In RobinHankin/hyper2: The Hyperdirichlet Distribution, Mark 2

set.seed(0)
knitr::opts_chunk$set(echo = TRUE)
library("hyper2")
library("magrittr")
options("digits" = 5)

knitr::includme_graphics(system.file("help/figures/hyper2.png", package = "hyper2"))

To cite the hyper2 package in publications, please use @hankin2017_rmd. Soling is a type of boat raced in the 2000 Summer Olympics. Here I analyse race data taken from wikipedia using a Plackett-Luce extension of the Bradley-Terry model.

soling_table <- read.table("soling.txt")
soling_table

Thus we see, reading column 1, that in race 1, norway came fifth, nz third, netherlands first, and so on. We can present this information in a rank table format:

ordertable_to_ranktable(soling_table)

and also convert it to a likelihood function:

soling <- ordertable2supp(soling_table)
head(soling)

We can also consider observations from the round robins and quarter finals:

soling_rr1 <- read.table("soling_rr1.txt")
soling_rr2 <- read.table("soling_rr2.txt")
soling_qf  <- read.table("soling_qf.txt" )
soling_rr1

Thus, for example, taking soling_rr1[1,2] == TRUE we see that Germany beat Sweden in round robin 1. To incorporate this information we need a little bespoke function:

rr <- function(H,M){
    for(i in seq_len(nrow(M)-1)){
        for(j in (i+1):ncol(M)){
            if(M[i,j]){
                winner <- rownames(M)[i]
                loser  <- rownames(M)[j]
            } else {
                winner <- rownames(M)[j]
                loser <-  rownames(M)[i]
            }
            H[winner] %<>% inc
            H[c(winner,loser)] %<>% dec
        }
    }
    return(H)
}

We can see the effect on the evaluate of incorporating the additional observations into the Plackett-Luce likelihoods:

H <- soling  # before new information
soling_maxp <- maxp(H) 
H %<>% rr(soling_rr1)
H %<>% rr(soling_rr2)
H %<>% rr(soling_qf)
soling_after <- H # after new information
soling_after_maxp <- maxp(soling_after)
par(pty="s")
plot(soling_maxp,soling_after_maxp,asp=1,pch=16,xlim=c(0,0.3),ylim=c(0,0.3))
abline(0,1)

Figure \@ref(fig:showdiff) shows a modest change. We might ask whether the additional observations are consistent with the original Placket-Luce likelihood:

(soling_diff <- soling_after - soling)

So soling_diff is the difference between H--- which is soling plus the observations from the roundrobins and quarter finals---and soling without the extra information. In other words, the information in the roundrobins and quarter finals.

equalp.test(soling_diff)

Package dataset {-}

Following lines create soling.rda, residing in the data/ directory of the package.

save(soling,soling_after, soling_maxp,soling_after_maxp,soling_table,
     soling_rr1, soling_rr2, soling_qf,
  file="soling.rda")

References {-}

RobinHankin/hyper2 documentation built on April 21, 2024, 11:38 a.m.