rms.curv                package:MASS                R Documentation

Relative Curvature Measures for Non-Linear Regression

Description:

     Calculates the root mean square parameter effects and intrinsic
     relative curvatures, c^theta and c^iota, for a fitted nonlinear
     regression, as defined in Bates & Watts, section 7.3, p. 253 et
     seq.

Usage:

     rms.curv(obj)

Arguments:

     obj: Fitted model object of class '"nls"'.  The model must be
          fitted using the default algorithm. 

Details:

     The method of section 7.3.1 of Bates & Watts is implemented.  The
     function '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, 'print.rms.curv', prints the 'pc' and 'ic'
     components only, suitably annotated.

     If either 'pc' or 'ic' exceeds some threshold (0.3 has been
     suggested) the curvature is unacceptably high for the planar
     assumption.

Value:

     A list of class 'rms.curv' with components 'pc' and 'ic' for
     parameter effects and intrinsic relative curvatures multiplied by
     sqrt(F), 'ct' and 'ci' for c^theta and c^iota (unmultiplied), and
     'C' the C-array as used in section 7.3.1 of Bates & Watts.

References:

     Bates, D. M, and Watts, D. G. (1988) _Nonlinear Regression
     Analysis and its Applications._ Wiley, New York.

See Also:

     'deriv3'

Examples:

     # The treated sample from the Puromycin data
     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

