Count occurrences of pairs in rankings — compare

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

Usage

compare_ranks(x, y)

Arguments

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

Value

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.

Author

David Schoch

Examples

library(igraph)
tg <- threshold_graph(100, 0.2)
compare_ranks(degree(tg), closeness(tg)) # only concordant pairs
#> $concordant
#> [1] 4708
#> 
#> $discordant
#> [1] 0
#> 
#> $ties
#> [1] 242
#> 
#> $left
#> [1] 0
#> 
#> $right
#> [1] 0
#> 
compare_ranks(degree(tg), betweenness(tg)) # no discordant pairs
#> $concordant
#> [1] 1865
#> 
#> $discordant
#> [1] 0
#> 
#> $ties
#> [1] 242
#> 
#> $left
#> [1] 0
#> 
#> $right
#> [1] 2843
#> 
## Rank Correlation
cor(degree(tg), closeness(tg), method = "kendall") # 1
#> [1] 1
cor(degree(tg), betweenness(tg), method = "kendall") # not 1, although no discordant pairs
#> [1] 0.629392