dy.d_: Partial Derivative dy/d[wrt]

Description Usage Arguments Value Note Author(s) References Examples

View source: R/dy_d_wrt.R

Description

Returns the numerical partial derivate of y with respect to [wrt] any regressor for a point of interest. Finite difference method is used with NNS.reg estimates as f(x+h) and f(x-h) values.

Usage

1
2
3
dy.d_(x, y, wrt, eval.points = "median", order = NULL, stn = 0.99,
  h = 0.05, n.best = NULL, mixed = FALSE, plot = FALSE,
  noise.reduction = "mean")

Arguments

x

a numeric matrix or data frame.

y

a numeric vector with compatible dimsensions to x.

wrt

integer; Selects the regressor to differentiate with respect to.

eval.points

numeric or options: ("mean", median", "last"); Regressor points to be evaluated. (eval.points="median") (default) to find partial derivatives at the median of every variable. Set to (eval.points="last") to find partial derivatives at the last value of every variable. Set to (eval.points="mean") to find partial derivatives at the mean value of every variable. Set to (eval.points="all") to find partial derivatives at every observation.

order

integer; NNS.reg "order", defaults to NULL.

stn

numeric [0,1]; Signal to noise parameter, sets the threshold of NNS.dep which reduces "order" when (order=NULL). Defaults to 0.99 to ensure high dependence for higher "order" and endpoint determination.

h

numeric [0,...]; Percentage step used for finite step method. Defaults to h=.05 representing a 5 percent step from the value of the regressor.

n.best

integer; Sets the number of closest regression points to use in estimating finite difference points in NNS.reg. NULL (default) Uses ceiling(sqrt(ncol(x))).

mixed

logical; FALSE (default) If mixed derivative is to be evaluated, set (mixed=TRUE). Only for single valued eval.points.

plot

logical; FALSE (default) Set to (plot=TRUE) to view plot.

noise.reduction

the method of determing regression points options: ("mean","median","mode","off"); In low signal to noise situations, (noise.reduction="median") uses medians instead of means for partitions, while (noise.reduction="mode") uses modes instead of means for partitions. (noise.reduction="off") allows for maximum possible fit in NNS.reg. Default setting is (noise.reduction="mean").

Value

Returns:

Retuns a vector of partial derivatives when (eval.points="all").

Note

For known function testing and analysis, regressors should be transformed via expand.grid to fill the dimensions with (order="max"). Example provided below.

Author(s)

Fred Viole, OVVO Financial Systems

References

Viole, F. and Nawrocki, D. (2013) "Nonlinear Nonparametric Statistics: Using Partial Moments" http://amzn.com/1490523995

Examples

1
2
3
4
5
6
7
8
9
set.seed(123);x_1<-runif(100);x_2<-runif(100); y<-x_1^2*x_2^2
B=cbind(x_1,x_2)
## To find derivatives of y wrt 1st regressor
dy.d_(B,y,wrt=1,eval.points=c(.5,.5))

## Known function analysis: [y = a^2 * b^2]
x_1<-seq(0,1,.1);x_2<-seq(0,1,.1)
B=expand.grid(x_1,x_2); y<-B[,1]^2*B[,2]^2
dy.d_(B,y,wrt=1,eval.points=c(.5,.5),order="max")

NNS documentation built on Oct. 1, 2017, 1:02 a.m.