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Specify starting values for EM algorithm

Source: R/specify_initial_values.R
specify_initial_values.Rd

A function that allows the user to specify starting values for the EM algorithm in a structure accepted by JANE.

Usage

specify_initial_values(
  A,
  D,
  K,
  model,
  family = "bernoulli",
  noise_weights = FALSE,
  n_interior_knots = NULL,
  U,
  omegas,
  mus,
  p,
  Z,
  beta,
  beta2,
  precision_weights,
  precision_noise_weights
)

Arguments

A

A square matrix or sparse matrix of class 'dgCMatrix' representing the adjacency matrix of the network of interest.

D

An integer specifying the dimension of the latent positions.

K

An integer specifying the total number of clusters.

model

A character string specifying the model:

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

  • 'RS': undirected network with degree heterogeneity (and connection strength heterogeneity if working with weighted network)

  • 'RSR': directed network with degree heterogeneity (and connection strength heterogeneity if working with weighted network)

family

A character string specifying the distribution of the edge weights.

  • 'bernoulli': for unweighted networks; utilizes a Bernoulli distribution with a logit link (default)

  • 'lognormal': for weighted networks with positive, non-zero, continuous edge weights; utilizes a log-normal distribution with an identity link

  • 'poisson': for weighted networks with edge weights representing non-zero counts; utilizes a zero-truncated Poisson distribution with a log link

noise_weights

A logical; if TRUE then a Hurdle model is used to account for noise weights, if FALSE simply utilizes the supplied network (converted to an unweighted binary network if a weighted network is supplied, i.e., (A > 0.0)*1.0) and fits a latent space cluster model (default is FALSE).

n_interior_knots

An integer specifying the number of interior knots used in fitting a natural cubic spline for degree heterogeneity (and connection strength heterogeneity if working with weighted network) models (i.e., 'RS' and 'RSR' only; default is NULL).

U

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

omegas

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

mus

A numeric \(K \times D\) matrix specifying the mean vectors 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.

Z

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

beta

A numeric vector specifying the regression coefficients for the logistic regression model. Specifically, a vector of length
1 + (model =="RS")*(n_interior_knots + 1) +
(model =="RSR")*2*(n_interior_knots + 1).

beta2

A numeric vector specifying the regression coefficients for the zero-truncated Poisson or log-normal GLM. Specifically, a vector of length
1 + (model =="RS")*(n_interior_knots + 1) +
(model =="RSR")*2*(n_interior_knots + 1).
Only relevant when noise_weights = TRUE & family != 'bernoulli'.

precision_weights

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

precision_noise_weights

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

Value

A list of S3 class "JANE.initial_values" representing starting values for the EM algorithm, in a structure accepted by JANE.

Details

To match JANE, this function will remove isolates from the adjacency matrix A and determine the total number of actors after excluding isolates. If this is not done, errors with respect to incorrect dimensions in the starting values will be generated when executing JANE.

Similarly to match JANE, if an unsymmetric adjacency matrix A is supplied for model %in% c('NDH', 'RS') the user will be asked if they would like to proceed with converting A to a symmetric matrix (i.e., A <- 1.0 * ( (A + t(A)) > 0.0 )). Additionally, if a weighted network is supplied and noise_weights = FALSE, then the network will be converted to an unweighted binary network (i.e., (A > 0.0)*1.0).

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
sim_data <- JANE::sim_A(N = 100L, 
                        model = "RSR",
                        mus = mus, 
                        omegas = omegas, 
                        p = p, 
                        params_LR = list(beta0 = beta0),
                        remove_isolates = TRUE)

# Specify starting values
D <- 3L
K <- 5L
N <- nrow(sim_data$A)
n_interior_knots <- 5L

U <- matrix(stats::rnorm(N*D), nrow = N, ncol = D)
omegas <- stats::rWishart(n = K, df = D+1, Sigma = diag(D))
mus <- matrix(stats::rnorm(K*D), nrow = K, ncol = D)
p <- extraDistr::rdirichlet(n = 1, rep(3,K))[1,]
Z <-  extraDistr::rdirichlet(n = N, alpha = rep(1, K))
beta <- stats::rnorm(n = 1 + 2*(1 + n_interior_knots))

my_starting_values <- JANE::specify_initial_values(A = sim_data$A,
                                                   D = D,
                                                   K = K,
                                                   model = "RSR",
                                                   n_interior_knots = n_interior_knots,
                                                   U = U,
                                                   omegas = omegas, 
                                                   mus = mus, 
                                                   p = p, 
                                                   Z = Z,
                                                   beta = beta)         

# Run JANE using my_starting_values (no need to specify D and K as function will 
# determine those values from my_starting_values)
res <- JANE::JANE(A = sim_data$A,
                  initialization = my_starting_values,
                  model = "RSR")
# }