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

In minpack.lm: R Interface to the Levenberg-Marquardt Nonlinear Least-Squares Algorithm Found in MINPACK, Plus Support for Bounds

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 informula 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 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.
...	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.

See Also

nls.lm, nls, nls.lm.control, optim

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 documentation built on Sept. 11, 2023, 9:07 a.m.