SJpearsonPMF {SimJoint}

Simulate joint with marginal PMFs and Pearson correlations.

Description

Sample from marginal probability mass functions via Latin hypercube sampling and then simulate the joint distribution with Pearson correlations. Use xSJpearsonPMF() for the freedom of supplying the noise matrix, which can let the dependency structure of the result joint distribution be characterized by a certain copula. See the copula section in the package vignette for details.

Usage

SJpearsonPMF(
  PMFs,
  sampleSize,
  cor,
  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 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

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::SJpearsonPMF(
  PMFs = PMFs, sampleSize = N, cor = Rey, errorType = "meanSquare",
  seed = 456, maxCore = 2, convergenceTail = 8, verbose = TRUE)})


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




# =============================================================================
# Play with random nonparametric PMFs.
# =============================================================================
set.seed(123)
N = 2000L
K = 20L


# Create totally random nonparametric PMFs:
PMFs = lapply(1L : K, function(x)
{
  p = runif(2, 1, 10)
  result = data.frame(
    val = sort(rnorm(200)), P = runif(200))
  result$P = result$P / sum(result$P)
  result
})


# Create a valid correlation matrix upper-bounded by `frechetUpperCor`.
while(TRUE)
{
  targetCor = matrix(runif(K * K, -0.1, 0.3), ncol = K)
  targetCor[lower.tri(targetCor)] = t(targetCor)[lower.tri(t(targetCor))]
  diag(targetCor) = 1
  if(min(eigen(targetCor)$values) >= 0) break # Break once the correlation
  # matrix is semi-positive definite. This loop could be running for quite
  # a long time if we do not bound `runif()`.
}


result = SimJoint::SJpearsonPMF(
  PMFs = PMFs, sampleSize = N, cor = targetCor, stochasticStepDomain = c(0, 1),
  errorType = "meanSquare", seed = 456, maxCore = 2, convergenceTail = 8)


# Visualize errors and correlation matrices.
par(mfrow = c(2, 2))
hist(result$cor - targetCor, breaks = K * K, main = NULL,
     xlab = "Error", cex.lab = 1.5, cex.axis = 1.25)
hist(result$cor / targetCor - 1, breaks = K * K, main = NULL,
     xlab = "Relative error", ylab = "", cex.lab = 1.5, cex.axis = 1.25)
zlim = range(range(targetCor[targetCor < 1]), range(result$cor[result$cor < 1]))
col = colorRampPalette(c("blue", "red", "yellow"))(K * K)
tmp = targetCor[, K : 1L]
image(tmp, xaxt = "n", yaxt = "n", zlim = zlim, bty = "n",
      main = "Target cor", col = col)
tmp = result$cor[, K : 1L]
image(tmp, xaxt = "n", yaxt = "n", zlim = zlim, bty = "n",
      main = "Cor reached", col = col)
par(mfrow = c(1, 1))