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Likelihood and log-likelihood evaluation for a Mallows mixture model

Source: R/get_mallows_loglik.R
get_mallows_loglik.Rd

Compute either the likelihood or the log-likelihood value of the Mallows mixture model parameters for a dataset of complete rankings.

Usage

get_mallows_loglik(
  rho,
  alpha,
  weights,
  metric = c("footrule", "spearman", "cayley", "hamming", "kendall", "ulam"),
  rankings,
  observation_frequency = NULL,
  log = TRUE
)

Arguments

rho

A matrix of size n_clusters x n_items whose rows are permutations of the first n_items integers corresponding to the modal rankings of the Mallows mixture components.

alpha

A vector of n_clusters non-negative scalar specifying the scale (precision) parameters of the Mallows mixture components.

weights

A vector of n_clusters non-negative scalars specifying the mixture weights.

metric

Character string specifying the distance measure to use. Available options are "kendall", "cayley", "hamming", "ulam", "footrule", and "spearman".

rankings

A matrix with observed rankings in each row.

observation_frequency

A vector of observation frequencies (weights) to apply to each row in rankings. This can speed up computation if a large number of assessors share the same rank pattern. Defaults to NULL, which means that each row of rankings is multiplied by 1. If provided, observation_frequency must have the same number of elements as there are rows in rankings, and rankings cannot be NULL.

log

A logical; if TRUE, the log-likelihood value is returned, otherwise its exponential. Default is TRUE.

Value

The likelihood or the log-likelihood value corresponding to one or more observed complete rankings under the Mallows mixture rank model with distance specified by the metric argument.

See also

Other rank functions: compute_expected_distance(), compute_observation_frequency(), compute_rank_distance(), create_ranking(), sample_mallows()

Examples

# Simulate a sample from a Mallows model with the Kendall distance

n_items <- 5
mydata <- sample_mallows(
  n_samples = 100,
  rho0 = 1:n_items,
  alpha0 = 10,
  metric = "kendall")

# Compute the likelihood and log-likelihood values under the true model...
get_mallows_loglik(
  rho = rbind(1:n_items, 1:n_items),
  alpha = c(10, 10),
  weights = c(0.5, 0.5),
  metric = "kendall",
  rankings = mydata,
  log = FALSE
  )
#> [1] 1.724993e-68

get_mallows_loglik(
  rho = rbind(1:n_items, 1:n_items),
  alpha = c(10, 10),
  weights = c(0.5, 0.5),
  metric = "kendall",
  rankings = mydata,
  log = TRUE
  )
#> [1] -156.0306

# or equivalently, by using the frequency distribution
freq_distr <- compute_observation_frequency(mydata)
get_mallows_loglik(
  rho = rbind(1:n_items, 1:n_items),
  alpha = c(10, 10),
  weights = c(0.5, 0.5),
  metric = "kendall",
  rankings = freq_distr[, 1:n_items],
  observation_frequency = freq_distr[, n_items + 1],
  log = FALSE
  )
#> [1] 1.458226e-47

get_mallows_loglik(
  rho = rbind(1:n_items, 1:n_items),
  alpha = c(10, 10),
  weights = c(0.5, 0.5),
  metric = "kendall",
  rankings = freq_distr[, 1:n_items],
  observation_frequency = freq_distr[, n_items + 1],
  log = TRUE
  )
#> [1] -107.8443