```
# NOT RUN {
fm01ML <- lmer(Yield ~ 1|Batch, Dyestuff, REML = FALSE)
## see ?"profile-methods"
mySumm <- function(.) { s <- sigma(.)
c(beta =getME(., "beta"), sigma = s, sig01 = unname(s * getME(., "theta"))) }
(t0 <- mySumm(fm01ML)) # just three parameters
## alternatively:
mySumm2 <- function(.) {
c(beta=fixef(.),sigma=sigma(.), sig01=sqrt(unlist(VarCorr(.))))
}
set.seed(101)
## 3.8s (on a 5600 MIPS 64bit fast(year 2009) desktop "AMD Phenom(tm) II X4 925"):
system.time( boo01 <- bootMer(fm01ML, mySumm, nsim = 100) )
## to "look" at it
if (requireNamespace("boot")) {
boo01
## note large estimated bias for sig01
## (~30% low, decreases _slightly_ for nsim = 1000)
## extract the bootstrapped values as a data frame ...
head(as.data.frame(boo01))
## ------ Bootstrap-based confidence intervals ------------
## warnings about "Some ... intervals may be unstable" go away
## for larger bootstrap samples, e.g. nsim=500
## intercept
(bCI.1 <- boot::boot.ci(boo01, index=1, type=c("norm", "basic", "perc")))# beta
## Residual standard deviation - original scale:
(bCI.2 <- boot::boot.ci(boo01, index=2, type=c("norm", "basic", "perc")))
## Residual SD - transform to log scale:
(bCI.2L <- boot::boot.ci(boo01, index=2, type=c("norm", "basic", "perc"),
h = log, hdot = function(.) 1/., hinv = exp))
## Among-batch variance:
(bCI.3 <- boot::boot.ci(boo01, index=3, type=c("norm", "basic", "perc"))) # sig01
## Copy of unexported stats:::format.perc helper function
format.perc <- function(probs, digits) {
paste(format(100 * probs, trim = TRUE,
scientific = FALSE, digits = digits),
"%")
}
## Extract all CIs (somewhat awkward)
bCI.tab <- function(b,ind=length(b$t0), type="perc", conf=0.95) {
btab0 <- t(sapply(as.list(seq(ind)),
function(i)
boot::boot.ci(b,index=i,conf=conf, type=type)$percent))
btab <- btab0[,4:5]
rownames(btab) <- names(b$t0)
a <- (1 - conf)/2
a <- c(a, 1 - a)
pct <- format.perc(a, 3)
colnames(btab) <- pct
return(btab)
}
bCI.tab(boo01)
## Graphical examination:
plot(boo01,index=3)
## Check stored values from a longer (1000-replicate) run:
(load(system.file("testdata","boo01L.RData", package="lme4")))# "boo01L"
plot(boo01L, index=3)
mean(boo01L$t[,"sig01"]==0) ## note point mass at zero!
} ## if boot package available
# }
```

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