Description Usage Arguments Details Value Note References See Also Examples
Perform modelbased (Semi)parametric bootstrap for mixed models.
1 2 3 4 5 
x 
a fitted 
FUN 
a function taking a fitted

nsim 
number of simulations, positive integer; the bootstrap B (or R). 
seed 
optional argument to 
use.u 
logical, indicating whether the spherical
random effects should be simulated / bootstrapped as
well. If 
re.form 
formula, 
type 
character string specifying the type of
bootstrap, 
verbose 
logical indicating if progress should print output 
.progress 
character string  type of progress bar
to display. Default is 
PBargs 
a list of additional arguments to the
progress bar function (the package authors like

parallel 
The type of parallel operation to be used (if any).
If missing, the
default is taken from the option 
ncpus 
integer: number of processes to be used in parallel operation: typically one would choose this to be the number of available CPUs. 
cl 
An optional parallel or snow cluster for use if

The semiparametric variant is only partially implemented, and
we only provide a method for lmer
and
glmer
results.
The working name for bootMer() was
“simulestimate()”, as it is an extension of simulate
(see simulate.merMod), but we want to emphasize its potential
for valid inference.
If use.u
is FALSE
and type
is
"parametric"
, each simulation generates new values of both
the “spherical” random effects u and the
i.i.d. errors ε, using rnorm()
with parameters corresponding to the fitted model x
.
If use.u
is TRUE
and type=="parametric"
,
only the i.i.d. errors (or, for GLMMs, response values drawn from
the appropriate distributions) are resampled, with the values of
u staying fixed at their estimated values.
If use.u
is TRUE
and type=="semiparametric"
,
the i.i.d. errors are sampled from the distribution of (response)
residuals. (For GLMMs, the resulting
sample will no longer have the same properties as the original
sample, and the method may not make sense; a warning is generated.)
The semiparametric bootstrap is currently an experimental feature,
and therefore may not be stable.
The case where use.u
is FALSE
and
type=="semiparametric"
is not implemented; Morris (2002)
suggests that resampling from the estimated values of u is not
good practice.
an object of S3 class
"boot"
,
compatible with boot package's
boot()
result.
If you are using parallel="snow"
, you will need to run
clusterEvalQ(cl,library("lme4"))
before calling
bootMer
to make sure that the
lme4
package is loaded on all of the workers; you may
additionally need to use clusterExport
if you are using a summary function that calls any objects
from the environment.
Davison, A.C. and Hinkley, D.V. (1997) Bootstrap Methods and Their Application. Cambridge University Press.
Morris, J. S. (2002). The BLUPs Are Not ‘best’ When It Comes to Bootstrapping. Statistics & Probability Letters 56(4): 425–430. doi:10.1016/S01677152(02)00041X.
confint.merMod
,
for a more specific approach to bootstrap confidence
intervals on parameters.
refit()
, or PBmodcomp()
from the pbkrtest package, for parametric bootstrap comparison
of models.
boot()
, and then
boot.ci
, from the boot package.
profilemethods
, for likelihoodbased inference,
including confidence intervals.
pvalues
,
for more general approaches to inference and pvalue computation
in mixed models.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55  if (interactive()) {
fm01ML < lmer(Yield ~ 1Batch, Dyestuff, REML = FALSE)
## see ?"profilemethods"
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))
##  Bootstrapbased 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))
## Amongbatch variance:
(bCI.3 < boot::boot.ci(boo01, index=3, type=c("norm", "basic", "perc"))) # sig01
confint(boo01)
confint(boo01,type="norm")
confint(boo01,type="basic")
## Graphical examination:
plot(boo01,index=3)
## Check stored values from a longer (1000replicate) run:
(load(system.file("testdata","boo01L.RData", package="lme4")))# "boo01L"
plot(boo01L, index=3)
mean(boo01L$t[,"sig01"]==0) ## note point mass at zero!
}
}

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