# rms.curv

##### Relative Curvature Measures for Non-Linear Regression

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

- Keywords
- nonlinear

##### 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

##### Examples

```
# NOT RUN {
# 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
# }
```

*Documentation reproduced from package MASS, version 7.3-51.4, License: GPL-2 | GPL-3*