JANE (version 2.1.0)

sim_A: Simulate unweighted or weighted networks, with or without noise edges, from latent space cluster models

Description

Simulate an unweighted or weighted network, with or without noise edges, from a \(D\)-dimensional latent space cluster model with \(K\) clusters and \(N\) actors. The squared euclidean distance is used (i.e., \(dist(U_i,U_j)^2\)), where \(U_i\) and \(U_j\) are the respective actor's positions in a \(D\)-dimensional social space.

Usage

sim_A(
  N,
  mus,
  omegas,
  p,
  model = "NDH",
  family = "bernoulli",
  params_LR,
  params_weights = NULL,
  noise_weights_prob = 0,
  mean_noise_weights,
  precision_noise_weights,
  remove_isolates = TRUE
)

Value

A list containing the following components:

A

A sparse adjacency matrix of class 'dgCMatrix' representing the "true" underlying unweighted network with no noise edges.

W

A sparse adjacency matrix of class 'dgCMatrix' representing the unweighted or weighted network, with or without noise. Note, if family = 'bernoulli' and noise_weights_prob = 0, then A = W.

q_prob

A numeric scalar representing the proportion of non-edges in the "true" underlying network converted to noise edges. See 'Details' for how this value is computed.

Z_U

A numeric \(N \times K\) cluster assignment matrix with rows representing the cluster an actor belongs to (i.e., indicated by a value of 1.0).

Z_W

A numeric \(|E| \times 4\) edge weight cluster assignment matrix, with \(|E|\) representing the total number of edges in the network (for undirected networks, only the upper diagonal edges are retained). The first two columns (i.e., 'i' and 'j') contains the specific indices of the edge between the \(i^{th}\) and \(j^{th}\) actors, the third column (i.e., 'weight') contains the specific edge weight, and the fourth column (i.e., 'Z_W') represents a noise-cluster label, where 1 denotes a non-noise edge and 2 denotes a noise edge. Will be NULL if noise_weights_prob = 0.

U

A numeric \(N \times D\) matrix with rows representing an actor's position in a \(D\)-dimensional social space.

mus

The inputted numeric \(K \times D\) mus matrix.

omegas

The inputted numeric \(D \times D \times K\) omegas array.

p

The inputted numeric vector p of length \(K\).

noise_weights_prob

The inputted numeric scalar noise_weights_prob.

mean_noise_weights

The inputted numeric scalar mean_noise_weights. Will be NULL if noise_weights_prob = 0.

precision_noise_weights

The inputted numeric scalar precision_noise_weights. Will be NULL if noise_weights_prob = 0.

model

The inputted model character string.

family

The inputted family character string.

params_LR

The inputted params_LR list. If model != "NDH", will have an additional element "RE" containing a numeric \(N \times 1\) matrix representing the actor specific random sociality effect (i.e., s) OR a \(N \times 2\) matrix representing the actor specific random sender and receiver effects (i.e., s and r, respectively).

params_weights

The inputted params_weights list. If model != "NDH", will have an additional element "RE" containing a numeric \(N \times 1\) matrix representing the actor specific random sociality effect (i.e., s) OR a \(N \times 2\) matrix representing the actor specific random sender and receiver effects (i.e., s and r, respectively).

Arguments

N

An integer specifying the number of actors in the network.

mus

A numeric \(K \times D\) matrix specifying the mean vectors of the \(K\) \(D\)-variate normal distributions for the latent positions.

omegas

A numeric \(D \times D \times K\) array specifying the precision matrices of the \(K\) \(D\)-variate normal distributions for the latent positions.

p

A numeric vector of length \(K\) specifying the mixture weights of the finite multivariate normal mixture distribution for the latent positions.

model

A character string specifying the type of model used to simulate the network:

• 'NDH': generates an undirected network with no degree heterogeneity (or connection strength heterogeneity if working with weighted network)

• 'RS': generates an undirected network with degree heterogeneity (and connection strength heterogeneity if working with weighted network), specifically by including actor specific random sociality effects

• 'RSR': generates a directed network with degree heterogeneity (and connection strength heterogeneity if working with weighted network), specifically by including actor specific random sender and receiver effects

family

A character string specifying the distribution of the edge weights.

• 'bernoulli': generates an unweighted network from a latent space cluster model

• 'lognormal': generates a weighted network by first simulating an unweighted network using a latent space cluster model, and then assigning edge weights based on a log-normal GLM utilizing an identity link

• 'poisson': generates a weighted network by first simulating an unweighted network using a latent space cluster model, and then assigning edge weights based on a zero-truncated Poisson GLM utilizing a log link

params_LR

A list containing the parameters of the logistic regression model to simulate the unweighted network, including:

• 'beta0': a numeric value specifying the intercept parameter for the logistic regression model

• 'precision_R_effects': precision parameters for random degree heterogeneity effects, specific to the logistic regression model:

  • 'NDH': does not apply, can leave as missing

  • 'RS': a numeric value specifying the precision parameter of the normal distribution of the random sociality effect, if missing will generate from a gamma(shape = 1, rate = 1)

  • 'RSR': a numeric matrix specifying the precision matrix of the multivariate normal distribution of the random sender and receiver effects, if missing will generate from a Wishart(df = 3, Sigma = \(I_2\))

params_weights

Only relevant when family %in% c('lognormal', 'poisson'). A list containing the parameters of the GLMs for the edge weights, including:

• 'beta0': a numeric value specifying the intercept parameter for the zero-truncated Poisson or log-normal GLM

• 'precision_R_effects': precision parameters for random connection strength heterogeneity effects, specific to the zero-truncated Poisson or log-normal GLM:

  • 'NDH': does not apply, can leave as missing

  • 'RS': a numeric value specifying the precision parameter of the normal distribution of the random sociality effect, if missing will generate from a gamma(shape = 1, rate = 1)

  • 'RSR': a numeric matrix specifying the precision matrix of the multivariate normal distribution of the random sender and receiver effects, if missing will generate from a Wishart(df = 3, Sigma = \(I_2\))

• 'precision_weights': a positive, non-zero, numeric representing the precision (on the log scale) of the log-normal weight distribution. Only relevant when family = 'lognormal'

noise_weights_prob

A numeric in [0,1] representing the proportion of all edges in the simulated network that are noise edges (default is 0.0).

mean_noise_weights

A numeric representing the mean of the noise weight distribution. Only relevant when family %in% c('lognormal', 'poisson') and noise_weights_prob>0.0. For family = 'poisson' value has to be > 0.0, for family = "lognormal" the mean is on the log scale.

precision_noise_weights

A positive, non-zero, numeric representing the precision (on the log scale) of the log-normal noise weight distribution. Only relevant when family = 'lognormal' and noise_weights_prob>0.0.

remove_isolates

A logical; if TRUE then isolates from the network are removed (default is TRUE).

Details

The returned scalar q_prob represents the proportion of non-edges in the simulated network to be converted to noise edges, computed as \(\frac{p_{noise} \times D_{A}}{(1-D_{A}) \times (1-p_{noise})}\), where \(D_{A}\) is the density of the simulated network without noise and \(p_{noise}\) is the inputted noise_weights_prob.

Examples

# \donttest{

mus <- matrix(c(-1,-1,1,-1,1,1), 
              nrow = 3,
              ncol = 2, 
              byrow = TRUE)
omegas <- array(c(diag(rep(7,2)),
                  diag(rep(7,2)), 
                  diag(rep(7,2))), 
                dim = c(2,2,3))
p <- rep(1/3, 3)
beta0 <- 1.0

# Simulate an undirected, unweighted network, with no noise and no degree heterogeneity
JANE::sim_A(N = 100L, 
            model = "NDH",
            mus = mus, 
            omegas = omegas, 
            p = p, 
            params_LR = list(beta0 = beta0),
            remove_isolates = TRUE)

# Simulate a directed, weighted network, with degree and strength heterogeneity but no noise
JANE::sim_A(N = 100L, 
            model = "RSR",
            family = "lognormal",
            mus = mus, 
            omegas = omegas, 
            p = p, 
            params_LR = list(beta0 = beta0),
            params_weights = list(beta0 = 2,
                                  precision_weights = 1),
            remove_isolates = TRUE)

# Simulate an undirected, weighted network, with noise and degree and strength heterogeneity
JANE::sim_A(N = 100L, 
            model = "RS",
            family = "poisson",
            mus = mus, 
            omegas = omegas, 
            p = p, 
            params_LR = list(beta0 = beta0),
            params_weights = list(beta0 = 2),
            noise_weights_prob = 0.1,
            mean_noise_weights = 1,
            remove_isolates = TRUE)
# }