curvature: Calculate (IE) Intrinsic curvature and (PE) Parameter...

In nlr: Nonlinear Regression Modelling using Robust Methods

Description

IE and PE are measures to identify the linear approximation of nonlinear model is appropriate or no. This function may not be called explicitly by user.

Usage

curvature(gradient, hessian, sigma)

Arguments

gradient	n by p gradient of fited model.
hessian	n by p by p array of hessian for the nonlinear model.
sigma	estimated standard deviation.

Details

Gauss Newton method of estimation is based on linear approximation to nonlinear model. The linear approximation to function might not be appropriate. PE and IE is used to identify the parameter effect and intrinsic effect of model. Big values represent the linear approximation to nonlinear model is not correct.

Value

List of curvature values.

• pe: Parameter Effect curvature.

• int: Intrinsic effect curvature.

• a: A matrix.

• cutf: cut of point

  1/√{F(.95,p,n-p)}

  , if PE or IE be biger than cut of point then either of them has larg curvature.

Note

curvature is a model checking tool. From the OLS estimate output included carvature that can be accessed by curvature slot of the output object, therefore do not need to be called explicitly by user.

Author(s)

Hossein Riazoshams, May 2014. Email: [e-mail] URL http://www.riazoshams.com/nlr/

References

Bates, D.M., and Watts, D. G. (1980). Relative curvature measures of nonlinearity, J. R. statistic. Ser. B 42: 1-25.

Examples

 crbdt<-list(xr=nlr::carbon$year,yr=nlr::carbon$co2)
 ScalExp<- convexpr2nlform(yr ~ p1 + exp(-(p2 - p3 * xr)),
                        selfStart=function(data){
                            y1 <-as.double(data$yr)
                            p1<-min(y1)
                            y<-log(y1-p1+10*.Machine$double.eps)
                            x<-as.double(data$xr)
                            b1<-lm(y~x)
                            p2<- -b1$coefficients[1]
                            p3<- b1$coefficients[2]
                            return(list(p1=p1,p2=p2,p3=p3))
                        },
                        name="Scaled Exp convex",
                        start=list(p1=700,p2=21,p3=0.01)
)
 carbon.ols <- nlr(formula=ScalExp, data=crbdt, 
                  control=nlr.control(method="OLS"))
carbon.ols$curvature                  

nlr documentation built on July 31, 2019, 5:09 p.m.