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.
This short document discusses a dataset first presented by @hankin2010,
although here only the first 52 observations are used. A
volleyball set is a Bernoulli trial between two disjoint subsets
of the players. The two subsets are denoted (after the game) as the
winners and the losers: these are denoted by 1
and 0
respectively.
volleyball_table <- as.matrix(read.table("volleyball.txt",header=TRUE)) nrow(volleyball_table) head(volleyball_table)
Each row of volleyball_table
is a set. Thus the first line shows a
game between a team comprising p1
, p4
, and p8
against a team
comprising p5
and p6
. Player p9
did not play; team p1 p4 p8
won. We may use function volley()
to convert this to a likelihood
function:
volleyball <- volley(volleyball_table) (volleyball_maxp <- maxp(volleyball))
The original synthetic dataset was prepared using Zipf's law for the players' strengths, so we may test the hypothesis that this is the case; $H_0\colon p_i\propto i^{-1}$:
zipf <- function(n){jj <- 1/(1:n); jj/sum(jj)} zipf(9) (null_support <- loglik(indep(zipf(9)),volleyball)) (alternative_support <- loglik(indep(volleyball_maxp),volleyball)) (Lambda <- 2*(alternative_support-null_support)) pchisq(Lambda,df=8,lower.tail=FALSE)
somewhat disappointingly rejecting the null with a $p$-value of about 4\% (and indeed--just---with a two units of support per degree of freedom criterion). However, it is not clear to me the extent to which Wilks's theorem is applicable here [Wilks is an asymptotic result; recall that we have only 52 observations here], nor whether the support criterion is appropriate with 8 degrees of freedom.
Following lines create volleyball.rda
, residing in the data/
directory of the package.
save(volleyball_table,volleyball_maxp,volleyball,file="volleyball.rda")
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