Optimize Pseudoposterior for an Ordinal Markov Random Field Model

The function mppe estimates the parameters for the ordinal MRF by optimizing the pseudoposterior with the Newton-Raphson method.

Usage

mppe(
  x,
  interaction_prior = c("Cauchy", "UnitInfo"),
  cauchy_scale = 2.5,
  threshold_alpha = 0.5,
  threshold_beta = 0.5,
  convergence_criterion = sqrt(.Machine$double.eps),
  maximum_iterations = 1000,
  thresholds,
  interactions
)

Arguments

x: A dataframe or matrix with n rows and p columns, containing binary and ordinal variables for n independent observations and p variables in the network. Variables are recoded as non-negative integers (0, 1, ..., m) if not done already. Unobserved categories are collapsed into other categories after recoding. See reformat_data for details.
interaction_prior: The prior distribution for the interaction effects. Currently, two prior densities are implemented: The Unit Information prior (interaction_prior = "UnitInfo") and the Cauchy prior (interaction_prior = "Cauchy"). Defaults to "Cauchy".
cauchy_scale: The scale of the Cauchy prior for interactions. Defaults to 2.5.
threshold_alpha, threshold_beta: The shape parameters of the Beta-prime prior for the thresholds. Default to 0.5.
convergence_criterion: The convergence criterion for the pseudoposterior values in the EM algorithm. Defaults to sqrt(.Machine$double.eps).
maximum_iterations: The maximum number of EM iterations used. Defaults to 1e3. A warning is issued if the procedure has not converged in maximum_iterations iterations.
thresholds: A matrix with p rows and max(m) columns, containing the category thresholds for each node. Used as starting values in the Newton-Raphson procedure. Optional.
interactions: A matrix with p rows and p columns, containing the pairwise association estimates in the off-diagonal elements. Used as starting values in the Newton-Raphson procedure. Optional.

Value

A list containing:

interactions: A matrix with p rows and p columns, containing the maximum pseudoposterior estimates of the pairwise associations in the off-diagonal elements.
thresholds: A matrix with p rows and max(m) columns, containing the maximum pseudoposterior estimates of the category thresholds for each node.
hessian: A square matrix with sum(m) + p(p-1)/2 rows and columns, evaluated at the maximum pseudoposterior estimates. The top-left square contains the thresholds, the bottom-right square the associations (of the form (1,2), (1, 3), ..., (2, 1), ...).

In the case that interaction_prior = "UnitInfo", the list also contains the p by p matrix unit_info, which contains the asymptotic variances that are used to set the unit information prior for the association effects in the bgms function.