Draw Samples from the Plackett-Luce Model

This function draws samples from the Plackett-Luce model, using Algorithm 2.1, "Efficient Sampling from Plackett-Luce," in Xia (2019), page 20, Section 2.2.3 Sampling from Random Utility Models. The name rpluce is a convention that follows random generations of numbers from statistical distributions such as rnorm or rmultinom.

Usage

rpluce(n, t, prob, choices = NULL, seed = NULL)

Arguments

n

The total number of samples to draw.

t

The number of items or alternatives to choose from.

prob

A vector of choice probabilities.

choices

A vector of choices to be ranked.

seed

An optional seed for the random number generator.

Value

A data frame of rankings of t items for n assessors.

Details

Input: A parameter \(\overrightarrow{\gamma} = (\gamma_1, \cdots, \gamma_m)\) of Plackett-Luce.

Output: A ranking \(R \in \mathcal{L}(\mathcal{A})\) from \(pi_{\overrightarrow{\gamma}} ( \cdot )\) under Plackett–Luce.
1: Let \(R = \emptyset\) and \(A = \mathcal{A}\).
2: for \(t = 1\) to \(m\) do
3: Choose an alternative \(a_{i_t}\) from \(A\) with probability proportional to \(\gamma_{i_t}\).
4: \(R \leftarrow R \succ a_{i_t}\) and \(A \leftarrow A \ \{ a_{i_t} \}\).
5: end for
6: return \(R\).

Examples

rpluce(n = 10, t = 3, prob = c(0.5, 0.3, 0.2), seed = 123)
#>    1st 2nd 3rd
#> 1    c   a   b
#> 2    a   c   b
#> 3    b   c   a
#> 4    a   b   c
#> 5    a   b   c
#> 6    a   b   c
#> 7    c   a   b
#> 8    b   c   a
#> 9    a   c   b
#> 10   a   c   b