ordertable2supp: Translate order tables to support functions

In hyper2: The Hyperdirichlet Distribution, Mark 2

Translate order tables to support functions

Description

\loadmathjax

Wikipedia gives a nice summary in table form of Formula 1 racing results on pages like https://en.wikipedia.org/wiki/2017_Formula_One_World_Championship (at World Drivers' Championship standings) but the data format is commonly used for many sports [see ordertable.Rd] and function ordertable2supp() translates such tables into a hyper2 support function and also a order table.

Both functions interpret zero to mean “Did not finish” (wikipedia usually signifies DNF as a blank).

Usage

ordertable2supp(x, noscore, incomplete=TRUE)
ordervec2supp(d)

Arguments

x	Data frame, see details
d	A named numeric vector giving order; zero entries are interpreted as that competitor coming last (due to, e.g., not finishing)
incomplete	Boolean, with FALSE meaning to insist that each rank 1,2,...,n is present [zero meaning did not place] and default TRUE allowing for gaps. See examples.
noscore	Character vector giving the abbreviations for a non-finishing status such as “did not finish” or “disqualified”. A missing argument is interpreted as c("Ret", "WD", "DNS", "DSQ", "DNP", "NC")

Details

Function ordertable2supp() is intended for use on order tables such as found at https://en.wikipedia.org/wiki/2019_Moto3_season. This is a common format, used for Formula 1, motoGP, and other racing sports. Prepared text versions are available in the package in the inst/ directory, for example inst/motoGP_2019.txt. Use read.table() to create a data frame which can be interpreted by ordertable2supp().

Function ordervec2supp() takes an order vector d and returns the corresponding Plackett-Luce loglikelihood function as a hyper2 object. It requires a named vector; names of the elements are interpreted as names of the players. Use argument pnames to supply the players' names (see the examples).

> x <- c(b=2,c=3,a=1,d=4,e=5) # a: 1st, b: 2nd, c: 3rd etc
> ordervec2supp(x)
log( a * (a + b + c + d + e)^-1 * (a + b + d + e)^-1 * b * (b + d +
e)^-1 * c * (d + e)^-1 * e)

\mjdeqn \frac

aa+b+c+d+e\cdot \fracbb+c+d+e\cdot \fraccc+d+e\cdot \fracdd+e\cdot \fracee omitted

Note carefully the difference between ordervec2supp() and rankvec_likelihood(), which takes a character vector:

>  names(sort(x))
[1] "a" "b" "c" "d" "e"
> rankvec_likelihood(names(sort(x)))
log( a * (a + b + c + d + e)^-1 * b * (b + c + d + e)^-1 * c * (c + d +
e)^-1 * d * (d + e)^-1)
> rankvec_likelihood(names(sort(x))) == ordervec2supp(x)
[1] TRUE
> 

Function order_obs() was used in the integer-indexed paradigm but is obsolete in the name paradigm.

Value

Returns a hyper2 object

Author(s)

Robin K. S. Hankin

See Also

ordertable

Examples

ordertable2supp(soling_table)


a1 <- c(a=2,b=3,c=1,d=5,e=4) # a: 2nd, b: 3rd, c: 1st, d: 5th, e: 4th
a2 <- c(a=1,b=0,c=0,d=2,e=3) # a: 2nd, b: DNF, c: DNF, d: 2nd, e: 3rd
a3 <- c(a=1,b=3,c=2)         # a: 1st, b: 3rd, c: 2nd. NB only a,b,c competed
a4 <- c(a=1,b=3,c=2,d=0,e=0) # a: 1st, b: 3rd, c: 2nd, d,e: DNF


## ordervec2supp() may be added [if the observations are independent]:

H1 <- ordervec2supp(a1) + ordervec2supp(a2) + ordervec2supp(a3)
H2 <- ordervec2supp(a1) + ordervec2supp(a2) + ordervec2supp(a4)

## Thus H1 and H2 are identical except for the third race.  In H1, 'd'
## and 'e' did not compete, but in H2, 'd' and 'e' did not finish (and
## notionally came last):

pmax(H1)
pmax(H2)   # d,e not finishing affects their estimated strength

hyper2 documentation built on Aug. 21, 2022, 1:05 a.m.