# run_asymmetric_mcmc: Run the BSBT MCMC algorithm with n types of individuals and... In BSBT: The Bayesian Spatial Bradley--Terry Model

## 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

 ```1 2 3 4 5 6 7 8 9``` ```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

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17``` ```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 March 15, 2021, 1:07 a.m.