keenersk {raincin}

Keener's method applying a nonlinear skweing function for Rating and Ranking

Description

Calculate ratings and provide rankings using Keener's method applying a nonlinear skweing function, without using Laplace's Rule of Succession, and using Laplace's Rule of Succession

Usage

keenersk(
  jpMat,
  method = "keenersk",
  irreducibility = 0.01,
  ties.method = "average"
)

Arguments

jpMat

a Judge-Presenter matrix, or a User-Movie matrix

method

a character string specifying Keener's method applying a nonlinear skweing function, including "keenersk", "keenerskwolrs"

irreducibility

a non-negative parameter, which is the ratio of the value of each element in the pertubation matrix to the average value in the normalized proportaion matrix.

ties.method

a character string specifying how ties are treated, including "average", "first", "last", "random", "max", "min", from base::rank

Details

1. keenersk: Keener's method with Laplace's Rule of Succession, applying a nonlinear skweing function

2. keenerskwolrs: Keener's method without Laplace's Rule of Succession, applying a nonlinear skweing function

Author(s)

Jiangtao Gou

References

Gou, J. and Wu, S. (2020). A Judging System for Project Showcase: Rating and Ranking with Incomplete Information. Technical Report.

Keener, J. P. (1993). The Perron-Frobenius theorem and the ranking of football teams. SIAM Review 35, 80-93.

Langville, A. N. and Meyer, C. D. (2012). Who's Number 1?: The Science of Rating and Ranking. Princeton University Press.

Examples

library(popdemo)
jpMat <- matrix(data=c(5,4,3,0, 5,5,3,1, 0,0,0,5, 0,0,2,0, 4,0,0,3, 1,0,0,4),
nrow=6,
byrow=TRUE)
result <- keenersk(jpMat,
method = 'keenersk',
irreducibility = 0)
print(result)