dr4plEst: Private function to fit the 4PL model to dose-response data
In dr4pl: Dose Response Data Analysis using the 4 Parameter Logistic (4pl) Model

Private function that actually fits the 4PL model to data. If the Hill bounds are attained at the end of optimization processes, then an indicator of convergence failure so that dr4pl.default can look for a remedy for convergence failure.

dr4plEst(
  dose,
  response,
  init.parm,
  trend,
  method.init,
  method.optim,
  method.robust,
  use.Hessian,
  level,
  upperl,
  lowerl,
  ...
)

`dose`	Vector of dose levels
`response`	Vector of responses
`init.parm`	Vector of initial parameters of the 4PL model supplied by a user.
`trend`	Indicator of whether a dose-response curve is a decreasing θ[3]<0 or increasing curve θ[3]>0. The default is "auto" which indicates that the trend of the curve is automatically determined by data. The option "decreasing" will impose a restriction θ[3]<=0 while the option "increasing" will impose a restriction θ[3]>=0 in an optimization process.
`method.init`	Method of obtaining initial values of the parameters. Should be one of "logistic" for the logistic method or "Mead" for the Mead method. The default option is the Mead method.
`method.optim`	Method of optimization of the parameters. This argument is directly delivered to the `constrOptim` function provided in the "base" package of R.
`method.robust`	Parameter to select loss function for the robust estimation method to be used to fit a model. The argument NULL indicates the sum of squares loss, "absolute" indicates the absolute deviation loss, "Huber" indicates Huber's loss and "Tukey" indicates Tukey's biweight loss.
`use.Hessian`	Indicator of whether the Hessian matrix (TRUE) or the gradient vector is used in the Hill bounds.
`level`	Confidence level to be used in Hill bounds computation.
`upperl`	upper limit to init.parm
`lowerl`	lower limit to init.parm
`...`	Further arguments to be passed to `constrOptim`.