Intraclass correlation standard error I am in the last stage of my paper review and it is very close to getting submitted. However, there is a comment I am highly struggling with:
The reviewer wants to know what the ICC and the s.e. of the ICC is.
The model I have is a linear mixed effect model looking like:
mixedmodel <- lmer(y ~ x1 + x2 + x3 + (1 | countries), weights=weight, Alldata)

Before I had never heard about the ICC. When looking for documentation, I do find information on ICC, but not on how to calculate the s.e. of the ICC. 
Can anyone please help me with this? I am using R.
 A: You can easily get the ICC from the sjstats-package, which also offers bootstrapping. I would try bootstrapping to obtain se- and p-values (you can also take a look at this discussion in the r-sig-mailinglist for other approaches, but bootstrapping is one recommendation, two).
library(sjstats) # for ICC and bootstrapping
library(dplyr)   # for the pipe
library(lme4)

# compute ICC
fit <- lmer(Reaction ~ Days + (Days | Subject), sleepstudy)
icc(fit)
> Linear mixed model
>  Family: gaussian (identity)
> Formula: Reaction ~ Days + (Days | Subject)
>
>   ICC (Subject): 0.483090

# compute SE of ICC
dummy <- sleepstudy %>% 
  # generate 100 bootstrap replicates of dataset
  bootstrap(100) %>% 
  # run mixed effects regression on each bootstrap replicate
  mutate(models = lapply(.$strap, function(x) {
    lmer(Reaction ~ Days + (Days | Subject), data = x)
  })) %>% 
  # compute ICC for each "bootstrapped" regression
  mutate(icc = unlist(lapply(.$models, icc)))

# now compute SE and p-values for the bootstrapped ICC
boot_se(dummy, icc)
>   term   std.err
> 1  icc 0.1024704

boot_p(dummy, icc)
>   term      p.value
> 1  icc 1.936526e-08



*

*The above code takes the sleepstudy dataset and creates 100 bootstrap-samples, which are saved as "list-variable" named strap, in a new data frame. 

*This list-variable (i.e. the data frame with this variable), containing the 100 bootstrap-samples, is then "piped" into the lapply-command to run 100 lmer-commands (which are saved in another list-variable named models, see mutate-command). 

*This list-variable is then used to compute the ICC with the sjstats::icc function, so you have 100 ICC-values (for all models applied to the 100 bootstrap-samples) in the variable named icc.
Now boot_se and boot_p compute the standard error and p-value of any bootstrapped values, in this case the ICC-values.
