rPLMIX function

Random sample from a mixture of Plackett-Luce models

Draw a random sample of complete orderings/rankings from a $G$-component mixture of Plackett-Luce models.

rPLMIX(n = 1, K, G, p = t(matrix(1/K, nrow = K, ncol = G)),
  ref_order = t(matrix(1:K, nrow = K, ncol = G)), weights = rep(1/G,
  G), format_output = "ordering")

Arguments

• n: Number of observations to be sampled. Default is 1.
• K: Number of possible items.
• G: Number of mixture components.
• p: Numeric G$$x$$K matrix of component-specific support parameters. Default is equal support parameters (uniform mixture components).
• ref_order: Numeric G$$x$$K matrix of component-specific reference orders. Default is forward orders (identity permutations) in each row, corresponding to Plackett-Luce mixture components (see 'Details').
• weights: Numeric vector of $G$ mixture weights. Default is equal weights.
• format_output: Character string indicating the format of the returned simulated dataset ("ordering" or "ranking"). Default is "ordering".

Returns

If $G=1$, a numeric N$$x$$K matrix of simulated complete sequences. If $G>1$, a list of two named objects:

• comp: Numeric vector of $N$ mixture component memberships.

• sim_data: Numeric N$$x$$K matrix of simulated complete sequences.

Details

Positive values are required for p and weights arguments (normalization is not necessary).

The ref_order argument accommodates for the more general mixture of Extended Plackett-Luce models (EPL), involving the additional reference order parameters (Mollica and Tardella 2014). A permutation of the first $K$ integers can be specified in each row of the ref_order argument to generate a sample from a $G$-component mixture of EPL. Since the Plackett-Luce model is a special instance of the EPL with the reference order equal to the identity permutation $(1,\dots,K)$, the default value of the ref_order argument is forward orders.

Examples

K <- 6
G <- 3
support_par <- matrix(1:(G*K), nrow=G, ncol=K)
weights_par <- c(0.50, 0.25, 0.25)

set.seed(47201)
simulated_data <- rPLMIX(n=5, K=K, G=G, p=support_par, weights=weights_par)
simulated_data$comp
simulated_data$sim_data

Author(s)

Cristina Mollica and Luca Tardella