JANE (version 2.1.0)

summary.JANE: Summarizing JANE fits

Description

S3 summary method for object of class "JANE".

Usage

# S3 method for JANE
summary(object, true_labels = NULL, initial_values = FALSE, ...)

Value

A list of S3 class "summary.JANE" containing the following components (Note: \(N\) is the number of actors in the network, \(K\) is the number of clusters, and \(D\) is the dimension of the latent space):

coefficients

A list containing the estimated coefficients from the logistic regression model (i.e., 'beta_LR') and, if relevant, the estimated coefficients from the zero- truncated Poisson or log-normal GLM (i.e., 'beta_GLM').

U

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

p

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

mus

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

omegas

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

Z_U

A numeric \(N \times K\) matrix with rows containing the estimated conditional probability that an actor belongs to the cluster \(K = k\) for \(k = 1,\ldots,K\).

uncertainty

A numeric vector of length \(N\) containing the uncertainty of the \(i^{th}\) actor's classification, derived as 1 - \(max_k \hat{Z}^{U}_{ik}\).

cluster_labels

A numeric vector of length \(N\) containing the cluster assignment of each actor based on a hard clustering rule of \(\{h | \hat{Z}^{U}_{ih} = max_k \hat{Z}^{U}_{ik}\}\).

Z_W

A numeric \(|E| \times 6\) 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, the fourth column (i.e., 'hat_zij1') contains the estimated conditional probability that the specific edge is a non-noise edge, the fifth column (i.e., 'hat_zij2') contains the estimated conditional probability that the specific edge is a noise edge, and the sixth column (i.e., 'noise_edge_cluster_labels') contains the noise-edge cluster assignment of each edge based on a hard clustering rule of \(\{h | \hat{Z}^{W}_{eh} = max(\hat{Z}^{W}_{e1}, \hat{Z}^{W}_{e2})\}\) for \(e = 1,\ldots,|E|\), where \(\hat{Z}^{W}_{e1}\) and \(\hat{Z}^{W}_{e2}\) are the estimated conditional probabilities that the \(e^{th}\) edge is a non-noise and noise edge, respectively (labels defined as, 1: non-noise edge and 2: noise edge). Will be NULL if noise_weights = FALSE or initial_values = TRUE.

q_prob

A numeric scalar representing the estimated proportion of non-edges in the "true" unobserved network that were converted to noise edges.

precision_weights

A numeric scalar representing the estimated precision (on the log scale) of the log-normal weight distribution. Only relevant for family = 'lognormal' & noise_weights = TRUE.

precision_noise_weights

A numeric scalar representing the estimated precision (on the log scale) of the log-normal noise weight distribution. Only relevant for family = 'lognormal' & noise_weights = TRUE.

IC

Information criteria values of the optimal fit selected, including

• 'BIC_model': BIC computed from logistic regression or Hurdle model component

• 'BIC_mbc': BIC computed from model based clustering component

• 'ICL_mbc': ICL computed from model based clustering component

• 'Total_BIC': sum of 'BIC_model' and 'BIC_mbc'

• 'Total_ICL': sum of 'BIC_model' and 'ICL_mbc'

input_params

A list with the following components:

• model: A character string containing the specific model used (i.e., 'NDH', 'RS', or 'RSR')

• family: A character string containing the specific family used (i.e., 'bernoulli', 'poisson', or 'lognormal')

• noise_weights: A logical; if TRUE then the approach utilizing a Hurdle model accounting for noise edges was utilized

• IC_selection: A character string containing the specific information criteria used to select the optimal fit (i.e., 'BIC_model', 'BIC_mbc', 'ICL_mbc', 'Total_BIC', or 'Total_ICL')

• case_control: A logical; if TRUE then the case/control approach was utilized

• DA_type: A character string containing the specific deterministic annealing approach utilized (i.e., 'none', 'cooling', 'heating', or 'hybrid')

• priors: A list of the prior hyperparameters used. See specify_priors for definitions.

clustering_performance

(only if true_labels is !NULL) A list with the following components:

• CER: A list with two components: (i) misclassified: The indices of the misclassified actors in a minimum error mapping between the cluster labels and the known true cluster labels (i.e., true_labels) and (ii) errorRate: The error rate corresponding to a minimum error mapping between the cluster labels and the known true cluster labels (see classError for details)

• ARI: A numeric value containing the adjusted Rand index comparing the cluster labels and the known true cluster labels (see adjustedRandIndex for details)

• NMI: A numeric value containing the normalized mutual information comparing the cluster labels and the known true cluster labels (see NMI for details)

• confusion_matrix: A numeric table containing the confusion matrix comparing the cluster labels and the known true cluster labels.

Arguments

object

An object of S3 class "JANE", a result of a call to JANE.

true_labels

(optional) A numeric, character, or factor vector of known true cluster labels. Must have the same length as number of actors in the fitted network. Need to account for potential isolates removed (default is NULL).

initial_values

A logical; if TRUE then summarize fit using the starting parameters used in the EM algorithm (default is FALSE, i.e., the results after the EM algorithm is run are summarized).

...

Unused.

Examples

# \donttest{
# Simulate network
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
sim_data <- JANE::sim_A(N = 100L, 
                        model = "NDH",
                        mus = mus, 
                        omegas = omegas, 
                        p = p, 
                        params_LR = list(beta0 = beta0), 
                        remove_isolates = TRUE)
                        
# Run JANE on simulated data
res <- JANE::JANE(A = sim_data$A,
                  D = 2L,
                  K = 3L,
                  initialization = "GNN", 
                  model = "NDH",
                  case_control = FALSE,
                  DA_type = "none")
                  
# Summarize fit 
summary(res)

# Summarize fit and compare to true cluster labels
summary(res, true_labels = apply(sim_data$Z_U, 1, which.max))

# Summarize fit using starting values of EM algorithm
summary(res, initial_values = TRUE)
# }