| nls {stats} | R Documentation |
Determine the nonlinear least-squares estimates of the nonlinear model
parameters and return a class nls object.
nls(formula, data, start, control, algorithm,
trace, subset, weights, na.action, model,
lower, upper, ...)
formula |
a nonlinear model formula including variables and parameters |
data |
an optional data frame in which to evaluate the variables in
formula |
start |
a named list or named numeric vector of starting estimates |
control |
an optional list of control settings. See
nls.control for the names of the settable control values and
their effect. |
algorithm |
character string specifying the algorithm to use.
The default algorithm is a Gauss-Newton algorithm. Other possible
values are "plinear" for the Golub-Pereyra algorithm for
partially linear least-squares models and "port" for the
"nl2sol" algorithm from the Port package. |
trace |
logical value indicating if a trace of the iteration
progress should be printed. Default is FALSE. If
TRUE the residual sum-of-squares and the parameter values
are printed at the conclusion of each iteration. When the
"plinear" algorithm is used, the conditional estimates of
the linear parameters are printed after the nonlinear
parameters. When the "port" algorithms are used the
objective function value printed is half the residual sum-of-squares. |
subset |
an optional vector specifying a subset of observations to be used in the fitting process. |
weights |
an optional numeric vector of (fixed) weights. When present, the objective function is weighted least squares. not yet implemented |
na.action |
a function which indicates what should happen
when the data contain NAs. The default is set by
the na.action setting of options, and is
na.fail if that is unset. The “factory-fresh”
default is na.omit. Value na.exclude
can be useful. |
model |
logical. If true, the model frame is returned as part of
the object. Default is FALSE |
lower, upper |
vector of lower and upper bounds, replicated to be as long as
start. If unspecified, all parameters are assumed to be
unconstrained. Bounds can only be used with the "port"
algorithm. They are ignored, with a warning, if given for other
algorithms. |
... |
Additional optional arguments. None are used at present. |
Do not use nls on artificial "zero-residual" data.
The nls function uses a relative-offset convergence criterion
that compares the numerical imprecision at the current parameter
estimates to the residual sum-of-squares. This performs well on data of
the form
y = f(x, theta) + eps
(with
var(eps) > 0). It
fails to indicate convergence on data of the form
y = f(x, theta)
because the criterion amounts to
comparing two components of the round-off error. If you wish to test
nls on artificial data please add a noise component, as shown
in the example below.
An nls object is a type of fitted model object. It has methods
for the generic functions coef, formula,
resid, print, summary,
AIC, fitted and vcov.
Variables in formula are looked for first in data, then
the environment of formula (added in 1.9.1) and finally along
the search path. Functions in formula are searched for first
in the environment of formula (added in 1.9.1) and then along
the search path.
A list of
m |
an nlsModel object incorporating the model |
data |
the expression that was passed to nls as the data
argument. The actual data values are present in the environment of
the m component. |
Douglas M. Bates and Saikat DebRoy
Bates, D.M. and Watts, D.G. (1988) Nonlinear Regression Analysis and Its Applications, Wiley
Bates, D. M. and Chambers, J. M. (1992) Nonlinear models. Chapter 10 of Statistical Models in S eds J. M. Chambers and T. J. Hastie, Wadsworth & Brooks/Cole.
http://netlib.bell-labs.com/netlib/port/ for the Port library
DNase1 <- subset(DNase, Run == 1)
## using a selfStart model
fm1DNase1 <- nls( density ~ SSlogis(log(conc), Asym, xmid, scal), DNase1)
summary( fm1DNase1 )
## using conditional linearity
fm2DNase1 <- nls( density ~ 1/(1 + exp((xmid - log(conc))/scal)),
data = DNase1,
start = list(xmid = 0, scal = 1),
alg = "plinear", trace = TRUE)
summary( fm2DNase1 )
## without conditional linearity
fm3DNase1 <- nls( density ~ Asym/(1 + exp((xmid - log(conc))/scal)),
data = DNase1,
start = list(Asym = 3, xmid = 0, scal = 1),
trace = TRUE)
summary( fm3DNase1 )
## using the nl2sol algorithm
fm4DNase1 <- nls( density ~ Asym/(1 + exp((xmid - log(conc))/scal)),
data = DNase1,
start = list(Asym = 3, xmid = 0, scal = 1),
trace = TRUE, algorithm = "port")
summary(fm4DNase1)
## weighted nonlinear regression
Treated <- Puromycin[Puromycin$state == "treated", ]
weighted.MM <- function(resp, conc, Vm, K)
{
## Purpose: exactly as white book p.451 -- RHS for nls()
## Weighted version of Michaelis-Menten model
## ------------------------------------------------------------
## Arguments: 'y', 'x' and the two parameters (see book)
## ------------------------------------------------------------
## Author: Martin Maechler, Date: 23 Mar 2001, 18:48
pred <- (Vm * conc)/(K + conc)
(resp - pred) / sqrt(pred)
}
Pur.wt <- nls( ~ weighted.MM(rate, conc, Vm, K), data = Treated,
start = list(Vm = 200, K = 0.1),
trace = TRUE)
## The two examples below show that you can fit a model to
## artificial data with noise but not to artificial data
## without noise.
x = 1:10
y = x # perfect fit
yeps = y + rnorm(length(y), sd = 0.01) # added noise
nls(yeps ~ a + b*x, start = list(a = 0.12345, b = 0.54321),
trace = TRUE)
## Not run:
nls(y ~ a + b*x, start = list(a = 0.12345, b = 0.54321),
trace = TRUE)
## End(Not run)