calculate_backward_probability: Calculate Backward Probability

Description

Function to calculate probability of assigning a set of specific ranks to an specific item given its rank in the consensus ranking

Usage

calculate_backward_probability(
  item_ordering,
  partial_ranking,
  current_ranking,
  remaining_set,
  rho,
  alpha,
  n_items,
  metric = "footrule"
)

Value

backward_auxiliary_ranking_probability A numerical value of creating the previous augmented ranking using the same item ordering used to create the new augmented ranking in calculate_forward_probability function.

Arguments

item_ordering: A vector of integer values to represent the specified queue of which unranked item to assign a rank for the proposed augmented ranking
partial_ranking: An incomplete rank sequence vector of the original observed incomplete ranking which contains NAs
current_ranking: An complete rank sequence vector of the proposed augmented ranking obtained from calculate_forward_probability function
remaining_set: A vector of integer values to represent the elements (ranks) missing from original observed ranking
rho: Numeric vector specifying the consensus ranking
alpha: Numeric value of the scale parameter
n_items: Integer is the number of items in a ranking
metric: A character string specifying the distance metric to use in the Bayesian Mallows Model. Available options are "footrule", "spearman", "cayley", "hamming", "kendall", and "ulam".