Plot Some Posterior Ellipses

library(SIBER)
library(dplyr)
library(ggplot2)
library(ellipse)

# load in the included demonstration dataset
data("demo.siber.data")
#
# create the siber object
siber.example <- createSiberObject(demo.siber.data)

# Calculate summary statistics for each group: TA, SEA and SEAc
group.ML <- groupMetricsML(siber.example)

# options for running jags
parms <- list()
parms$n.iter <- 2 * 10^4   # number of iterations to run the model for
parms$n.burnin <- 1 * 10^3 # discard the first set of values
parms$n.thin <- 10     # thin the posterior by this many
parms$n.chains <- 2        # run this many chains

# define the priors
priors <- list()
priors$R <- 1 * diag(2)
priors$k <- 2
priors$tau.mu <- 1.0E-3

# fit the ellipses which uses an Inverse Wishart prior
# on the covariance matrix Sigma, and a vague normal prior on the 
# means. Fitting is via the JAGS method.
ellipses.posterior <- siberMVN(siber.example, parms, priors)

# The posterior estimates of the ellipses for each group can be used to
# calculate the SEA.B for each group.
SEA.B <- siberEllipses(ellipses.posterior)

siberDensityPlot(SEA.B, xticklabels = colnames(group.ML), 
                xlab = c("Community | Group"),
                ylab = expression("Standard Ellipse Area " ('permille' ^2) ),
                bty = "L",
                las = 1,
                main = "SIBER ellipses on each group"
                )

# how many of the posterior draws do you want?
n.posts <- 10

# decide how big an ellipse you want to draw
p.ell <- 0.95

# for a standard ellipse use
# p.ell <- pchisq(1,2)




# a list to store the results
all_ellipses <- list()

# loop over groups
for (i in 1:length(ellipses.posterior)){
  
  # a dummy variable to build in the loop
  ell <- NULL
  post.id <- NULL
  
  for ( j in 1:n.posts){
    
    # covariance matrix
    Sigma  <- matrix(ellipses.posterior[[i]][j,1:4], 2, 2)
    
    # mean
    mu     <- ellipses.posterior[[i]][j,5:6]
    
    # ellipse points
    
    out <- ellipse::ellipse(Sigma, centre = mu , level = p.ell)
    
    
    ell <- rbind(ell, out)
    post.id <- c(post.id, rep(j, nrow(out)))
    
  }
  ell <- as.data.frame(ell)
  ell$rep <- post.id
  all_ellipses[[i]] <- ell
}

ellipse_df <- bind_rows(all_ellipses, .id = "id")


# now we need the group and community names

# extract them from the ellipses.posterior list
group_comm_names <- names(ellipses.posterior)[as.numeric(ellipse_df$id)]

# split them and conver to a matrix, NB byrow = T
split_group_comm <- matrix(unlist(strsplit(group_comm_names, "[.]")),
                           nrow(ellipse_df), 2, byrow = TRUE)

ellipse_df$community <- split_group_comm[,1]
ellipse_df$group     <- split_group_comm[,2]

ellipse_df <- dplyr::rename(ellipse_df, iso1 = x, iso2 = y)

first.plot <- ggplot(data = demo.siber.data, aes(iso1, iso2)) +
  geom_point(aes(color = factor(group):factor(community)), size = 2)+
  ylab(expression(paste(delta^{15}, "N (permille)")))+
  xlab(expression(paste(delta^{13}, "C (permille)"))) + 
  theme(text = element_text(size=15))
print(first.plot)

second.plot <- first.plot + facet_wrap(~factor(group):factor(community))
print(second.plot)

# rename columns of ellipse_df to match the aesthetics

third.plot <- second.plot + 
  geom_polygon(data = ellipse_df,
              mapping = aes(iso1, iso2,
                             group = rep,
                             color = factor(group):factor(community),
                             fill = NULL),
               fill = NA,
               alpha = 0.2)
print(third.plot)