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`selfStart` Construct Self-starting Nonlinear Models

Description

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().

Usage

selfStart(model, initial, parameters, template)

Arguments

`model`	a function object defining a nonlinear model or a nonlinear `formula` object of the form `~ expression`.
`initial`	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.
`parameters`	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.
`template`	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.

Details

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.

Value

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.

Author(s)

José Pinheiro and Douglas Bates

Examples

## self-starting logistic model

## The "initializer" (finds initial values for parameters from data):
initLogis <- function(mCall, data, LHS) {
    xy <- data.frame(sortedXyData(mCall[["input"]], 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")], nm = mCall[c("Asym", "xmid", "scal")])
}

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


# '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":
pos.st <- which("package:stats" == search())
mSS <- apropos("^SS..", where = TRUE, ignore.case = FALSE)
(mSS <- unname(mSS[names(mSS) == pos.st]))
fSS <- sapply(mSS, get, pos = pos.st, mode = "function")
all(sapply(fSS, inherits, "selfStart"))  # -> TRUE

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

selfStart Construct Self-starting Nonlinear Models