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Simulate a reduced rank correlation matrix with multiple groups

Source: R/random_correlation_matrix.R
group_cor_mat.Rd

Creates a symmetric correlation matrix with user-defined structure, rank and groupings.

Usage

group_cor_mat(
  n = c(5, 5),
  within.cor = 0.5,
  between.cor = 0.2,
  range = NULL,
  rank = 4,
  skew = 0,
  pos.def = FALSE,
  small.positive = NULL,
  return.groups = FALSE
)

Arguments

n

A vector defining the size of each group.

within.cor

A vector defining the baseline correlation within each group. If only one value is supplied, all groups will be assigned the same correlation.
Note: -1 < within.cor < 1.

between.cor

A scalar defining the baseline correlation between groups.
Note: between.cor <= within.cor.

range

A scalar defining the range of correlations around the baseline. By default, range = 1 - max(within.cor) which ensures the matrix is positive semi-definite. Note: max(within.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.

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.

return.groups

When TRUE (default is FALSE), a list is returned with additional entries containing the members of each group.

Value

A symmetric correlation matrix with defined rank and groupings. When pos.def = TRUE, the correlation matrix is guaranteed to be positive (semi)-definite. When return.groups = TRUE, a list is returned with additional entries containing the group members.

Examples

# Simulate and visualise a correlation matrix with 2 groups containing 5 and 10 members,
# correlations of 0.4 within groups and 0 between groups and rank equal to 4
cor_ls <- group_cor_mat(
  n = c(5, 10),
  within.cor = 0.4,
  between.cor = 0,
  rank = 4,
  return.groups = TRUE
)

plot_matrix(
  mat = cor_ls$cor.mat,
  group.df = cor_ls$group.df,
  order = TRUE
)