BBTm.with.formula {speedyBBT}R Documentation

Bayesian Bradley–Terry model with comparison and player specific effect and formula

Description

This function fits the Bradley-Terry model with comparison and player specific effects. Each comparison can be assigned a real value to allow for a specific effect for the comparison, such as bias, ordering or home/away effect. The value of this effect is denoted kappa. The player specific effects are described through a formula and data.frame containing the value. The function places a normal prior distribution on both kappa and the player specific parameters beta.

Usage

BBTm.with.formula(
  outcome,
  player1,
  player2,
  formula = NULL,
  data = NULL,
  advantage = NULL,
  kappa.initial = NULL,
  kappa.var = NULL,
  player.prior.var = NULL,
  beta.initial = NULL,
  n.iter = 1000,
  hyperparameter = TRUE,
  chi = 0.01,
  psi = 0.01
)

Arguments

outcome

vector of outcomes. 1 if player2 is the winner, 0 if player1 is the winner

player1

vector of first players.

player2

vector of second players.

formula

formula with no left-hand-side specifying the player specific effects

data

data.frame with a row corresponding to each player and column corresponding to each covariate.

advantage

(optional) a vector with the value of the comparisons specific effect for each comparison

kappa.initial

(optional) an initial value for the comparison specific value kappa

kappa.var

(optional) the prior variance of the he comparison specific value kappa

player.prior.var

(optional) matrix specifying the prior covariance of the player correlation parameters

beta.initial

(optional) vector containing the values of the player specific parameters for the first MCMC iteration

n.iter

number of MCMC samples to be drawn

hyperparameter

boolean indicating if inference should be performed for the prior variance hyperparameter. If TRUE the prior variance (main diagonal of the covariance matrix) must be set to 1.

chi

rate parameter for the inverse-gamma prior distribution on the hyperparameter

psi

shape parameter for the inverse-gamma prior distribution on the hyperparameter

Details

If player.prior.var is omitted, independent and identical N(0, 5^2) prior distributions are placed on each object quality parameter.

If beta.initialis omitted, it is set to a vector of zeroes.

If kappa.var is omitted, it is set to N(0, 5^2), if kappa.initial is omitted it is set to 0.5.

Value

A data frame containing samples from the posterior distribution


[Package speedyBBT version 1.0 Index]