\HeaderA{rms.curv}{Relative Curvature Measures for Non-Linear Regression}{rms.curv}
\aliasA{print.rms.curv}{rms.curv}{print.rms.curv}
\keyword{nonlinear}{rms.curv}
\begin{Description}\relax
Calculates the root mean square parameter effects and intrinsic relative
curvatures, \eqn{c^\theta}{} and \eqn{c^\iota}{}, for a fitted nonlinear regression, as
defined in Bates \& Watts, section 7.3, p. 253 et seq.
\end{Description}
\begin{Usage}
\begin{verbatim}
rms.curv(obj)
\end{verbatim}
\end{Usage}
\begin{Arguments}
\begin{ldescription}
\item[\code{obj}] Fitted model object of class \code{"nls"}.  The model must be fitted using the
default algorithm.

\end{ldescription}
\end{Arguments}
\begin{Details}\relax
The method of section 7.3.1 of Bates \& Watts is implemented.  The
function \code{deriv3} should be used generate a model function with first
derivative (gradient) matrix and second derivative (Hessian) array
attributes.  This function should then be used to fit the nonlinear
regression model.

A print method, \code{print.rms.curv}, prints the \code{pc} and
\code{ic} components only, suitably annotated.

If either \code{pc} or \code{ic} exceeds some threshold (0.3 has been
suggested) the curvature is unacceptably high for the planar assumption.
\end{Details}
\begin{Value}
A list of class \code{rms.curv} with components \code{pc} and \code{ic}
for parameter effects and intrinsic relative curvatures multiplied by
sqrt(F), \code{ct} and \code{ci} for \eqn{c^\theta}{} and \eqn{c^\iota}{} (unmultiplied),
and \code{C} the C-array as used in section 7.3.1 of Bates \& Watts.
\end{Value}
\begin{References}\relax
Bates, D. M, and Watts, D. G. (1988)
\emph{Nonlinear Regression Analysis and its Applications.}
Wiley, New York.
\end{References}
\begin{SeeAlso}\relax
\code{\LinkA{deriv3}{deriv3}}
\end{SeeAlso}
\begin{Examples}
\begin{ExampleCode}
# The treated sample from the Puromycin data
data(Puromycin)
mmcurve <- deriv3(~ Vm * conc/(K + conc), c("Vm", "K"),
                  function(Vm, K, conc) NULL)
Treated <- Puromycin[Puromycin$state == "treated", ]
(Purfit1 <- nls(rate ~ mmcurve(Vm, K, conc), data = Treated,
                start = list(Vm=200, K=0.1)))
rms.curv(Purfit1)
##Parameter effects: c^theta x sqrt(F) = 0.2121
##        Intrinsic: c^iota  x sqrt(F) = 0.092
\end{ExampleCode}
\end{Examples}

