selfStart {stats}R Documentation

Construct Self-starting Nonlinear Models


Construct self-starting nonlinear models to be used in nls, etc. Via function initial to compute approximate parameter values from data, such models are “self-starting”, i.e., do not need a start argument in, e.g., nls().


selfStart(model, initial, parameters, template)



a function object defining a nonlinear model or a nonlinear formula object of the form ~ expression.


a function object, taking arguments mCall, data, and LHS, and ..., representing, respectively, a matched call to the function model, a data frame in which to interpret the variables in mCall, and the expression from the left-hand side of the model formula in the call to nls. This function should return initial values for the parameters in model. The ... is used by nls() to pass its control and trace arguments for the cases where initial() itself calls nls() as it does for the ten self-starting nonlinear models in R's stats package.


a character vector specifying the terms on the right hand side of model for which initial estimates should be calculated. Passed as the namevec argument to the deriv function.


an optional prototype for the calling sequence of the returned object, passed as the function.arg argument to the deriv function. By default, a template is generated with the covariates in model coming first and the parameters in model coming last in the calling sequence.


nls() calls getInitial and the initial function for these self-starting models.

This function is generic; methods functions can be written to handle specific classes of objects.


a function object of class "selfStart", for the formula method obtained by applying deriv to the right hand side of the model formula. An initial attribute (defined by the initial argument) is added to the function to calculate starting estimates for the parameters in the model automatically.


José Pinheiro and Douglas Bates

See Also

nls, getInitial.

Each of the following are "selfStart" models (with examples) SSasymp, SSasympOff, SSasympOrig, SSbiexp, SSfol, SSfpl, SSgompertz, SSlogis, SSmicmen, SSweibull.

Further, package nlme's nlsList.


## self-starting logistic model

## The "initializer" (finds initial values for parameters from data):
initLogis <- function(mCall, data, LHS, ...) {
    xy <- sortedXyData(mCall[["x"]], LHS, data)
    if(nrow(xy) < 4)
        stop("too few distinct input values to fit a logistic model")
    z <- xy[["y"]]
    ## transform to proportion, i.e. in (0,1) :
    rng <- range(z); dz <- diff(rng)
    z <- (z - rng[1L] + 0.05 * dz)/(1.1 * dz)
    xy[["z"]] <- log(z/(1 - z))		# logit transformation
    aux <- coef(lm(x ~ z, xy))
    pars <- coef(nls(y ~ 1/(1 + exp((xmid - x)/scal)),
                     data = xy,
                     start = list(xmid = aux[[1L]], scal = aux[[2L]]),
                     algorithm = "plinear", ...))
    setNames(pars [c(".lin", "xmid", "scal")],
             mCall[c("Asym", "xmid", "scal")])

mySSlogis <- selfStart(~ Asym/(1 + exp((xmid - x)/scal)),
                       initial = initLogis,
                       parameters = c("Asym", "xmid", "scal"))

getInitial(weight ~ mySSlogis(Time, Asym, xmid, scal),
           data = subset(ChickWeight, Chick == 1))

# 'first.order.log.model' is a function object defining a first order
# compartment model
# 'first.order.log.initial' is a function object which calculates initial
# values for the parameters in 'first.order.log.model'
# self-starting first order compartment model
## Not run: 
SSfol <- selfStart(first.order.log.model, first.order.log.initial)

## End(Not run)

## Explore the self-starting models already available in R's  "stats": <- which("package:stats" == search())
mSS <- apropos("^SS..", where = TRUE, = FALSE)
(mSS <- unname(mSS[names(mSS) ==]))
fSS <- sapply(mSS, get, pos =, mode = "function")
all(sapply(fSS, inherits, "selfStart"))  # -> TRUE

## Show the argument list of each self-starting function:
str(fSS, give.attr = FALSE)

[Package stats version 4.4.0 Index]