Some practical advice on polynomial regression analysis from blocked response surface designs

Communications in Statistics - Theory and Methods

Volumn 29, Issue 9-10, 2000, Pages 2157-2180

  Gilmour, Steven G ^a   Trinca, Luzia A ^b  

^a QUEEN MARY UNIVERSITY OF LONDON   (United Kingdom)

^b SÃO PAULO STATE UNIVERSITY UNESP   (Brazil)

Author keywords

Industrial experiments; Inter block analysis; Lack of fit; Linear mixed model; Prediction; Pure error; Second order model

Indexed keywords

EID: 0003073952     PISSN: 03610926     EISSN: None     Source Type: Journal    
DOI: 10.1080/03610920008832601     Document Type: Article

References (22)

1. Atkinson, A. C. and Donev, A. N. (1989). "The construction of exact D-optirnum experimental designs with application to blocking response surface designs", Biometrika, 76, 515-526.
2. Bailey, R. A. (1981). "A unified approach to design of experiments", J. Roy. Statist. Soc., Series A, 144, 214-223.
3. Box, G. E. P. and Draper, N. R. (1987). Empirical Model Building and Response Surfaces, New York: Wiley.
4. Cook, R. D. and Nachtsheim, C. J. (1989). "Computer-aided blocking of factorial and response surface designs", Technometrics, 31, 339-346.
5. Draper, N. R. and Smith, H. (1998). Applied Regression Analysis, 3rd edition, New York: Wiley.
6. Genstat 5 Committee (1993). Genstat® 5 Release 3 Reference Manual, Oxford: Clarendon Press.
7. Gilmour, A. R., Thompson, R. and Cullis, B. R. (1995). "An efficient algorithm for REML estimation in linear mixed models", Biometrics, 51, 1440-1450.
8. Hinkelmann, K. and Kempthorne, O. (1994). Design and Analysis of Experiments, volume 1, New York: Wiley.
9. Kacker, R. N. and Harville, D. A. (1981). "Unbiasedness of two-stage estimation and prediction procedures for mixed linear models", Communs Statist. Theory Meth., 10, 1249-1261.
10. Kacker, R. N. and Harville, D. A. (1984). "Approximations for standard errors of estimators of fixed and random effects in mixed linear models", J. Am. Statist. Ass., 79, 853-862.
11. Kenward, M. G. and Roger, J. H. (1997). "Small sample inference for fixed effects from restricted maximum likelihood", Biometrics, 53, 983-997.
12. Khuri, A. I. (1992). "Response surface models with random block effects", Technometrics, 34, 26-37.
13. Khuri, A. I. (1994). "Effect of blocking on the estimation of a response surface", J. Appl. Statist., 21, 305-316.
14. Khuri, A. I. and Cornell, J. A. (1996). Response Surfaces, 2nd edition, New York: Dekker.
15. Littell, R. C., Milliken, G. A., Stroup, W. W. and Wolfinger, R. D. (1996). SAS® System for Mixed Models, Cary, NC: SAS Institute Inc.
16. Mead, R. (1988). The Design of Experiments, Cambridge: Cambridge University Press.
17. Myers, R. H. and Montgomery, D. C. (1995). Response Surface Methodology, New York: Wiley.
18. Rao, P. S. R. S. (1997). Variance Components Estimation, London: Chapman & Hall.
19. SAS Institute (1990). SAS®/STAT Users Guide, 4th edition, volume 2, Cary: SAS Institute Inc.
20. Trinca, L. A. and Gilmour, S. G. (1998). "Variance dispersion graphs for comparing blocked response surface designs", J. Qual. Technol., 30, 314-327.
21. Trinca, L. A. and Gilmour, S. G. (1999). "Difference variance dispersion graphs for comparing response surface designs with applications in food technology", Appl. Statist., 48, 441-455.
22. Trinca, L. A. and Gilmour, S. G. (2000). "An algorithm for arranging response surface designs in small blocks", Comput. Statist. Data Anal., in press.