rrank | R Documentation |
A function for producing ranks randomly, consistent with a specified strength vector
rrank(n = 1, p, pnames=NULL, fill = FALSE, rnames=NULL)
## S3 method for class 'ranktable'
print(x, ...)
rrank_single(p)
rorder_single(p)
n |
Number of observations |
p |
Strength vector |
pnames |
Character vector (“player names”) specifying names of the columns |
rnames |
Character vector (“row names” or “race names”) specifying names of the rows |
fill |
Boolean, with default |
x , ... |
Arguments passed to the print method |
If n=1
, rrank()
returns a vector; if n>1
it returns
a matrix with n
rows, each corresponding to a ranking. The
canonical example is a race in which the probability of competitor
i
coming first is p_i/\sum p_j
, where the
summation is over the competitors who have not already finished.
If, say, the first row of rrank()
is c(2,5,1,3,4)
, then
competitor 2 came first, competitor 5 came second, competitor 1 came
third, and so on.
Note that function rrank()
returns an object of class
ranktable
, which has its own special print method. The column
names appear as “c1, c2, ...
” which is intended to be read
“came first”, “came second”, and so on. The difference
between rank and order can be confusing.
> x <- c(a=3.01, b=1.04, c=1.99, d=4.1) > x a b c d 3.01 1.04 1.99 4.10 > rank(x) a b c d 3 1 2 4 > order(x) [1] 2 3 1 4
In the above, rank()
shows us that element a
of x
(viz 3.01) is the third largest, element b
(viz 1.04) is the
smallest, and so on; order(x)
shows us that the smallest element
x
is x[2]
, the next smallest is x[3]
, and so on.
Thus x[order(x)] == sort(x)
, and rank(x)[order(x)] ==
seq_along(x)
. In the current context we want ranks not orders; we want
to know who came first, who came second, and so on:
R> rrank(2,(4:1)/10) c1 c2 c3 c4 [1,] 2 3 1 4 [2,] 1 3 2 4 R>
In the above, each row is a race; we have four runners and two races. In the first race (the top row), runner number 2 came first, runner 3 came second, runner 1 came third, and so on. In the second race (bottom row), runner 1 came first, etc. Taking the first race as an example:
Rank: who came first? runner 2. Who came second? runner 3.
Who came third? runner 1. Who came fourth? runner 4. Recall that the
Placket-Luce likelihood for a race in which the rank statistic was
2314
(the first race) would be
\frac{p_2}{p_2+p_3+p_1+p_4}\cdot
\frac{p_3}{p_3+p_1+p_4}\cdot
\frac{p_1}{p_1+p_4}\cdot
\frac{p_4}{p_4}
.
Order: where did runner 1 come? third. Where did runner 2
come? first. Where did runner 3 come? second. Where did runner 4
come? fourth. Thus the order statistic would be 3124
.
Function rrank()
is designed for rank_likelihood()
, which
needs rank data, not order data. Vignette
“skating_analysis
” gives another discussion.
Note that function rrank()
returns an object of class
“rrank
”, which has its own print method. This can be
confusing. Further details are given at ranktable.Rd
.
Function rrank_single()
is a low-level helper function:
> p <- c(0.02,0.02,0.9,0.02,0.02,0.02) # competitor 3 the strongest > rank_single(p) [1] 3 2 4 6 4 1
Above, we see from p
that competitor 3 is the strongest, coming
first with 90% probability. And indeed the resulting rank statistic
given by rorder_single()
shows competitor 3 coming first, 2
coming second, and so on. Compare rrank_single()
:
> rorder_single(p) [1] 6 3 1 4 5 2 >
Above we see see from rrank_single(p)
that competitor 1 came
sixth, competitor 2 came third, and competitor 3 came first (as you
might expect, as competitor 3 is the strongest). Note that the R idiom
for rorder_single()
is the same as that used in the
permutations package for inverting a permutation: o[o] <-
seq_along(o)
.
Similar functionality is given by rrace()
, documented at
rhyper3.
Robin K. S. Hankin
ordertrans
,rank_likelihood
,skating
,rhyper3
rrank_single(zipf(9))
ptrue <- (4:1)/10
names(ptrue) <- letters[1:4]
rrank(10,p=ptrue)
H <- rank_likelihood(rrank(40,p=ptrue))
## Following code commented out because they take too long:
# mH <- maxp(H) # should be close to ptrue
# H <- H + rank_likelihood(rrank(30,mH)) # run some more races
# maxp(H) # revised estimate with additional data
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.