Profile method for merMod objects
The log() method and the more flexible logProf()
utility transform a lmer profile into one where logarithms of standard deviations
are used, while varianceProf converts from the
standard-deviation to the variance scale; see Details.
## S3 method for class 'merMod'
profile(fitted, which = NULL, alphamax = 0.01,
maxpts = 100, delta = NULL,
delta.cutoff = 1/8, verbose = 0, devtol = 1e-09,
maxmult = 10, startmethod = "prev", optimizer = NULL,
control=NULL, signames = TRUE,
parallel = c("no", "multicore", "snow"),
ncpus = getOption("profile.ncpus", 1L), cl = NULL,
prof.scale = c("sdcor","varcov"),
...)
## S3 method for class 'thpr'
as.data.frame(x, ...)
## S3 method for class 'thpr'
log(x, base = exp(1))
logProf(x, base = exp(1), ranef = TRUE,
sigIni = if(ranef) "sig" else "sigma")
varianceProf(x, ranef = TRUE)fitted |
a fitted model, e.g., the result of |
which |
NULL value, integer or character vector indicating which parameters to profile: default (NULL) is all parameters. For integer, i.e., indexing, the parameters are ordered as follows:
Alternatively, |
alphamax |
a number in (0,1), such that |
maxpts |
maximum number of points (in each direction, for each parameter) to evaluate in attempting to construct the profile. |
delta |
stepping scale for deciding on next point to profile.
The code uses the local derivative of the profile at the current
step to establish a change in the focal parameter that will lead
to a step of |
delta.cutoff |
stepping scale (see |
verbose |
level of output from internal calculations. |
devtol |
tolerance for fitted deviances less than baseline (supposedly minimum) deviance. |
maxmult |
maximum multiplier of the original step size allowed, defaults to 10. |
startmethod |
method for picking starting conditions for optimization (STUB). |
optimizer |
(character or function) optimizer to use (see
|
control |
a |
signames |
logical indicating if abbreviated names of the form
|
... |
potential further arguments for various methods. |
x |
an object of class |
base |
the base of the logarithm. Defaults to natural logarithms. |
ranef |
logical indicating if the sigmas of the random effects
should be |
sigIni |
character string specifying the initial part of the sigma parameters to be log transformed. |
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
|
prof.scale |
whether to profile on the standard
deviation-correlation scale ( |
The log method and the more flexible logProf()
function transform the profile into one where \log(σ) is
used instead of σ.
By default all sigmas including the standard deviations of the random
effects are transformed i.e., the methods return a profile with all
of the .sigNN
parameters replaced by .lsigNN. If ranef is false, only
".sigma", the standard deviation of the errors, is transformed
(as it should never be zero, whereas random effect standard
deviations (.sigNN) can be reasonably be zero).
The forward and backward splines for the log-transformed parameters
are recalculated.
Note that correlation parameters are not handled sensibly at present
(i.e., they are logged rather than taking a more applicable
transformation such as an arc-hyperbolic tangent,
atanh(x)=log((1+x)/(1-x))/2).
The varianceProf function works similarly, including
non-sensibility for correlation parameters, by squaring all
parameter values, changing the names by appending sq
appropriately (e.g. .sigNN to .sigsqNN).
Setting prof.scale="varcov" in the original
profile() call is a more computationally
intensive, but more correct, way to compute confidence
intervals for covariance parameters.
Methods for function profile (package
stats), here for profiling (fitted) mixed effect models.
profile(<merMod>) returns an object of S3 class
"thpr",
which is data.frame-like.
Notable methods for such a profile object
confint(), which returns the
confidence intervals based on the profile,
and three plotting methods
(which require the lattice package),
xyplot, densityplot, and
splom.
In addition, the
log() (see above) and as.data.frame()
methods can transform "thpr" objects in useful ways.
The plotting methods xyplot etc, for class
"thpr".
For (more expensive) alternative confidence intervals:
bootMer.
if (interactive()) {
fm01ML <- lmer(Yield ~ 1|Batch, Dyestuff, REML = FALSE)
system.time(
tpr <- profile(fm01ML, optimizer="Nelder_Mead", which="beta_")
)## fast; as only *one* beta parameter is profiled over
## full profiling (default which means 'all) needs
## ~2.6s (on a 2010 Macbook Pro)
system.time( tpr <- profile(fm01ML))
## ~1s, + possible warning about bobyqa convergence
(confint(tpr) -> CIpr)
## Not run:
stopifnot(all.equal(unname(CIpr),
array(c(12.1985292, 38.2299848, 1486.4515,
84.0630513, 67.6576964, 1568.54849), dim = 3:2),
tol= 1e-07))# 1.37e-9 {64b}
## End(Not run)
library("lattice")
xyplot(tpr)
xyplot(tpr, absVal=TRUE) # easier to see conf.int.s (and check symmetry)
xyplot(tpr, conf = c(0.95, 0.99), # (instead of all five 50, 80,...)
main = "95% and 99% profile() intervals")
xyplot(logProf(tpr, ranef=FALSE),
main = expression("lmer profile()s"~~ log(sigma)*" (only log)"))
densityplot(tpr, main="densityplot( profile(lmer(..)) )")
densityplot(varianceProf(tpr), main=" varianceProf( profile(lmer(..)) )")
splom(tpr)
splom(logProf(tpr, ranef=FALSE))
doMore <- lme4:::testLevel() > 2
if(doMore) { ## not typically, for time constraint reasons
## Batch and residual variance only
system.time(tpr2 <- profile(fm01ML, which=1:2, optimizer="Nelder_Mead"))
print( xyplot(tpr2) )
print( xyplot(log(tpr2)) )# log(sigma) is better
print( xyplot(logProf(tpr2, ranef=FALSE)) )
## GLMM example
gm1 <- glmer(cbind(incidence, size - incidence) ~ period + (1 | herd),
data = cbpp, family = binomial)
## running ~ 10-12 seconds on a modern machine {-> "verbose" while you wait}:
print( system.time(pr4 <- profile(gm1, verbose=TRUE)) )
print( xyplot(pr4, layout=c(5,1), as.table=TRUE) )
print( xyplot(log(pr4), absVal=TRUE) ) # log(sigma_1)
print( splom(pr4) )
print( system.time( # quicker: only sig01 and one fixed effect
pr2 <- profile(gm1, which=c("theta_", "period2"))))
print( confint(pr2) )
## delta..: higher underlying resolution, only for 'sigma_1':
print( system.time(
pr4.hr <- profile(gm1, which="theta_", delta.cutoff=1/16)))
print( xyplot(pr4.hr) )
}
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