Abstract
In the interpretation of the geometry of second-order response surface models, standard errors and confidence intervals for the eigenvalues of the second-order coefficient matrix play an important role. In this article, we propose a new method for estimating the standard errors, and hence approximate confidence intervals, of these eigenvalues. The method is simple in both concept and execution. It involves the refitting of a full quadratic model after rotating the coordinate system to coincide with the canonical axes. The estimated standard errors of the pure quadratic terms from this refitting are then used as approximate standard errors of the eigenvalues. Because this approach is based on the canonical form, it is geometrically intuitive and easily taught. Our method is intended as a way for practitioners to get quick estimates of the standard errors of the eigenvalues. In our justification of the approach, we show that it is equivalent to using the delta method proposed by Carter, Chinchilli, and Campbell.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 238-246 |
| Number of pages | 9 |
| Journal | Technometrics |
| Volume | 38 |
| Issue number | 3 |
| DOIs | |
| State | Published - Aug 1996 |
Funding
This work was supported by a grant from the Alfred P. Sloan Foundation and the National Science Foundation (EEC 8721545). We thank Douglas Bates, George Box, Howard Fuller, Ilya Gertsbakh, Spencer Graves, and John Peterson for helpful discussions while writing this article. We also thank the Center for Quality and Productivity Improvement’s reports committee, the Technometricse ditors, and referees for helpful comments on an earlier draft.
Keywords
- Canonical analysis
- Confidence intervals
- Delta method
- Response surface methodology
ASJC Scopus subject areas
- Statistics and Probability
- Modeling and Simulation
- Applied Mathematics