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#' @title A credible interval plot of posterior of sigma squared
#' @description It returns a credible interval plot of idiosyncratic variance, sigma squared. The lines are 95% intervals, while the circles are posterior mean.
#'
#' @param Gibbs Result of Gibbs sampler from DIFM function.
#' @param burnin Number of burn-in. If not specified, it uses the first tenths as burn-in period.
#' @param permutation Permutation of variables. If not specified, no permutation.
#' @param main.bool Add title of the plots.
#'
#' @return A credible interval plot of sigma squared
#' @export
plot_sigma2.CI <- function(Gibbs, burnin = NA, permutation = NA, main.bool = TRUE){
n.iter <- dim(Gibbs$sigma2)[1]
r <- dim(Gibbs$sigma2)[2]
if(is.na(burnin)){burnin <- round(n.iter / 10)}
turns <- seq(burnin + 1, n.iter)
repermute <- 1:r
if( !is.na(permutation[1]) ){repermute <- order(permutation)}
sigma2.CI <- matrix(NA, 3, r)
sigma2.CI[1,] <- apply(Gibbs$sigma2[turns,repermute], 2, quantile, 0.025)
sigma2.CI[2,] <- apply(Gibbs$sigma2[turns,repermute], 2, mean)
sigma2.CI[3,] <- apply(Gibbs$sigma2[turns,repermute], 2, quantile, 0.975)
yrange <- c(min(sigma2.CI[1,]), max(sigma2.CI[3,]))
if(main.bool){maint = expression(paste(sigma^2, " Confidence Interval"))}
if(!main.bool){maint = ""}
plot(sigma2.CI[2,], main = maint, pch = 19, ylim = yrange, xlab = "Variables", ylab = "")
for(i in 1:r){lines(rep(i,2), c(sigma2.CI[1,i], sigma2.CI[3,i]))}
}
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