xSJpearsonPMF {SimJoint}

Simulate joint with marginal PMFs, Pearson correlations and uncorrelated support matrix.

Description

Sample from marginal probability mass functions via Latin hypercube sampling and then simulate the joint distribution with Pearson correlations. Users specify the uncorrelated random source instead of using permuted marginal samples to left-multiply the correlation matrix decomposition.

Usage

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

Arguments

PMFs

A list of data frames. Each data frame has 2 columns, a value vector and a probability vector. Probabilities should sum up to 1. Let the size of PMFs be K.

sampleSize

An integer. The sample size N.

cor

A K x K positive semi-definite correlation matrix.

noise

An N x K arbitrary numeric matrix where columns are (more or less) uncorrelated. Exact zero correlations are unnecessary.

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

Pearson 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.
# 3 PDFs, 2 nonparametric PMFs, 5 parametric PMFs:
PMFs = c(
  apply(cbind(rnorm(N), rchisq(N, 4), rbeta(N, 4, 2)), 2, function(x)
    data.frame(val = sort(x), P = 1.0 / N)),
  list(data.frame(val = 1:3 + 0.0, P = c(0.3, 0.45, 0.25))),
  list(data.frame(val = 1:4 + 0.0, P = c(0.2, 0.3, 0.4, 0.1))),
  apply(cbind(rpois(N, 1), rpois(N, 5), rpois(N, 10),
              rnbinom(N, 3, 0.2), rnbinom(N, 6, 0.8)), 2, function(x)
                data.frame(val = as.numeric(sort(x)), P = 1.0 / N))
)


# Create the target correlation matrix `Rey`:
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]
  }
}


system.time({result = SimJoint::xSJpearsonPMF(
  PMFs = PMFs, sampleSize = N, noise = matrix(runif(N * K), ncol = K),
  cor = Rey, errorType = "meanSquare", seed = 456, maxCore = 1,
  convergenceTail = 8, verbose = TRUE)})


# Check relative errors.
summary(as.numeric(abs(result$cor / Rey - 1)))