Paired Comparisons of Chocolate Pudding
This is an example dataset from Davidson 1970 comprising paired comparisons of chocolate pudding, with six brands in total. The responses include tied outcomes, i.e. no preference.
pudding
A data frame with 15 records and 6 variables:
iThe first brand in the comparison.
jThe second brand in the comparison.
r_ijThe frequency of paired comparisons of brand i and brand j.
w_ijThe frequency of preferences for i over j.
w_jiThe frequency of preferences for j over i.
t_ijThe frequency of no preference between i and j.
Davidson, R. R. (1970). On extending the Bradley-Terry model to accommodate ties in paired comparison experiments. Journal of the American Statistical Association, 65, 317–328.
# create orderings for each set of paired comparisons
# wins for brand i and wins for brand j
i_wins <- data.frame(Winner = pudding$i, Loser = pudding$j)
j_wins <- data.frame(Winner = pudding$j, Loser = pudding$i)
# ties: use an array list (easier with R >= 3.6.0)
if (getRversion() < "3.6.0"){
n <- nrow(pudding)
ties <- data.frame(Winner = array(split(pudding[c("i", "j")], 1:n), n),
Loser = rep(NA, 15))
} else {
ties <- data.frame(Winner = asplit(pudding[c("i", "j")], 1),
Loser = rep(NA, 15))
}
head(ties, 2)
# convert to rankings
R <- as.rankings(rbind(i_wins, j_wins, ties),
input = "orderings")
head(R, 2)
tail(R, 2)
# define weights as frequencies of each ranking
w <- unlist(pudding[c("w_ij", "w_ji", "t_ij")])
# fit Plackett-Luce model: limit iterations to match paper
mod <- PlackettLuce(R, npseudo = 0, weights = w, maxit = 7)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.