Fractional polynomial response surface models

Steven G. Gilmour; Luiza A. Trinca

doi:10.1198/108571105X29029

Fractional polynomial response surface models

Steven G. Gilmour^*, Luiza A. Trinca

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

9 Citations (Scopus)

Abstract

Second-order polynomial models have been used extensively to approximate the relationship between a response variable and several continuous factors. However, sometimes polynomial models do not adequately describe the important features of the response surface. This article describes the use of fractional polynomial models. It is shown how the models can be fitted, an appropriate model selected, and inference conducted. Polynomial and fractional polynomial models are fitted to two published datasets, illustrating that sometimes the fractional polynomial can give as good a fit to the data and much more plausible behavior between the design points than the polynomial model.

Original language	English
Pages (from-to)	50-60
Number of pages	11
Journal	JOURNAL OF AGRICULTURAL BIOLOGICAL AND ENVIRONMENTAL STATISTICS
Volume	10
Issue number	1
DOIs	https://doi.org/10.1198/108571105X29029
Publication status	Published - Mar 2005

Keywords

Box-Tidwell transformations
Empirical modeling
Nonlinear regression
Parametric modeling
Response surface methodology

Access to Document

10.1198/108571105X29029

Cite this

@article{649138aff9564c1996a88dc6a80f05ac,

title = "Fractional polynomial response surface models",

abstract = "Second-order polynomial models have been used extensively to approximate the relationship between a response variable and several continuous factors. However, sometimes polynomial models do not adequately describe the important features of the response surface. This article describes the use of fractional polynomial models. It is shown how the models can be fitted, an appropriate model selected, and inference conducted. Polynomial and fractional polynomial models are fitted to two published datasets, illustrating that sometimes the fractional polynomial can give as good a fit to the data and much more plausible behavior between the design points than the polynomial model.",

keywords = "Box-Tidwell transformations, Empirical modeling, Nonlinear regression, Parametric modeling, Response surface methodology",

author = "Gilmour, {Steven G.} and Trinca, {Luiza A.}",

year = "2005",

month = mar,

doi = "10.1198/108571105X29029",

language = "English",

volume = "10",

pages = "50--60",

journal = "JOURNAL OF AGRICULTURAL BIOLOGICAL AND ENVIRONMENTAL STATISTICS",

issn = "1085-7117",

publisher = "Springer New York",

number = "1",

}

TY - JOUR

T1 - Fractional polynomial response surface models

AU - Gilmour, Steven G.

AU - Trinca, Luiza A.

PY - 2005/3

Y1 - 2005/3

N2 - Second-order polynomial models have been used extensively to approximate the relationship between a response variable and several continuous factors. However, sometimes polynomial models do not adequately describe the important features of the response surface. This article describes the use of fractional polynomial models. It is shown how the models can be fitted, an appropriate model selected, and inference conducted. Polynomial and fractional polynomial models are fitted to two published datasets, illustrating that sometimes the fractional polynomial can give as good a fit to the data and much more plausible behavior between the design points than the polynomial model.

AB - Second-order polynomial models have been used extensively to approximate the relationship between a response variable and several continuous factors. However, sometimes polynomial models do not adequately describe the important features of the response surface. This article describes the use of fractional polynomial models. It is shown how the models can be fitted, an appropriate model selected, and inference conducted. Polynomial and fractional polynomial models are fitted to two published datasets, illustrating that sometimes the fractional polynomial can give as good a fit to the data and much more plausible behavior between the design points than the polynomial model.

KW - Box-Tidwell transformations

KW - Empirical modeling

KW - Nonlinear regression

KW - Parametric modeling

KW - Response surface methodology

UR - http://www.scopus.com/inward/record.url?scp=16344380465&partnerID=8YFLogxK

U2 - 10.1198/108571105X29029

DO - 10.1198/108571105X29029

M3 - Article

AN - SCOPUS:16344380465

SN - 1085-7117

VL - 10

SP - 50

EP - 60

JO - JOURNAL OF AGRICULTURAL BIOLOGICAL AND ENVIRONMENTAL STATISTICS

JF - JOURNAL OF AGRICULTURAL BIOLOGICAL AND ENVIRONMENTAL STATISTICS

IS - 1

ER -

Fractional polynomial response surface models

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this