In RobinHankin/hyper2: The Hyperdirichlet Distribution, Mark 2

set.seed(0)
options(width = 120)
knitr::opts_chunk$set(echo = TRUE)
library("hyper2")
library("magrittr")

The 2019 FIM motoGP world championship

Here I analyse a series of Grand Prix motorcycling race results using the hyper2 package which implements the Plackett-Luce likelihood function. Consider the following dataset, taken from Wikipedia:

moto_table <- read.table("motoGP_2019.txt")
head(moto_table)

Each row is a driver (rider?) and each column (after the first) a venue. Taking the first row we see that Marquez came second in Qatar (QAT), first in Argentina, retired in Austin, and so on. In the first column, we see the result from Qatar (QAT) in which Marquez came second, Dovizioso first, Vinales third, and so on. Notation used also includes six different classes of no-score such as "Ret" for retired, "WD" for withdrawn, and so on. I now use package function ordertable2supp(), that translates data of this type into a log-likelihood. In the package, object moto is the corresponding Plackett-Luce likelihood function; we drop the final column which is the points scored by each rider.

moto <- ordertable2supp(moto_table[,-ncol(moto_table)])
head(moto)

Above, we see a small part of the Placket-Luce likelihood function for the 2019 results. We can find the maximum likelihood estimator by using the maxp() function:

moto_maxp <- maxp(moto)
moto_maxp

dotchart(moto_maxp,pch=16)

pie(moto_maxp)

In figures \@ref(fig:dotchartmoto) and \@ref(fig:piechartmoto), note the dominance of Marquez. It is sometimes preferable to plot the estimated strengths on a log scale:

dotchart(log10(moto_maxp),pch=16)

(in figure \@ref(fig:dotchartlogmoto ) observe that the bottom-ranked player, Lecuona, has a ML strength of zero but the estimate is slightly positive for numerical reasons).

Package dataset {-}

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

save(moto,moto_table,moto_maxp,file="moto.rda")

RobinHankin/hyper2 documentation built on May 6, 2024, 4:25 p.m.