minpack.lm: nlsLM – R documentation

Become an expert in R — Interactive courses, Cheat Sheets, certificates and more!

nlsLM

Standard 'nls' framework that uses 'nls.lm' for fitting

Description

nlsLM is a modified version of nls that uses nls.lm for fitting. Since an object of class 'nls' is returned, all generic functions such as anova, coef, confint, deviance, df.residual, fitted, formula, logLik, predict, print, profile, residuals, summary, update, vcov and weights are applicable.

Usage

nlsLM(formula, data = parent.frame(), start, jac = NULL, 
      algorithm = "LM", control = nls.lm.control(), 
      lower = NULL, upper = NULL, trace = FALSE, subset, 
      weights, na.action, model = FALSE, ...)

Arguments

`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`formula` and `weights`. Can also be a list or an environment, but not a matrix.
`start`	a named list or named numeric vector of starting estimates.
`jac`	A function to return the Jacobian.
`algorithm`	only method `"LM"` (Levenberg-Marquardt) is implemented.
`control`	an optional list of control settings. See `nls.lm.control` for the names of the settable control values and their effect.
`lower`	A numeric vector of lower bounds on each parameter. If not given, the default lower bound for each parameter is set to `-Inf`.
`upper`	A numeric vector of upper bounds on each parameter. If not given, the default upper bound for each parameter is set to `Inf`.
`trace`	logical value indicating if a trace of the iteration progress should be printed. Default is `FALSE`. If `TRUE`, the residual (weighted) sum-of-squares and the parameter values are printed at the conclusion of each iteration.
`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. See the `wfct` function for options for easy specification of weighting schemes.
`na.action`	a function which indicates what should happen when the data contain `NA`s. 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`.
`...`	Additional optional arguments. None are used at present.

Details

The standard nls function was modified in several ways to incorporate the Levenberg-Marquardt type nls.lm fitting algorithm. The formula is transformed into a function that returns a vector of (weighted) residuals whose sum square is minimized by nls.lm. The optimized parameters are then transferred to nlsModel in order to obtain an object of class 'nlsModel'. The internal C function C_nls_iter and nls_port_fit were removed to avoid subsequent "Gauss-Newton", "port" or "plinear" types of optimization of nlsModel. Several other small modifications were made in order to make all generic functions work on the output.

Value

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.
`call`	the matched call.
`convInfo`	a list with convergence information.
`control`	the control `list` used, see the `control` argument.
`na.action`	the `"na.action"` attribute (if any) of the model frame.
`dataClasses`	the `"dataClasses"` attribute (if any) of the `"terms"` attribute of the model frame.
`model`	if `model = TRUE`, the model frame.
`weights`	if `weights` is supplied, the weights.

Author(s)

Andrej-Nikolai Spiess and Katharine M. Mullen

References

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.

J.J. More, "The Levenberg-Marquardt algorithm: implementation and theory," in Lecture Notes in Mathematics 630: Numerical Analysis, G.A. Watson (Ed.), Springer-Verlag: Berlin, 1978, pp. 105-116.

Examples

### Examples from 'nls' doc ###
DNase1 <- subset(DNase, Run == 1)
## using a selfStart model
fm1DNase1 <- nlsLM(density ~ SSlogis(log(conc), Asym, xmid, scal), DNase1)
## using logistic formula
fm2DNase1 <- nlsLM(density ~ Asym/(1 + exp((xmid - log(conc))/scal)),
                 data = DNase1, 
                 start = list(Asym = 3, xmid = 0, scal = 1))

## all generics are applicable
coef(fm1DNase1)
confint(fm1DNase1)
deviance(fm1DNase1)
df.residual(fm1DNase1)
fitted(fm1DNase1)
formula(fm1DNase1)
logLik(fm1DNase1)
predict(fm1DNase1)
print(fm1DNase1)
profile(fm1DNase1)
residuals(fm1DNase1)
summary(fm1DNase1)
update(fm1DNase1)
vcov(fm1DNase1)
weights(fm1DNase1)

## weighted nonlinear regression using 
## inverse squared variance of the response
## gives same results as original 'nls' function
Treated <- Puromycin[Puromycin$state == "treated", ]
var.Treated <- tapply(Treated$rate, Treated$conc, var)
var.Treated <- rep(var.Treated, each = 2)
Pur.wt1 <- nls(rate ~ (Vm * conc)/(K + conc), data = Treated, 
               start = list(Vm = 200, K = 0.1), weights = 1/var.Treated^2)
Pur.wt2 <- nlsLM(rate ~ (Vm * conc)/(K + conc), data = Treated, 
               start = list(Vm = 200, K = 0.1), weights = 1/var.Treated^2)
all.equal(coef(Pur.wt1), coef(Pur.wt2))

## 'nlsLM' can fit zero-noise data
## in contrast to 'nls'
x <- 1:10
y <- 2*x + 3                           
## Not run: 
nls(y ~ a + b * x, start = list(a = 0.12345, b = 0.54321))

## End(Not run)
nlsLM(y ~ a + b * x, start = list(a = 0.12345, b = 0.54321))

### Examples from 'nls.lm' doc
## values over which to simulate data 
x <- seq(0,5, length = 100)
## model based on a list of parameters 
getPred <- function(parS, xx) parS$a * exp(xx * parS$b) + parS$c 
## parameter values used to simulate data
pp <- list(a = 9,b = -1, c = 6) 
## simulated data with noise  
simDNoisy <- getPred(pp, x) + rnorm(length(x), sd = .1)
## make model
mod <- nlsLM(simDNoisy ~ a * exp(b * x) + c, 
             start = c(a = 3, b = -0.001, c = 1), 
             trace = TRUE)     
## plot data
plot(x, simDNoisy, main = "data")
## plot fitted values
lines(x, fitted(mod), col = 2, lwd = 2)

## create declining cosine
## with noise
TT <- seq(0, 8, length = 501)
tau <- 2.2
N0 <- 1000
a <- 0.25
f0 <- 8
Ndet <- N0 * exp(-TT/tau) * (1 + a * cos(f0 * TT))
N <- Ndet +  rnorm(length(Ndet), mean = Ndet, sd = .01 * max(Ndet))
## make model
mod <- nlsLM(N ~ N0 * exp(-TT/tau) * (1 + a * cos(f0 * TT)), 
             start = c(tau = 2.2, N0 = 1500, a = 0.25, f0 = 10), 
             trace = TRUE)  

## plot data
plot(TT, N, main = "data")
## plot fitted values
lines(TT, fitted(mod), col = 2, lwd = 2)

minpack.lm

R Interface to the Levenberg-Marquardt Nonlinear Least-Squares Algorithm Found in MINPACK, Plus Support for Bounds

v1.2-1

GPL-3

Authors

Timur V. Elzhov, Katharine M. Mullen, Andrej-Nikolai Spiess, Ben Bolker

Initial release