Construct Self-starting Nonlinear Models

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Description

Construct self-starting nonlinear models.

Usage

1
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 three arguments: mCall, data, and LHS, 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.

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

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

See Also

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

Examples

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## self-starting logistic model

SSlogis <- selfStart(~ Asym/(1 + exp((xmid - x)/scal)),
  function(mCall, data, LHS)
  {
    xy <- sortedXyData(mCall[["x"]], LHS, data)
    if(nrow(xy) < 4) {
      stop("Too few distinct x values to fit a logistic")
    }
    z <- xy[["y"]]
    if (min(z) <= 0) { z <- z + 0.05 * max(z) } # avoid zeroes
    z <- z/(1.05 * max(z))              # scale to within unit height
    xy[["z"]] <- log(z/(1 - z))         # logit transformation
    aux <- coef(lm(x ~ z, xy))
    parameters(xy) <- list(xmid = aux[1], scal = aux[2])
    pars <- as.vector(coef(nls(y ~ 1/(1 + exp((xmid - x)/scal)),
                             data = xy, algorithm = "plinear")))
    setNames(c(pars[3], pars[1], pars[2]),
             mCall[c("Asym", "xmid", "scal")])
  }, 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)

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