compare_ranks function

Count occurrences of pairs in rankings

Counts the number of concordant, discordant and (left/right) ties between two rankings.

compare_ranks(x, y)

Arguments

• x: A numeric vector.
• y: A numeric vector with the same length as x.

Returns

A list containing - concordant: number of concordant pairs: x[i] > x[j] and y[i] > y[j]

• discordant: number of discordant pairs: x[i] > x[j] and y[i] < y[j]

• ties: number of tied pairs: x[i] == x[j] and y[i] == y[j]

• left: number of left ties: x[i] == x[j] and y[i] != y[j]

• right: number of right ties: x[i] != x[j] and y[i] == y[j]

Details

Explicitly calculating the number of occurring cases is more robust than using correlation indices as given in the cor function. Especially left and right ties can significantly alter correlations.

Examples

library(igraph)
tg <- threshold_graph(100, 0.2)
compare_ranks(degree(tg), closeness(tg)) # only concordant pairs
compare_ranks(degree(tg), betweenness(tg)) # no discordant pairs
## Rank Correlation
cor(degree(tg), closeness(tg), method = "kendall") # 1
cor(degree(tg), betweenness(tg), method = "kendall") # not 1, although no discordant pairs

Author(s)

David Schoch