Relative Curvature Measures for Non-Linear Regression

Usage

rms.curv(obj, fit.val=<<see below>>, data=obj$call$data)

Arguments

obj Fitted model object of class nls. The model must be fitted using the default algorithm.
fit.val An optional fitted values vector with the gradient matrix and Hessian array as attributes, as produced by the model function obtained by using the function deriv3 of David Smith. Extracted from the fitted model object by default.
data Optional data frame for variables. Extracted from the fitted model object call (if any data frame is specified) by default.

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.

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

### Not usable in R
> # 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(vel ~ 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 


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