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(
outcome,
player1,
player2,
lambda.initial = NULL,
player.prior.var = NULL,
beta.initial = NULL,
n.iter = 1000,
formula = NULL,
data = NULL,
advantage = NULL,
kappa.initial = NULL,
kappa.var = NULL,
hyperparameter = TRUE,
chi = 0.01,
psi = 0.01,
burn.in = 100,
n.thin = 1,
verbose = interactive()
)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.
- lambda.initial
(optional) Vector containing the values of the player parameters for the first MCMC iteration.
- 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.
- formula
Formula with no left-hand-side specifying the player specific effects.
- data
Data frame with a row corresponding to each player and a 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 comparison specific value kappa.
- 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.
- burn.in
The number of iterations to use for a burn.in, default is 100.
- n.thin
(optional) The number of iterations to thin the MCMC samples by. Default is 1.
- verbose
(optional) A boolean indicating if progress should be printed to the console. Default is
interactive()therefore progress is shown if run interactively, but disabled in non-interactive contexts.
Value
A "mcmc" object containing samples from the posterior distribution.
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.
Examples
# \donttest{
#####################
## Wimbledon 2019 ##
####################
# Fit model where the quality of each player depends on their rank
# and the number of points they had immediately before the tournament.
# Allow an effect for a match being in the first or second week.
wimbledonModel <- BBTm(
outcome = wimbledon$matches$outcome,
player2 = wimbledon$matches$loser,
player1 = wimbledon$matches$winner,
advantage = wimbledon$matches$secondWeek,
formula = ~ rank + points,
data = wimbledon$players,
n.iter = 1000, verbose = FALSE
)
# Plot posterior distributions
hist(parameter(wimbledonModel, "kappa"),
main = "", xlab = expression(kappa), freq = FALSE
)
# }