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Since Rankcluster 0.92, ranks have to be given to the functions in the ranking notation.
The ranking representation \(r=(r_1,...,r_m)\) contains the ranks assigned to the objects, and means that the \(i\)th object is in \(r_i\)th position.
The ordering representation \(o=(o_1,...,o_m)\) means that object \(o_i\) is in the \(i\)th position.
Let us consider the following example to illustrate both notations: a judge, which has to rank three holidays destinations according to its preferences, O1 = Countryside, O2 = Mountain and O3 = Sea, ranks first Sea (O3), second Countryside (O1), and last Mountain (O2).
The ordering result of the judge is o = (3, 1, 2) (the first object is O3, then O1 and O2) whereas the ranking result is r = (2, 3, 1) (O1 is in second position, O2 in third position and O3 in first position).
Since Rankcluster 0.92, ranks have to be given to the functions in the ranking notation.
The parameter must be a matrix with every row corresponding to a rank.
data(words)
head(words$data)
#> A B C D E
#> [1,] 1 3 4 5 2
#> [2,] 1 4 2 3 5
#> [3,] 3 2 5 4 1
#> [4,] 3 2 5 4 1
#> [5,] 4 1 2 5 3
#> [6,] 4 1 5 3 2One row corresponds to one rank. The first column corresponds to the
position on the object A, the second to the position of
object B and so on.
For converting your data from ordering notation to ranking, you can
use the convertRank function. This function works only for
univariate and non-partially missing ranks.
For multivariate ranks, the differents variable are combined by
column and an extra parameter (m) indicates the size of
each dimension.
data(big4)
head(big4$data)
#> A.uefa B.uefa C.uefa D.uefa A.pl B.pl C.pl D.pl
#> 1992-1993 1 2 3 4 1 2 3 4
#> 1993-1994 1 3 2 4 1 3 2 4
#> 1994-1995 1 3 2 4 1 2 4 3
#> 1995-1996 1 3 2 4 1 2 3 4
#> 1996-1997 1 2 3 4 1 3 2 4
#> 1997-1998 1 3 2 4 2 3 1 4
big4$m
#> [1] 4 4The big4 dataset is composed of the rankings (in ranking
notation) of the “Big Four” English football teams (A: Manchester, B:
Liverpool, C: Arsenal, D: Chelsea) to the English Championship (Premier
League) and according to the UEFA coefficients (statistics used in
Europe for ranking and seeding teams in international competitions),
from 1993 to 2013.
Each variable corresponds to the ranking of four elements, so
m = c(4, 4). In the data matrix, the first
four columns correspond to the rankings in Premier League and the four
next to the ranking accoding to the uefa coefficient.
Rankcluster manages partial missing ranks. Missing positions are
denoted by 0.
For example 5 0 1 2 0 indicates that the position of the
second and fifth objects are unknown.
Rankcluster manages tied positions in ranks. Tied position are replaced by the lowest position they share.
For example, assume there are five objects to rank. If the output
rank in ranking notation is 4 3 4 1 1, the 1
for both the objects number 4 and 5 indicates that either object 4 is in
first position and object 5 in second or object 5 in second position and
object 4 in first. Then the object number 2 is in third position, then
objects 1 and 3 are in fourth and fifth or fifth and fourth.
These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.