### Abstract

A graphical approach is proposed for the purpose of assessing the overall prediction capability of a nonlinear design inside a region of interest R. A visual description is given of the behavior of the mean-squared error of prediction throughout the region R. More explicitly, for each of several concentric surfaces inside R, quantile plots of the so-called estimated scaled mean-squared error of prediction (ESMSEP) are obtained. In addition, when the number of control (input) variables in the associated model is equal to one, plots of the maximum and minimum of the scaled mean-squared error of prediction (SMSEP) over a subset of the model's parameter space are developed. The latter plots are primarily used to compare several nonlinear designs. Two examples are presented to demonstrate the usefulness of the proposed plots.

Original language | English |
---|---|

Pages (from-to) | 433-443 |

Number of pages | 11 |

Journal | Computational Statistics and Data Analysis |

Volume | 27 |

Issue number | 4 |

Publication status | Published - 1998 Jun 5 |

Externally published | Yes |

### Fingerprint

### Keywords

- Nonlinear designs
- Prediction bias
- Prediction capability
- Quantile plots
- Scaled mean-squared error of prediction

### ASJC Scopus subject areas

- Statistics and Probability
- Computational Mathematics
- Computational Theory and Mathematics
- Applied Mathematics

### Cite this

*Computational Statistics and Data Analysis*,

*27*(4), 433-443.

**A graphical approach for evaluating and comparing designs for nonlinear models.** / Khuri, André I.; Lee, Juneyoung.

Research output: Contribution to journal › Article

*Computational Statistics and Data Analysis*, vol. 27, no. 4, pp. 433-443.

}

TY - JOUR

T1 - A graphical approach for evaluating and comparing designs for nonlinear models

AU - Khuri, André I.

AU - Lee, Juneyoung

PY - 1998/6/5

Y1 - 1998/6/5

N2 - A graphical approach is proposed for the purpose of assessing the overall prediction capability of a nonlinear design inside a region of interest R. A visual description is given of the behavior of the mean-squared error of prediction throughout the region R. More explicitly, for each of several concentric surfaces inside R, quantile plots of the so-called estimated scaled mean-squared error of prediction (ESMSEP) are obtained. In addition, when the number of control (input) variables in the associated model is equal to one, plots of the maximum and minimum of the scaled mean-squared error of prediction (SMSEP) over a subset of the model's parameter space are developed. The latter plots are primarily used to compare several nonlinear designs. Two examples are presented to demonstrate the usefulness of the proposed plots.

AB - A graphical approach is proposed for the purpose of assessing the overall prediction capability of a nonlinear design inside a region of interest R. A visual description is given of the behavior of the mean-squared error of prediction throughout the region R. More explicitly, for each of several concentric surfaces inside R, quantile plots of the so-called estimated scaled mean-squared error of prediction (ESMSEP) are obtained. In addition, when the number of control (input) variables in the associated model is equal to one, plots of the maximum and minimum of the scaled mean-squared error of prediction (SMSEP) over a subset of the model's parameter space are developed. The latter plots are primarily used to compare several nonlinear designs. Two examples are presented to demonstrate the usefulness of the proposed plots.

KW - Nonlinear designs

KW - Prediction bias

KW - Prediction capability

KW - Quantile plots

KW - Scaled mean-squared error of prediction

UR - http://www.scopus.com/inward/record.url?scp=0032486067&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0032486067&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0032486067

VL - 27

SP - 433

EP - 443

JO - Computational Statistics and Data Analysis

JF - Computational Statistics and Data Analysis

SN - 0167-9473

IS - 4

ER -