design.reg.polynom: Design for Polynomial Regression

In OPDOE: Optimal Design of Experiments

Description

Determines locations and number of replications for a polynomial regression design.

Needs specification of order of polynom, borders of intervall and total number of measurements as input.

Usage

design.regression.polynom(a, b, k, n)
design.reg.polynom(...)

Arguments

a	lower bound of interval
b	upper bound of interval
k	order of polynom
n	total number of planned measurements
...	only used for call wrapper design.reg.polynom

Details

Uses Legendre Polynomials to determine the support points for the design:

If a=-1, b=1: places k +1 support points in [-1,1], located at the roots of (1-x^{2})\frac{dP_{k}(x)}{dx} where P_{k}(x) is the Legendre polynomial of degree k).

Distributes the n measurements almost equally over the support points.

Value

Object of class design.regression

Note

design.reg.polynom is a call wrapper for backward compatibility for design.regression.polynom

Author(s)

Dieter Rasch, Juergen Pilz, L.R. Verdooren, Albrecht Gebhardt

References

Dieter Rasch, Juergen Pilz, L.R. Verdooren, Albrecht Gebhardt: Optimal Experimental Design with R, Chapman and Hall/CRC, 2011

Examples

x <- design.reg.polynom(10, 100, 3, 45)
x

Example output

Loading required package: gmp

Attaching package: 'gmp'

The following objects are masked from 'package:base':

    %*%, apply, crossprod, matrix, tcrossprod

Loading required package: polynom
Design for a  polynomial model
Order: 3 
Interval: [ 10 , 100 ]

( 1.000e+01 3.488e+01 7.512e+01 1.000e+02 )
(        12        11        11        11 )

OPDOE documentation built on May 1, 2019, 8:45 p.m.