ggol: Order statistics

Description

Various functions for calculating the likelihood function for order statistics

Usage

ggrl(H, ...)
general_grouped_rank_likelihood(H, ...)
goodbad(winners,losers)
elimination(all_players)
rank_likelihood(M,times=1)
rankvec_likelihood(v)
race(v)

Arguments

H: Object of class hyper2
...: Numeric or character vectors specifying groups of players with equal rank, with higher-ranking groups coming earlier in the argument list
all_players,winners,losers: Numeric or character vectors specifying competitors. See details
M: In function rank_likelihood(), a matrix with each row corresponding to a race (or judge). The columns correspond to the finishing order; thus a=M[i,j] means that competitor a finished in place j in race i
times: Vector specifying the number of times each row is observed
v: A character vector specifying ranks. Thus c("b","c","a") means that b came first, c second, and a third

Author

Robin K. S. Hankin

Details

These functions are designed to return likelihood functions, in the form of lists of hyper2() objects, for typical order statistics such as the results of rowing heats or MasterChef tournaments.

Function ggrl() is an easily-typed alias for general_grouped_rank_likelihood().

Function goodbad() is a convenience function for ggrl() in which a bunch of contestants is judged. It returns a likelihood function for the observation that the members of one subset were better than those of another. Thus goodbad(letters[1:3],letters[4:5]) corresponds to the observation that d and e were put into an elimination trial (and abc were not).

Function elimination() gives a likelihood function for situations where the weakest player is identified at each stage and subsequently eliminated from the competition. It is intended for situations like the Great British Bake-off and Masterchef in which the observation is which player was chosen to leave the show. In this function, argument all_players is sensitive to order, unlike choose_winners() and choose_losers() (an integer n is interpreted as letters[seq_len(n)]). Element i of all_players is the \(i^\mathrm{th}\) player to be eliminated. Thus the first element of all_players is the first player to be eliminated (and would be expected to have the lowest strength). The final element of all_players is the last player to be eliminated (or alternatively the only player not to be eliminated).

Function rank_likelihood() takes a matrix M with rows corresponding to a judge (or race); column names are interpreted as competitor names. A named vector is coerced to a one-row matrix. Each row of M is an order statistic: thus c(3,4,2,1) means that person 3 came first, person 4 came second, person 2 came third and person 1 came last. Note that in data frames like F1_table_2017, each column is a race.

Function rankvec_likelihood() takes a character vector of competitors with the order of elements corresponding to the finishing order; a Plackett-Luce likelihood function is returned. Thus v=c("d","b","c","a") corresponds to d coming first, b second, c third, and a fourth. Function race() is an arguably more memorable synonym.

An example of race() is given in inst/rowing.Rmd, and examples of ggrl() are given in inst/loser.Rmd and inst/masterchef.Rmd.

Examples

Run this code


W <- hyper2(pnames=letters[1:5])
W1 <- ggrl(W, 'a', letters[2:4],'e')  # 6-element list
W2 <- ggrl(W, 'b', letters[3:5],'a')  # 6-element list

like_single_list(equalp(W1),W1)
like_series(equalp(W1),list(W1,W2))

if(FALSE){  # takes too long
# run 10 races:
r1 <- rrank(10,p=(7:1)/28)
colnames(r1) <- letters[1:7]

# Likelihood function for r1:
W <- rank_likelihood(r1)

H <- hyper2()
for(i in 1:20){
  H <- H + race(sample(letters[1:5],sample(3,1),replace=FALSE))
}
equalp.test(H) # should not be significant (null is true)

H1 <- hyper2(pnames=letters[1:5])
H2 <- choose_losers(H1,letters[1:4],letters[1:2])   # {a,b} vs {c,d}; {a,b} lost
maxplist(H2,control=list(maxit=1))  # control set to save time
}