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.

## Format

A data frame with 15 records and 6 variables:

`i`

The first brand in the comparison.

`j`

The second brand in the comparison.

`r_ij`

The frequency of paired comparisons of brand i and brand j.

`w_ij`

The frequency of preferences for i over j.

`w_ji`

The frequency of preferences for j over i.

`t_ij`

The frequency of no preference between i and j.

## References

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.

## Examples

```
# 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)
#> Winner Loser
#> 1 1, 2 NA
#> 2 1, 3 NA
# convert to rankings
R <- as.rankings(rbind(i_wins, j_wins, ties),
input = "orderings")
head(R, 2)
#> [1] "1 > 2" "1 > 3"
tail(R, 2)
#> [1] "4 = 6" "5 = 6"
# 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)
#> Warning: Iterations have not converged.
```