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Simulate data from multiple Gaussian graphical models

simulate_multiggm.Rd

Generates K precision matrices with controlled shared structure and draws multivariate normal data from each. Follows the simulation design in Peterson et al. (2015, JASA) Section 5.1. Group 1 uses the base graph directly; groups 2 through K perturb the base graph by randomly flipping edges with probability perturb_prob.

Usage

simulate_multiggm(
  K = 2,
  p = 20,
  n = 100,
  graph_type = c("band", "random", "hub"),
  edge_prob = 0.1,
  perturb_prob = 0.1,
  signal = c(0.3, 0.6),
  seed = NULL
)

Arguments

K

Integer; number of sample groups. Default 2.

p

Integer; number of variables (nodes). Default 20.

n

Integer (scalar or length-K vector); sample size per group. If scalar, all groups have the same sample size. Default 100.

graph_type

Character; type of base graph:

  • band: AR(2)-like banded structure: edges between all nodes within distance 2 (i.e., (i, i+1) and (i, i+2)). Produces approximately 2p - 3 edges. Matches Peterson et al. Section 5.1.

  • random: Erdos-Renyi random graph where each edge is included independently with probability edge_prob.

  • hub: Star/hub graph with floor(p/5) hub nodes, each connected to approximately 40\

edge_prob

Numeric; probability of each edge in the base graph (used only for graph_type = "random"). Default 0.1.

perturb_prob

Numeric; for groups k = 2, ..., K, the probability that each edge is flipped (added if absent, removed if present) relative to the base graph. Controls how different the groups are. Set to 0 for identical graphs. Default 0.1.

signal

Numeric vector of length 2; magnitude range c(lo, hi) for off-diagonal precision entries where edges exist. Signs are chosen randomly. Default c(0.3, 0.6).

seed

Optional integer random seed for reproducibility.

Value

A list with components:

  • Omega_list: List of K true precision matrices (each p x p, symmetric positive definite). Off-diagonal entries are non-zero only where edges exist, after row-normalization to ensure positive definiteness.

  • adj_list: List of K true binary adjacency matrices (each p x p, 0/1). adj_list[[k]][i,j] = 1 if edge (i,j) exists in group k.

  • data_list: List of K data matrices (each n_k x p), drawn from \(N(0, \Omega_k^{-1})\) and column-centered.

  • S_list: List of K cross-product matrices (each p x p), where S_list[[k]] = t(X_k) %*% X_k after centering.

  • n_vec: Integer vector of length K with sample sizes.

  • K: Integer; number of groups.

  • p: Integer; number of variables.

See also

multiggm_mcmc()

Examples

sim <- simulate_multiggm(K = 2, p = 10, n = 100, seed = 42)
str(sim, max.level = 1)
#> List of 7
#>  $ Omega_list:List of 2
#>  $ adj_list  :List of 2
#>  $ data_list :List of 2
#>  $ S_list    :List of 2
#>  $ n_vec     : int [1:2] 100 100
#>  $ K         : num 2
#>  $ p         : num 10

# Check true edge counts
sapply(sim$adj_list, function(a) sum(a[upper.tri(a)]))
#> [1] 17 15