R: Optimize Pseudoposterior for an Ordinal Markov Random Field...

mppe {bgms}

R Documentation

Optimize Pseudoposterior for an Ordinal Markov Random Field Model

Description

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.

[Package bgms version 0.1.1 Index]