Implements the Luce's Choice Axiom to calculate pairwise probabilities in a set of choice probabilities. The Luce's Choice Axiom states that the probability of selecting one item over another from a pool of many items is not affected by the presence or absence of other items in the pool.
pairwise_probs(object, relative.probs = TRUE, ...)a named numeric vector with probabilities
logical, TRUE to return matrix with relative probs (prob - 0.5), otherwise true values are returned
additional arguments passed to methods
a matrix with pairwise probabilities
library("PlackettLuce")
library("ggplot2")
R = matrix(c(1, 2, 3, 0,
4, 1, 2, 3,
2, 1, 3, 4,
1, 2, 3, 0,
2, 1, 3, 0,
1, 0, 3, 2), nrow = 6, byrow = TRUE)
colnames(R) = c("apple", "banana", "grape", "pear")
mod = PlackettLuce(R)
coefs = coefficients(mod, log = FALSE)
pair_worth = pairwise_probs(coefs)
pair_worth
# plot the results
lvls = dimnames(pair_worth)[[1]]
pair_dat = data.frame(player1 = rep(lvls, times = length(lvls)),
player2 = rep(lvls, each = length(lvls)),
worth = as.vector(pair_worth))
pair_dat
pair_dat$player1 = factor(pair_dat$player1, levels = lvls)
pair_dat$player2 = factor(pair_dat$player2, levels = rev(lvls))
pair_dat$worth = round(pair_dat$worth, 2)
ggplot(pair_dat,
aes(x = player2,
y = player1,
fill = worth,
label = worth)) +
geom_tile(show.legend = FALSE) +
geom_text() +
scale_fill_gradient2(low = "#b2182b",
high = "#2166ac",
na.value = "white") +
scale_x_discrete(position = "top") +
theme_bw() +
theme(axis.text = element_text(color = "grey10"),
strip.text.x = element_text(color = "grey10"),
axis.text.x = element_text(angle = 90, hjust = 0),
panel.grid = element_blank()) +
labs(x = "",
y = "",
fill = "")