SJspearman {SimJoint}

Simulate joint given marginals and Spearman correlations.

Description

Reorder elements in each column of a matrix such that the column-wise Spearman correlations approximate a given correlation matrix.

Usage

SJspearman(
  X,
  cor,
  stochasticStepDomain = as.numeric(c(0, 1)),
  errorType = "meanSquare",
  seed = 123L,
  maxCore = 7L,
  convergenceTail = 8L,
  iterLimit = 100000L,
  verbose = TRUE
  )

Arguments

X

An N x K numeric matrix of K marginal distributions (samples). Columns are sorted.

cor

A K x K correlation matrix. The matrix should be positive semi-definite.

stochasticStepDomain

A numeric vector of size 2. Range of the stochastic step ratio for correcting the correlation matrix in each iteration. Default [0, 1]. See the package vignette for more details.

errorType

Cost function for convergence test.

"meanRela": average absolute relative error between elements of the target correlation matrix and the correlation matrix approximated in each iteration.

"maxRela": maximal absolute relative error.

"meanSquare": mean squared error. Default.

seed

An integer or an integer vector of size 4. A single integer seeds a pcg64 generator the usual way. An integer vector of size 4 supplies all the bits for a pcg64 object.

maxCore

An integer. Maximal threads to invoke. Default 7. Better be no greater than the total number of virtual cores on machine.

convergenceTail

An integer. If the last convergenceTail iterations resulted in equal cost function values, return. Default 8.

iterLimit

An integer. The maximal number of iterations. Default 100000.

verbose

A boolean value. TRUE prints progress.

Details

Algorithms are detailed in the package vignette.

Value

A list of size 2.

X

A numeric matrix of size N x K, the simulated joint distribution.

cor

Spearman correlation matrix of X.

Examples

# =============================================================================
# Use the same example from <https://cran.r-project.org/web/packages/
#                            SimMultiCorrData/vignettes/workflow.html>.
# =============================================================================
set.seed(123)
N = 10000L # Sample size.
K = 10L # 10 marginals.
# Sample from 3 PDFs, 2 nonparametric PMFs, 5 parametric PMFs:
marginals = cbind(
  rnorm(N), rchisq(N, 4), rbeta(N, 4, 2),
  LHSpmf(data.frame(val = 1:3, P = c(0.3, 0.45, 0.25)), N,
         seed = sample(1e6L, 1)),
  LHSpmf(data.frame(val = 1:4, P = c(0.2, 0.3, 0.4, 0.1)), N,
         seed = sample(1e6L, 1)),
  rpois(N, 1), rpois(N, 5), rpois(N, 10),
  rnbinom(N, 3, 0.2), rnbinom(N, 6, 0.8))
# The seeding for `LHSpmf()` is unhealthy, but OK for small examples.


marginals = apply(marginals, 2, function(x) sort(x))


# Create the target correlation matrix `Rey` treated as Spearman
# correlations.
set.seed(11)
Rey <- diag(1, nrow = 10)
for (i in 1:nrow(Rey)) {
  for (j in 1:ncol(Rey)) {
    if (i > j) Rey[i, j] <- runif(1, 0.2, 0.7)
    Rey[j, i] <- Rey[i, j]
  }
}


result = SimJoint::SJspearman(
  X = marginals, cor = Rey, errorType = "meanSquare", seed = 456,
  maxCore = 1, convergenceTail = 8, verbose = TRUE)


# Check relative errors.
summary(as.numeric(abs(cor(result$X, method = "spearman") / Rey - 1)))




# Another way to impose rank correlation is to supply rank matrix
# to SJpearson():
system.time({reorderedRanks = SimJoint::SJpearson(
  X = apply(marginals, 2, function(x) rank(x)), cor = Rey,
  errorType = "meanSquare", seed = 456, maxCore = 1,
  convergenceTail = 8, verbose = TRUE)})


# Reordering according to ranks:
result = apply(rbind(reorderedRanks$X, marginals), 2, function(x)
{
  x[(N + 1L) : (2L * N)][as.integer(x[1L : N])]
})


# Check the relative errors.
summary(as.numeric(abs(cor(result, method = "spearman") / Rey - 1)))