BBTm.ties {speedyBBT} | R Documentation |
This function uses MCMC to sample from the posterior distribution of the Bradley–Terry model with ties.A multivariate normal prior distribution on the player quality parameters can be specified. An exponential prior distribution is placed on the tie parameter theta, and a Metropolis- Hasting random walk algorithm is used to update this parameter.
BBTm.ties(
n.objects,
outcome,
player1,
player2,
player.prior.var = NULL,
theta.initial = NULL,
lambda.initial = NULL,
n.iter = 1000,
hyperparameter = TRUE,
chi = 0.01,
psi = 0.01,
rw.sd = 0.1,
theta.rate = 0.01
)
n.objects |
number of objects in the study |
outcome |
vector of outcomes. 0 if player 1 is the winner, 1 if player 2 is the winner, and 2 if it is a tie. |
player1 |
vector of first players. |
player2 |
vector of second players. |
player.prior.var |
(optional) matrix specifying the prior covariance of the player correlation parameters |
theta.initial |
(optional) value of the tied parameter there for the first MCMC iteration |
lambda.initial |
(optional) vector containing the values of the player 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 |
rw.sd |
number describing the standard deviation of normal distribution proposal distribution for theta |
theta.rate |
(optional) The rate parameter of the exponential prior distribution placed on theta |
If player.prior.var
is omitted, independent and identical
N(0, 5^2) prior distributions are placed on each object quality parameter.
If lambda.initial
is omitted, it is set to a vector of zeroes.
A data frame containing samples from the posterior distribution
############################################
## Deprivation in Dar es Salaam, Tanzania ##
## Seymour et al (2022) ##
############################################
#Construct covariance matrix based on spatial informartion
sigma <- expm::expm(darEsSalaam$adjacencyMatrix)
sigma <- diag(diag(sigma)^-0.5)%*% sigma %*%diag(diag(sigma)^-0.5)
##Not Run
#Fit BT model with ties
#darTiedModel <- BBTm.ties(n.objects = 452,
# outcome = darEsSalaam$comparisons$outcome,
# player1 = darEsSalaam$comparisons$subward1,
# player2 = darEsSalaam$comparisons$subward2,
# player.prior.var = sigma,
# hyperparameter = TRUE, rw.sd = 0.005)
#Get posterior means
#darTiedModel$lambda <- darTiedModel $lambda - colMeans(darTiedModel$lambda)
#lambda.mean <- rowMeans(darTiedModel$lambda)
#Generate trace plots
#plot(lambda.mean)
#plot(darTiedModel$theta[-c(1:100)], type = 'l')