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Simulate a structured correlation matrix with reduced rank

Source: R/random_correlation_matrix.R
struc_cor_mat.Rd

Creates a symmetric n x n correlation matrix with user-defined structure and rank.

Usage

struc_cor_mat(
  n = 5,
  base.cor = 0.5,
  range = NULL,
  rank = 3,
  skew = 0,
  base.mat = NULL,
  pos.def = FALSE,
  small.positive = NULL
)

Arguments

n

A scalar defining the dimensions of the correlation matrix.

base.cor

A scalar defining the baseline correlation.
Note: -1 < base.cor < 1.

range

A scalar defining the range of correlations around the baseline. By default, range = 1 - base.cor which ensures the matrix is positive semi-definite with defined rank. Note: base.cor + range <= 1.

rank

A scalar defining the rank of the correlation matrix.

skew

A scalar defining the skewness imposed on the correlations. Note: -1 < skew < 1.

base.mat

An optional n x n base correlation matrix. When supplied, base.cor and skew are ignored and noise is simulated based on rank.

pos.def

When TRUE (default is FALSE), the function bend of the R package `mbend` is used to bend a non-positive (semi)-definite matrix to be positive (semi)-definite.

small.positive

Argument passed to bend when pos.def = TRUE (default is 1e-8). Eigenvalues smaller than small.positive are replaced by this.
Note: 0 < small.positive < 0.1.

Value

A symmetric n x n correlation matrix with defined rank. When pos.def = TRUE, the correlation matrix is guaranteed to be positive (semi)-definite.

Examples

# Simulate and visualise a correlation matrix with 10 columns and rows, rank equal to 4 and
# negatively skewed correlations.
cor_mat <- struc_cor_mat(
  n = 10,
  base.cor = 0.3,
  range = 0.7,
  rank = 4,
  skew = -0.5
)

plot_matrix(
  mat = cor_mat,
  order = TRUE
)