R: Relative Curvature Measures for Non-Linear Regression

rms.curv {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. 253ff

### 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^θ and c^ι (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

[Package MASS version 7.3-35 Index]