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

To cite the hyper2 package in publications, please use @hankin2017_rmd. Function keep_flawed() can be confusing. Originally, the package included a function keep() but this used flawed logic, hence the name of its replacement. Here is a tiny example that should clarify things. We will use a subset of skating_table:

jj <- skating_table[1:3,1:6]
rownames(jj) <- letters[1:3]
jj

Above, rows of object jj correspond to competitors and columns to judges. Object jj does not function as a rank table because the entries are not sequential (judge J2, for example, has no second-ranked competitor).

We could convert explicitly:

a <- apply(jj,2,rank)
a

So each column is a permutation of 123. So, for example judge 1 ranked a first, b third, and c second. We can coerce to a hyper2 object with ordertable2supp():

OT <- ordertable2supp(a)
OT

(function ordertable2supp() does this automatically, so ordertable2supp(jj) would have given the same result). Now suppose we are interested only in the first two competitors, a and b, which are competitors 1 and 2.

keep_flawed(OT, c("a","b"))

Above, function keep_flawed() has effectively taken OT, set c=0, and then discarded the c^5 term. This process, while natural from a computing perspective, has the effect of replacing (a+c)^-4 with a^-4, which has no natural probabilistic interpretation: we are ignoring c's victories but nevertheless interpreting the joint strength term on the denominator [viz a+c] as a loss for a.

What happens if we keep only a?

keep_flawed(OT,"a")

the above support function is meaningless (?) as, having set b=0 we then treat a+b as simply a which sort of makes sense until we realise that (a+b)^-6 reduces to a^-6. It is as though a has wins only 3 trials out of 8, against a competitor of known zero strength whose (impossible) wins we ignore. Perhaps this has a natural interpretation in probability, but if so I don't see it.

Conclusions{-}

It does not seem possible to take a hyper2 object and discard certain players. It seems that the only way to discard players is to work with the original observation, discard players in the dataset according to some criterion, and coerce to a likelihood function.