nls | R Documentation |
Determine the nonlinear (weighted) least-squares estimates of the parameters of a nonlinear model.
nls(formula, data, start, control, algorithm, trace, subset, weights, na.action, model, lower, upper, ...)
formula |
a nonlinear model formula including variables and parameters. Will be coerced to a formula if necessary. |
data |
an optional data frame in which to evaluate the variables in
|
start |
a named list or named numeric vector of starting
estimates. When |
control |
an optional |
algorithm |
character string specifying the algorithm to use.
The default algorithm is a Gauss-Newton algorithm. Other possible
values are |
trace |
logical value indicating if a trace of the iteration
progress should be printed. Default is |
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. |
na.action |
a function which indicates what should happen
when the data contain |
model |
logical. If true, the model frame is returned as part of
the object. Default is |
lower, upper |
vectors of lower and upper bounds, replicated to
be as long as |
... |
Additional optional arguments. None are used at present. |
An nls
object is a type of fitted model object. It has methods
for the generic functions anova
, coef
,
confint
, deviance
,
df.residual
, fitted
,
formula
, logLik
, predict
,
print
, profile
, residuals
,
summary
, vcov
and weights
.
Variables in formula
(and weights
if not missing) are
looked for first in data
, then the environment of
formula
and finally along the search path. Functions in
formula
are searched for first in the environment of
formula
and then along the search path.
Arguments subset
and na.action
are supported only when
all the variables in the formula taken from data
are of the
same length: other cases give a warning.
Note that the anova
method does not check that the
models are nested: this cannot easily be done automatically, so use
with care.
A list of
m |
an |
data |
the expression that was passed to |
call |
the matched call with several components, notably
|
na.action |
the |
dataClasses |
the |
model |
if |
weights |
if |
convInfo |
a list with convergence information. |
control |
the control |
convergence, message |
for an To use these is deprecated, as they are available from
|
The default settings of nls
generally fail on artificial
“zero-residual” data problems.
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, θ) + eps
(with
var(eps) > 0
). It fails to indicate convergence on data of the form
y = f(x, θ)
because the criterion amounts to
comparing two components of the round-off error.
To avoid a zero-divide in computing the convergence testing value, a
positive constant scaleOffset
should be added to the denominator
sum-of-squares; it is set in control
, as in the example below;
this does not yet apply to algorithm = "port"
.
The algorithm = "port"
code appears unfinished, and does
not even check that the starting value is within the bounds.
Use with caution, especially where bounds are supplied.
Setting warnOnly = TRUE
in the control
argument (see nls.control
) returns a non-converged
object (since R version 2.5.0) which might be useful for further
convergence analysis, but not for inference.
Douglas M. Bates and Saikat DebRoy: David M. Gay for the Fortran code
used by algorithm = "port"
.
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.
https://www.netlib.org/port/ for the Port library documentation.
summary.nls
, predict.nls
,
profile.nls
.
Self starting models (with ‘automatic initial values’):
selfStart
.
require(graphics) DNase1 <- subset(DNase, Run == 1) ## using a selfStart model fm1DNase1 <- nls(density ~ SSlogis(log(conc), Asym, xmid, scal), DNase1) summary(fm1DNase1) ## the coefficients only: coef(fm1DNase1) ## including their SE, etc: coef(summary(fm1DNase1)) ## using conditional linearity fm2DNase1 <- nls(density ~ 1/(1 + exp((xmid - log(conc))/scal)), data = DNase1, start = list(xmid = 0, scal = 1), algorithm = "plinear") 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)) summary(fm3DNase1) ## using Port's nl2sol algorithm fm4DNase1 <- nls(density ~ Asym/(1 + exp((xmid - log(conc))/scal)), data = DNase1, start = list(Asym = 3, xmid = 0, scal = 1), 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 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)) summary(Pur.wt) ## Passing arguments using a list that can not be coerced to a data.frame lisTreat <- with(Treated, list(conc1 = conc[1], conc.1 = conc[-1], rate = rate)) weighted.MM1 <- function(resp, conc1, conc.1, Vm, K) { conc <- c(conc1, conc.1) pred <- (Vm * conc)/(K + conc) (resp - pred) / sqrt(pred) } Pur.wt1 <- nls( ~ weighted.MM1(rate, conc1, conc.1, Vm, K), data = lisTreat, start = list(Vm = 200, K = 0.1)) stopifnot(all.equal(coef(Pur.wt), coef(Pur.wt1))) ## Chambers and Hastie (1992) Statistical Models in S (p. 537): ## If the value of the right side [of formula] has an attribute called ## 'gradient' this should be a matrix with the number of rows equal ## to the length of the response and one column for each parameter. weighted.MM.grad <- function(resp, conc1, conc.1, Vm, K) { conc <- c(conc1, conc.1) K.conc <- K+conc dy.dV <- conc/K.conc dy.dK <- -Vm*dy.dV/K.conc pred <- Vm*dy.dV pred.5 <- sqrt(pred) dev <- (resp - pred) / pred.5 Ddev <- -0.5*(resp+pred)/(pred.5*pred) attr(dev, "gradient") <- Ddev * cbind(Vm = dy.dV, K = dy.dK) dev } Pur.wt.grad <- nls( ~ weighted.MM.grad(rate, conc1, conc.1, Vm, K), data = lisTreat, start = list(Vm = 200, K = 0.1)) rbind(coef(Pur.wt), coef(Pur.wt1), coef(Pur.wt.grad)) ## In this example, there seems no advantage to providing the gradient. ## In other cases, there might be. ## 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 <- 2*x + 3 # perfect fit ## terminates in an error, because convergence cannot be confirmed: try(nls(y ~ a + b*x, start = list(a = 0.12345, b = 0.54321))) ## adjusting the convergence test by adding 'scaleOffset' to its denominator RSS: nls(y ~ a + b*x, start = list(a = 0.12345, b = 0.54321), control = list(scaleOffset = 1, printEval=TRUE)) ## Alternatively jittering the "too exact" values, slightly: set.seed(27) yeps <- y + rnorm(length(y), sd = 0.01) # added noise nls(yeps ~ a + b*x, start = list(a = 0.12345, b = 0.54321)) ## the nls() internal cheap guess for starting values can be sufficient: x <- -(1:100)/10 y <- 100 + 10 * exp(x / 2) + rnorm(x)/10 nlmod <- nls(y ~ Const + A * exp(B * x)) plot(x,y, main = "nls(*), data, true function and fit, n=100") curve(100 + 10 * exp(x / 2), col = 4, add = TRUE) lines(x, predict(nlmod), col = 2) ## Here, requiring close convergence, you need to use more accurate numerical ## differentiation; the first fit gives Error: "step factor .. reduced below 'minFactor' .." options(digits = 10) # more accuracy for 'trace' ## IGNORE_RDIFF_BEGIN try(nlm1 <- update(nlmod, control = list(tol = 1e-7))) # where central diff. typically work: (nlm2 <- update(nlmod, control = list(tol = 8e-8, nDcentral=TRUE, warnOnly=TRUE), trace = TRUE)) ## 2nd fit still fails on some (less accurate) platforms => using warnOnly ## --> convergence tolerance 4.997e-8 (in 11 iter.) ## IGNORE_RDIFF_END ## The muscle dataset in MASS is from an experiment on muscle ## contraction on 21 animals. The observed variables are Strip ## (identifier of muscle), Conc (Cacl concentration) and Length ## (resulting length of muscle section). ## IGNORE_RDIFF_BEGIN if(requireNamespace("MASS", quietly = TRUE)) withAutoprint({ ## The non linear model considered is ## Length = alpha + beta*exp(-Conc/theta) + error ## where theta is constant but alpha and beta may vary with Strip. with(MASS::muscle, table(Strip)) # 2, 3 or 4 obs per strip ## We first use the plinear algorithm to fit an overall model, ## ignoring that alpha and beta might vary with Strip. musc.1 <- nls(Length ~ cbind(1, exp(-Conc/th)), MASS::muscle, start = list(th = 1), algorithm = "plinear") summary(musc.1) ## Then we use nls' indexing feature for parameters in non-linear ## models to use the conventional algorithm to fit a model in which ## alpha and beta vary with Strip. The starting values are provided ## by the previously fitted model. ## Note that with indexed parameters, the starting values must be ## given in a list (with names): b <- coef(musc.1) musc.2 <- nls(Length ~ a[Strip] + b[Strip]*exp(-Conc/th), MASS::muscle, start = list(a = rep(b[2], 21), b = rep(b[3], 21), th = b[1])) summary(musc.2) }) ## IGNORE_RDIFF_END
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