exact_loglik function

Vectorized calculation of ERGM exact log-likelihood

This function can be compared to ergm::ergm.exact with the statistics not centered at x, the vector of observed statistics.

exact_loglik(x, params, ..., as_prob = FALSE)

## Default S3 method:
exact_loglik(
  x,
  params,
  stats_weights,
  stats_statmat,
  target_offset = double(nrow(x)),
  stats_offset = lapply(stats_weights, function(i) double(length(i))),
  ...,
  as_prob = FALSE
)

exact_gradient(x, params, ...)

## Default S3 method:
exact_gradient(
  x,
  params,
  stats_weights,
  stats_statmat,
  target_offset = double(nrow(x)),
  stats_offset = lapply(stats_weights, function(i) double(length(i))),
  ...
)

exact_hessian(
  params,
  stats_weights,
  stats_statmat,
  stats_offset = lapply(stats_weights, function(i) double(length(i)))
)

Arguments

• x: Matrix. Observed statistics
• params: Numeric vector. Parameter values of the model.
• ...: Arguments passed to the default methods.
• as_prob: Logical scalar. When TRUE, the function returns probabilities instead of log-likelihoods.
• stats_weights: Either an integer vector or a list of integer vectors (see exact_loglik ).
• stats_statmat: Either a matrix or a list of matrices (see exact_loglik ).
• target_offset: Numeric vector of length nrow(target_stats).
• stats_offset: List of numeric vectors, each of length equal to the lengths of vectors in stats_weights (see details).

Sufficient statistics

One of the most important components of ergmito is calculating the full support of the model's sufficient statistics. Right now, the package uses the function ergm::ergm.allstats which returns a list of two objects:

• weights: An integer vector of counts.
• statmat: A numeric matrix with the rows as unique vectors of sufficient statistics.

Since ergmito can vectorize operations, in order to specify weights and statistics matrices for each network in the model, the user needs to pass two lists stats_weights and stats_statmat. While both lists have to have the same length (since its elements are matched), this needs not to be the case with the networks, as the user can specify a single set of weights and statistics that will be recycled (smartly).

In the case of offset terms, these can be passed directly via target_offset

and stats_offset. The first is a numeric vector of length equal to the number of networks in the model. The later is a list of vectors that is matched against stats_weights, so each of it's elements must be a numeric vector of the same length that in the list of weights. By default the offset terms are set to equal zero.

Examples

data(fivenets)
ans <- ergmito(fivenets ~ edges + nodematch("female"))

# This computes the likelihood for all the networks independently
with(ans$formulae, {
  exact_loglik(
    x      = target_stats,
    params = coef(ans),
    stats_weights = stats_weights,
    stats_statmat = stats_statmat
  )
})

# This should be close to zero
with(ans$formulae, {
  exact_gradient(
    x      = target_stats,
    params = coef(ans),
    stats_weights = stats_weights,
    stats_statmat = stats_statmat
  )
})

# Finally, the hessian
with(ans$formulae, {
  exact_hessian(
    params = coef(ans),
    stats_weights = stats_weights,
    stats_statmat = stats_statmat
  )
})