run_asymmetric_mcmc: Run the BSBT MCMC algorithm with n types of individuals and...

In BSBT: The Bayesian Spatial Bradley--Terry Model

Run the BSBT MCMC algorithm with n types of individuals and asymmetric variance

Description

This function runs the MCMC algorithm with n types of individuals, for example male and female. The types must share the same covariance matrix and the win matrices are entered as a list. The first item in the list acts as the baseline group. This model has an asymmetric variance structure, as the variance of the baseline is always smaller. For a model with thee types, f, g and h, the structure is as follows. The baseline is f, or the second type, g = f + d_1, and the third type, h = f + d_2. Here d_1 and d_2 are the discrepancy between each type and the baseline.

Usage

run_asymmetric_mcmc(
  n.iter,
  delta,
  covariance.matrix,
  win.matrices,
  estimates.initial,
  omega = 0.1,
  chi = 0.1
)

Arguments

n.iter	The number of iterations to be run
delta	The underrlaxed tuning parameter must be in (0, 1)
covariance.matrix	The output from the covariance matrix function, which contains the decomposed and inverted covariance matrix. The variance hyperparameter must be set to 1.
win.matrices	A list of n matrices where the ith matrix is the win matrix corresponding to only the ith level
estimates.initial	A list of vectors where the ith vector is the initial estimate for the ith level effect
omega	The value of the inverse gamma shape parameter
chi	The value of the inverse gamma scale parameter

Value

A list of MCMC output

• estimates - A list of matrices. Each matrix containing the iteration of the ith level

• alpha.sq - A matrix containing the iterations of alpha^2

• acceptance.rate - The acceptance rate for f and g

• time.taken - Time taken to run the MCMC algorithm in seconds

Examples

n.iter <- 10
delta <- 0.1
covariance.matrix <- list()
covariance.matrix$mean <- c(0, 0, 0)
covariance.matrix$decomp <- diag(3)
covariance.matrix$inv    <- diag(3)
men.comparisons <- data.frame("winner" = c(1, 3, 2, 2), "loser" = c(3, 1, 1, 3))
women.comparisons <- data.frame("winner" = c(1, 2, 1, 2), "loser" = c(3, 1, 3, 3))
men.win.matrix <- comparisons_to_matrix(3, men.comparisons)
women.win.matrix <- comparisons_to_matrix(3, women.comparisons)
f.initial <- c(0, 0, 0)
g.initial <- c(0, 0, 0)

win.matrices <- list(men.win.matrix, women.win.matrix)
estimates.initial <- list(f.initial, g.initial)

mcmc.output<- run_asymmetric_mcmc(n.iter, delta, covariance.matrix, win.matrices, estimates.initial)

BSBT documentation built on Aug. 9, 2022, 5:06 p.m.