Interpreting the Model Results

Interpretation

From the Fit! and Summary functions in previous section, we end up with two tables summarizing the mean estimates for the regression coefficients for the edge effects (out.edge_coef) and the posterior probabilities that nodes are influential (out.prob_nodes):

julia> out.edge_coef
435×5 DataFrame
 Row │ node1  node2  estimate  lower_bound  upper_bound 
     │ Int64  Int64  Float64   Float64      Float64     
─────┼──────────────────────────────────────────────────
   1 │     1      2     2.385       -1.976        6.157
   2 │     1      3     1.823       -5.257        7.595
   3 │     1      4     1.763       -4.514        6.009
  ⋮  │   ⋮      ⋮       ⋮           ⋮            ⋮
 433 │    28     29     3.51        -1.251        7.376
 434 │    28     30     1.949       -3.425        6.135
 435 │    29     30     2.785       -0.772        6.042
                                        429 rows omitted

julia> out.prob_nodes
30×1 DataFrame
 Row │ probability 
     │ Float64     
─────┼─────────────
   1 │        0.86
   2 │        0.92
   3 │        0.78
  ⋮  │      ⋮
  28 │        0.93
  29 │        0.89
  30 │        0.87
    24 rows omitted

Plot

The following R code can be used to plot the credible intervals of the edge regression coefficients.

First, we pass the data frame to R:

edges = out.edge_coef

using RCall
@rput edges

An alternative path is to save the data frame to file with CSV.write("edges.csv",out.edge_coef) and then read in R.

In R, we type

library(ggplot2)
library(tidyr)
nn <- length(edges$node1)
edges$edge <- 1:nn
edges <- transform(edges,rej=ifelse(lower_bound > 0 | upper_bound < 0,TRUE,FALSE))

plt <- edges %>% ggplot() + geom_errorbar(aes(x=factor(edge),ymin=lower_bound,
                                                                ymax=upper_bound,
                                                                color=rej)) +
        xlab("") + ylab("")+ ggtitle("95% Credible intervals for edge effects")+
        scale_color_manual(values=c("#82AFBC","#0E4B87")) + 
        theme(
            plot.title = element_text(hjust=0.5, size=rel(2)),
            axis.title.x = element_text(size=rel(1.2)),
            axis.title.y = element_text(size=rel(1.9), angle=90, vjust=0.5, hjust=0.5),
            axis.text.x = element_text(colour="grey", size=rel(1.8), hjust=.5, vjust=.5, face="plain"),
            axis.ticks.y = element_blank(),
            panel.background = element_rect(fill = NA, color = "black"),
            axis.line = element_line(colour = "grey"),
            strip.text = element_text(size = rel(1.5)),
            legend.position = "none"
        ) +
        coord_flip() + scale_x_discrete(labels=NULL,expand=expansion(add=4)) +
        geom_point(aes(x=factor(edge),y=estimate, color=rej),shape=18, size=2) +
        geom_hline(aes(yintercept=0),linetype="solid",color="#696969", size=1)
plt

The dark credible intervals are those that do not intersect zero which point at potential edges (interactions among microbes) that have a significant effect on the response.

The following R code can be used to plot posterior probabilities of being influencial nodes (micrones) on the response.

First, we pass the data frame to R:

nodes = out.prob_nodes

@rput nodes

An alternative path is to save the data frame to file with CSV.write("nodes.csv",out.prob_nodes) and then read in R.

nodes$microbe <- 1:length(nodes$probability)

axisTextY = 

## Plot:
plt2 <- ggplot(data=nodes,aes(x=microbe,y=probability)) + 
    geom_bar(stat="Identity", fill="#82AFBC") + xlab("Microbes") + ylab("") + 
    ggtitle("Posterior probability of influential node") +
    theme(
        plot.title = element_text(hjust=0.5, size=rel(2)),
        axis.title.x = element_text(size=rel(1.2)),
        axis.title.y = element_text(size=rel(1.9), angle=90, vjust=0.5, hjust=0.5),
        axis.text.y = element_text(colour="grey", size=rel(1.5), angle=0, hjust=.5, vjust=.5, face="plain"),
        panel.background = element_rect(fill = NA, color = "black"),
        axis.line = element_line(colour = "grey"),
        strip.text = element_text(size = rel(2))
    ) +
    geom_hline(aes(yintercept=0.5),linetype="solid",color="#696969", size=1)+
    scale_y_continuous(breaks = c(0,0.5,1),limits=c(0,1))
plt2

Each bar corresponds to the posterior probability of being an influential node (microbe) on the response. A horizontal line is drawn at 0.5, so that nodes with bars taller than the line can be considered influential.