new ones. Default is NULL.

ndraws

An integer specifying the number of values to simulate for each variable. Default is 500.

scrambled

A logical value indicating whether to use scrambled Halton draws. Default is FALSE.

dist

A character string specifying the distribution type. Options are "normal" and "truncated_normal". Default is "normal".

lower

A numeric value specifying the lower bound for truncated normal distribution. Default is -Inf.

upper

A numeric value specifying the upper bound for truncated normal distribution. Default is Inf.

Value

A matrix with N columns and ndraws rows containing the simulated values for the correlated random variables.

Examples

# Define mean, correlation, and standard deviations
means <- c(3, 2, 0.9)
sdevs <- c(0.25,1.5,0.8)
CORR <- matrix(c(1, -0.3, 0.5, -0.3, 1, -0.2, 0.5, -0.2, 1), 3, 3)

# Create the Cholesky decomposition matrix and set values for ndraws, etc.
ndraws <- 5000
scrambled <- TRUE
dist <- "normal"

# simulated the data
simulated_data <- corr_haltons(means, stdev=sdevs, correlations=CORR,
                                ndraws=ndraws, scrambled=scrambled,
                                dist=dist)

# look at the mean, standard deviation, and correlation of the simulated data
apply(simulated_data, 2, mean)
#> [1] 2.9991697 2.0247787 0.9048085
apply(simulated_data, 2, sd)
#> [1] 0.2473552 1.4834057 0.7913246
cor(simulated_data)
#>            [,1]       [,2]       [,3]
#> [1,]  1.0000000 -0.2942589  0.5091853
#> [2,] -0.2942589  1.0000000 -0.1922064
#> [3,]  0.5091853 -0.1922064  1.0000000

# providing a cholesky decomposition matrix
dist <- "normal"
cholesky <- chol(cor2cov(CORR, sdevs))
simulated_data <- corr_haltons(means, cholesky=cholesky, ndraws=ndraws,
                                scrambled=scrambled, dist=dist)
apply(simulated_data, 2, mean)
#> [1] 2.9991697 2.0247787 0.9048085
apply(simulated_data, 2, sd)
#> [1] 0.2473552 1.4834057 0.7913246
cor(simulated_data)
#>            [,1]       [,2]       [,3]
#> [1,]  1.0000000 -0.2942589  0.5091853
#> [2,] -0.2942589  1.0000000 -0.1922064
#> [3,]  0.5091853 -0.1922064  1.0000000

# Truncated normal
dist <- "truncated_normal"
lower <- 0
upper <- 30
simulated_data <- corr_haltons(means, cholesky=cholesky, ndraws=ndraws,
                                scrambled=scrambled, dist=dist,
                                lower=lower, upper=upper)
apply(simulated_data, 2, mean)
#> [1] 2.069626 3.317236 2.333870
apply(simulated_data, 2, sd)
#> [1] 0.8399966 5.3108743 1.6579825
cor(simulated_data)
#>           [,1]        [,2]        [,3]
#> [1,] 1.0000000  0.13032493  0.39069072
#> [2,] 0.1303249  1.00000000 -0.03192843
#> [3,] 0.3906907 -0.03192843  1.00000000