Model-based (Semi-)Parametric Bootstrap for Mixed Models
Perform model-based (Semi-)parametric bootstrap for mixed models.
bootMer(x, FUN, nsim = 1, seed = NULL, use.u = FALSE, re.form=NA,
type = c("parametric", "semiparametric"),
verbose = FALSE, .progress = "none", PBargs = list(),
parallel = c("no", "multicore", "snow"),
ncpus = getOption("boot.ncpus", 1L), cl = NULL)x |
|
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 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.
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/S0167-7152(02)00041-X.
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.
profile-methods, for likelihood-based inference,
including confidence intervals.
pvalues,
for more general approaches to inference and p-value computation
in mixed models.
if (interactive()) {
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
confint(boo01)
confint(boo01,type="norm")
confint(boo01,type="basic")
## 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!
}
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