Fitting Nonlinear Mixed-Effects Models
Fit a nonlinear mixed-effects model (NLMM) to data, via maximum likelihood.
nlmer(formula, data = NULL, control = nlmerControl(),
start = NULL, verbose = 0L, nAGQ = 1L, subset, weights, na.action,
offset, contrasts = NULL, devFunOnly = FALSE)formula |
a three-part “nonlinear mixed model” formula, of
the form |
data |
an optional data frame containing the variables named in
|
control |
a list (of correct class, resulting from
|
start |
starting estimates for the nonlinear model parameters, as a named numeric vector or as a list with components
|
verbose |
integer scalar. If |
nAGQ |
integer scalar - the number of points per axis for evaluating the adaptive Gauss-Hermite approximation to the log-likelihood. Defaults to 1, corresponding to the Laplace approximation. Values greater than 1 produce greater accuracy in the evaluation of the log-likelihood at the expense of speed. A value of zero uses a faster but less exact form of parameter estimation for GLMMs by optimizing the random effects and the fixed-effects coefficients in the penalized iteratively reweighted least squares (PIRLS) step. |
subset |
an optional expression indicating the subset of the rows
of |
weights |
an optional vector of ‘prior weights’ to be used
in the fitting process. Should be |
na.action |
a function that indicates what should happen when the
data contain |
offset |
this can be used to specify an a priori known
component to be included in the linear predictor during fitting.
This should be |
contrasts |
an optional |
devFunOnly |
logical - return only the deviance evaluation function. Note that because the deviance function operates on variables stored in its environment, it may not return exactly the same values on subsequent calls (but the results should always be within machine tolerance). |
Fit nonlinear mixed-effects models, such as those used in population pharmacokinetics.
Adaptive Gauss-Hermite quadrature (nAGQ > 1) is not
currently implemented for nlmer. Several other
methods, such as simulation or prediction with new data,
are unimplemented or very lightly tested.
A method argument was used in earlier versions of the lme4
package. Its functionality has been replaced by the nAGQ argument.
## nonlinear mixed models --- 3-part formulas ---
## 1. basic nonlinear fit. Use stats::SSlogis for its
## implementation of the 3-parameter logistic curve.
## "SS" stands for "self-starting logistic", but the
## "self-starting" part is not currently used by nlmer ... 'start' is
## necessary
startvec <- c(Asym = 200, xmid = 725, scal = 350)
(nm1 <- nlmer(circumference ~ SSlogis(age, Asym, xmid, scal) ~ Asym|Tree,
Orange, start = startvec))
## 2. re-run with "quick and dirty" PIRLS step
(nm1a <- update(nm1, nAGQ = 0L))
## 3. Fit the same model with a user-built function:
## a. Define formula
nform <- ~Asym/(1+exp((xmid-input)/scal))
## b. Use deriv() to construct function:
nfun <- deriv(nform,namevec=c("Asym","xmid","scal"),
function.arg=c("input","Asym","xmid","scal"))
nm1b <- update(nm1,circumference ~ nfun(age, Asym, xmid, scal) ~ Asym | Tree)
## 4. User-built function without using derivs():
## derivatives could be computed more efficiently
## by pre-computing components, but these are essentially
## the gradients as one would derive them by hand
nfun2 <- function(input, Asym, xmid, scal) {
value <- Asym/(1+exp((xmid-input)/scal))
grad <- cbind(Asym=1/(1+exp((xmid-input)/scal)),
xmid=-Asym/(1+exp((xmid-input)/scal))^2*1/scal*
exp((xmid-input)/scal),
scal=-Asym/(1+exp((xmid-input)/scal))^2*
-(xmid-input)/scal^2*exp((xmid-input)/scal))
attr(value,"gradient") <- grad
value
}
stopifnot(all.equal(attr(nfun(2,1,3,4),"gradient"),
attr(nfun(2,1,3,4),"gradient")))
nm1c <- update(nm1,circumference ~ nfun2(age, Asym, xmid, scal) ~ Asym | Tree)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.