Plot random terms of communityPGLMM

Daijiang Li

2020-12-17

This vignette will show how to visualize the var-covariance matrix of random terms for communityPGLMM models.

Main function

The main function to use is phyr::pglmm_plot_re() (alias: phyr::pglmm_plot_ranef(), phyr::communityPGLMM.show.re(), phyr::communityPGLMM.plot.re()). Here are the arguments of this function:

args(phyr::pglmm_plot_re)
## function (formula = NULL, data = NULL, family = "gaussian", sp.var = "sp", 
##     site.var = "site", tree = NULL, tree_site = NULL, repulsion = FALSE, 
##     x = NULL, show.image = TRUE, show.sim.image = FALSE, random.effects = NULL, 
##     add.tree.sp = TRUE, add.tree.site = FALSE, cov_ranef = NULL, 
##     tree.panel.space = 0.5, title.space = 5, tree.size = 3, ...) 
## NULL

Some brief explanation of arguments:

This function will return a hidden list, which includes all the var-cov matrices of random terms, simulated site by species matrices, individual plots, and all plots in one figure for both var-cov matrices and simulated ones. Therefore, we can extract specific plots and then update them or generate new figure with gridExtra::grid.arrange(). This is because all generated plots are based on lattice package and are all grid object. Therefore, we can also use gridExtra::arrangeGrob() to put multiple plots in one figure and then use ggplot2::ggsave() to save it as external file (e.g. PDF). Of course, pdf() and dev.off() will also work.

Simulate data

Now, let’s show how to use this function to help us understanding better the random terms.

library(ape)
library(phyr)
suppressPackageStartupMessages(library(dplyr))

set.seed(12345)
nspp <- 7
nsite <- 5
# Simulate a phylogeny that has a lot of phylogenetic signal (power = 1.3)
phy <- compute.brlen(rtree(n = nspp), method = "Grafen", power = 1.3)
# Simulate species means
sd.sp <- 1
mean.sp <- rTraitCont(phy, model = "BM", sigma = sd.sp^2)
Y.sp <- rep(mean.sp, times = nsite)
# Phylogenetically correlated response of species to env
sd.trait <- 1
trait <- rTraitCont(phy, model = "BM", sigma = sd.trait)
trait <- rep(trait, times = nsite)
# Simulate site means
sd.site <- 1
mean.site <- rnorm(nsite, sd = sd.site)
Y.site <- rep(mean.site, each = nspp)
# Site-specific environmental variation
sd.env <- 1
env <- rnorm(nsite, sd = sd.env)
# Generate covariance matrix for phylogenetic attraction
sd.attract <- 1
Vphy <- vcv(phy)
Vphy <- Vphy / (det(Vphy) ^ (1 / nspp))
V.attract <- kronecker(diag(nrow = nsite, ncol = nsite), Vphy)
Y.attract <- array(t(mvtnorm::rmvnorm(n = 1, sigma = sd.attract ^ 2 * V.attract)))
# Residual errors
sd.e <- 1
Y.e <- rnorm(nspp * nsite, sd = sd.e)
# Construct the dataset
d <- data.frame(sp = rep(phy$tip.label, times = nsite), 
                site = rep(1:nsite, each = nspp),
                env = rep(env, each = nspp))
# Simulate abundance data
d$Y <- Y.sp + Y.attract + trait * d$env + Y.e
head(d)
##   sp site       env          Y
## 1 t4    1 -1.060266 -1.3475684
## 2 t2    1 -1.060266  1.2422030
## 3 t5    1 -1.060266 -1.2711509
## 4 t3    1 -1.060266  1.8940820
## 5 t6    1 -1.060266  1.5771805
## 6 t7    1 -1.060266  0.3308875

# fit a model
mod_1 = pglmm(Y ~ 1 + env + (1|sp__) + (1|site) + (env|sp__) + (1|sp__@site),
              data = d, cov_ranef = list(sp = phy))
summary(mod_1)
## Linear mixed model fit by restricted maximum likelihood
## 
## Call:Y ~ 1 + env
## 
## logLik    AIC    BIC 
## -64.34 146.68 150.38 
## 
## Random effects:
##              Variance   Std.Dev
## 1|sp        2.085e-06 0.0014439
## 1|sp__      4.218e-01 0.6494991
## 1|site      1.235e-07 0.0003515
## env|sp      1.209e-06 0.0010993
## env|sp__    5.434e-01 0.7371383
## 1|[email protected] 1.375e-01 0.3707606
## residual    1.885e+00 1.3729463
## 
## Fixed effects:
##               Value Std.Error Zscore Pvalue
## (Intercept) 0.83092   0.63742 1.3036 0.1924
## env         0.75052   0.68819 1.0906 0.2755

Var-cov matrices of random terms

Plot var-cov matrices of all random terms in one figure

# plot var-cov matrices of random terms
mod1re = pglmm_plot_re(Y ~ 1 + env + (1|sp__) + (1|site) + (env|sp__) + (1|sp__@site),
                       data = d, cov_ranef = list(sp = phy), show.image = TRUE, 
                       show.sim.image = FALSE)

In the above plot, we can see that some of the panels are black-white but some have colors. This is because, by default, if a matrix has both positive and negative values, then the function will use red-blue color and will draw a key for that (use colorkey = FALSE to suppress it). If a matrix does not have negative values, then the function will use black/white color (use useAbs = FALSE to use color instead, and use colorkey = FALSE to suppress key if wanted). In both cases, value 0 will be white so that the structure of the var-cov matrix can be easier to see.

# all use color with useAbs = FALSE
pglmm_plot_re(Y ~ 1 + env + (1|sp__) + (1|site) + (env|sp__) + (1|sp__@site),
              data = d, cov_ranef = list(sp = phy), show.image = TRUE, 
              show.sim.image = FALSE, useAbs = FALSE)

For the above plot, notice that for 1|sp and 1|site, all values are either 1 or 0 even though we have a range in the key. We can suppress the key with colorkey = FALSE.

# suppress key with colorkey = FALSE
pglmm_plot_re(Y ~ 1 + env + (1|sp__) + (1|site) + (env|sp__) + (1|sp__@site),
              data = d, cov_ranef = list(sp = phy), show.image = TRUE, 
              show.sim.image = FALSE, useAbs = FALSE, colorkey = FALSE)

We can also just use colorkey = FALSE and still use black/white color for matrices that do not have negative values (without setting useAbs).

# suppress colorkey, let the function decide whether use color or not
pglmm_plot_re(Y ~ 1 + env + (1|sp__) + (1|site) + (env|sp__) + (1|sp__@site),
              data = d, cov_ranef = list(sp = phy), show.image = TRUE, 
              show.sim.image = FALSE, colorkey = FALSE)

To make all plots black or white, use useAbs = TRUE.

# all black and white
pglmm_plot_re(Y ~ 1 + env + (1|sp__) + (1|site) + (env|sp__) + (1|sp__@site),
              data = d, cov_ranef = list(sp = phy), show.image = TRUE, 
              show.sim.image = FALSE, useAbs = TRUE)