preference_index: Preference index from rankings

Description

Computes a preference index for each item in a ranking using Plackett–Luce worth parameters. For each item, the function estimates the probability of being ranked at the top or bottom of the sets in which it appears, and calculates a net winning probability as the difference between top and bottom probabilities.

Usage

preference_index(object)

Value

A gosset_df (data.frame subclass) with columns:

item: Item identifier (name).
n: Number of appearances of the item across sets.
top: Expected top probability (%).
bottom: Expected bottom probability (%).
net_winning: Net winning probability (%).
worth: Normalized worth parameter.

Arguments

object: A rankings object (from PlackettLuce) or a matrix that can be coerced to rankings with as.rankings.

Details

The preference index provides a model-based summary of performance across all ranking sets. Probabilities are derived from the fitted Plackett–Luce worth parameters, normalized to sum to one.

For each item:

top_probs is the expected probability (in percent) of being ranked first in its sets.
bottom_probs is the expected probability (in percent) of being ranked last in its sets.
net_winning_probs is the difference top_probs - bottom_probs, a relative preference score.
worth is the normalized worth parameter from the Plackett–Luce model.

The output is ordered by descending net winning probability, providing a leaderboard-style summary of items.

Examples

Run this code

library(PlackettLuce)

R = matrix(c(1, 2, 0, 0,
             4, 1, 2, 3,
             2, 1, 3, 0,
             1, 2, 3, 0,
             2, 1, 3, 0,
             1, 0, 3, 2),
           nrow = 6, byrow = TRUE)
colnames(R) = c("apple", "banana", "orange", "pear")
R = as.rankings(R)

preference_index(R)