Standard error for lme4 random effect predictions in lme4 - r

Question

I have an experiment with plants having different growth habits (growth_type), genotypes nested within growth types (ge), and blocks also nested within growth types (block). The objective is to test the influence of growth type and genotypes of plant performance. Here is a sample data and reproducible example.
data1 <- read.csv(text = "
growth_type,ge,block,performance
dwarf,A,1,128.32
dwarf,A,2,97.01
dwarf,A,3,91.05
dwarf,B,1,108.51
dwarf,B,2,121.11
dwarf,B,3,84.15
dwarf,C,1,132.55
dwarf,C,2,129.45
dwarf,C,3,122.33
tall,D,1,79.68
tall,D,2,122.5
tall,D,3,143.42
tall,E,1,149.29
tall,E,2,162.13
tall,E,3,135.42
tall,F,1,90.45
tall,F,2,127.4
tall,F,3,78.99")
These are the libraries I used:
library(dplyr)
library(lme4)
library(lsmeans)
The first step was fitting a model:
model.fit <-
lmer(performance ~ growth_type + (1 | block:growth_type) + (1 | ge:growth_type),
data = data1)
From this model, I can extract the fixed effect of growth type using lsmeans:
fixed.effect.estimates <- lsmeans::lsmeans(model.fit, "growth_type")
and this is the output:
What I need to obtain is the same output for the random effect. I am able to get the prediction interval, but I cannot get the standard error. This is what I tried:
# RANDOM EFFECT ESTIMATES
data1$pred.performance <-
predict(model.fit,
newdata = data1,
re.form= ~(1 | ge:growth_type))
pred.ge <- data1 %>%
distinct(ge, growth_type, pred.performance)
And this is what I've obtained. So far so good.
Then I used the bootMer function to build the prediction interval using bootstrapping.
mySumm <- function(.) {
predict(., newdata=pred.ge, re.form= ~(1 | ge:growth_type))
}
####Collapse bootstrap into median, 95% PI
sumBoot <- function(merBoot) {
return(
data.frame(fit = apply(merBoot$t, 2, function(x) as.numeric(quantile(x, probs=.5, na.rm=TRUE))),
lwr = apply(merBoot$t, 2, function(x) as.numeric(quantile(x, probs=.025, na.rm=TRUE))),
upr = apply(merBoot$t, 2, function(x) as.numeric(quantile(x, probs=.975, na.rm=TRUE)))
)
)
}
##lme4::bootMer() method 1
PI.boot1.time <- system.time(
boot1 <- lme4::bootMer(model.fit, mySumm, nsim=250, use.u=TRUE, type="parametric")
)
PI.boot1 <- sumBoot(boot1)
cbind(pred.ge, PI.boot1)
This is what I obtained:
In summary, my questions are:
how can I get the standard errors as I did for the fixed effect components?
why random effect estimates from lme4::predict are different from lme4::bootMer?
Sorry for a long explanation.