Model selection and cross validation in additive main effect and multiplicative interaction models

Crop Science

Volumn 43, Issue 3, 2003, Pages 865-873

  Dias, Carlos T Dos S ^a   Krzanowski, Wojtek J ^b  

^a UNIVERSITY OF SÃO PAULO   (Brazil)

^b Laver Building   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

AMMI; AMMI VISNAGA; EMBRYOPHYTA;

EID: 0038034110     PISSN: 0011183X     EISSN: None     Source Type: Journal    
DOI: 10.2135/cropsci2003.8650     Document Type: Article

References (42)

1. Cornelius, P.L. 1993. Statistical tests and retention of terms in the additive main effects and multiplicative interaction model for cultivar trials. Crop Sci. 33:1186-1193.
2. Cornelius, P.L., and J. Crossa. 1999. Prediction assessment of shrinkage estimators of multiplicative model for multi-environment cultivar trials. Crop Sci. 39:998-1009.
3. Cornelius, P.L., J. Crossa, and M.S. Seyedsadr. 1993. Tests and estimators of multiplicative models for variety trials, p. 156-166. In Proceedings of Annual Kansas State University Conference on Applied Statistics in Agriculture, 5th., Manhattan, KS. 25-27 Apr. 1993. Dep. of Statistics, Kansas State Univ., Manhattan, KS.
4. Cornelius, P.L, J. Crossa, and M.S. Seyedsadr. 1996. Statistical tests and estimators of multiplicative models for genotype-by-environment interaction, p. 199-234. In M.S. Kang and H.G. Gauch (ed.) Genotype-by-environment interaction. CRC Press, Boca Raton, FL.
5. Cornelius, P.L., M. Seyedsadr, and J. Crossa. 1992. Using the shifted multiplicative model to search for "separability" in crop cultivar trials. Theor. Appl. Genet. 84:161-172.
6. Crossa, J. 1990. Statistical analyses of multilocation trials. Adv. Agron. 44:55-85.
7. Crossa, J., P.L. Cornelius, and W. Yan. 2002. Biplot of linear-bilinear models for studying crossover genotype x environment interaction. Crop Sci. 42:619-633.
8. Crossa, J., P.N. Fox, W.H. Pfeifer, S. Rajaram, and H.G. Gauch. 1991. AMMI adjustment for satatistical analysis of na international wheat yield trial. Theor. Appl. Genet. 81:27-37.
9. Duarte, J.B., and R. Vencovsky. 1999. Interação genótipos x ambientes-uma introdução à análise "AMMI". Ribeirão Preto, S.P.
10. Eastment, H.T., and W.J. Krzanowski. 1982. Cross-validatory choice of the number of components from a principal component analysis. Technometrics 24:73-77.
11. Eberhart, S.A., and W.A. Russell. 1966. Stability parameters for comparing varieties. Crop Sci. 6:36-40.
12. Finlay, K.W., and G.N. Wilkinson. 1963. The analysis of adaptation in a plant-breeding programme. Austr. J. Agric. Res. 14:742-754.
13. Gabriel, K.R. 1978. Least squares approximation of matrices by additive and multiplicative models. J. Roy. Stat. Soc. Series B 40:186-196.
14. Gabriel, K.R. 2002. Le biplot-outil d'exploration de données multidimensionelles. Journal de la Societe Francaise de Statistique 143 (to appear).
15. Gauch, H.G. 1988. Model selection and validation for yield trials with interaction. Biometrics 44:705-715.
16. Gauch, H.G. 1992. Statistical analysis of regional yield trials; AMMI analysis of factorial designs. Elsevier Science, New York.
17. Gauch, H.G., and R.W. Zobel. 1988. Predictive and postdictive sucess of statistical analysis of yield trials. Theor. Appl. Genet. 76:1-10.
18. Gauch, H.G., and R.W. Zobel. 1996. AMMI analysis of yield trials. p. 85-122. In M.S. Kang and H.G. Gauch (ed.) Genotype by environment interaction. CRC Press, Boca Raton, FL.
19. Gollob, H.F. 1968. A statistical model which combines features of factor analytic and analysis of variance techniques. Psychometrika 33(1):73-115.
20. Good, I.J. 1969. Some applications of the singular decomposition of a matrix. Technometrics 11(4):823-831.
21. Jackson, J.E. 1991. A user's guide to principal components. Wiley and Sons, New York.
22. Jeffers, J.N.R. 1967. Two case studies in the application of principal component analysis. Appl. Stat. 16:225-236.
23. Kang, M.S., and R. Magari. 1996. New developments in selecting for phenotypic stability in crop breeding, p. 1-14. In M.S Kang and H.G. Gauch (ed.) Genotype by environment interaction. CRC Press, Boca Raton, FL.
24. Kendall, M.G. 1980. Multivariate analysis (2nd ed.). Charles Griffin & Co., London.
25. Krzanowski, W.J. 1979. Some exact percentage points of a statistic useful in analysis of variance and principal component analysis. Technometrics 21:261-263.
26. Krzanowski, W.J. 1987. Cross-validation in principal component analysis. Biometrics 43:575-584.
27. Krzanowski, W.J. 1988. Missing value imputation in multivariate data using the singular value decomposition of a matrix. Listy Biometycze-Biometrical Letters XXV (1,2):31-39.
28. Mandel, J. 1961. Non-additivity in two-way analysis of variance. J. Am. Statist. Assoc. 56:878-888.
29. Mandel, J. 1969. The partitioning of interaction in analysis of variance. J. Res. Int. Bur. Stand. Sect. B 73:309-328.
30. Mandel, J. 1971. A new analysis of variance model for non-additive data. Technometrics 13(1):1-18.
31. Piepho, H.P. 1994. Best linear unbiased prediction (BLUP) for regional yield trials: a comparison to additive main effects and multiplicative interaction (AMMI) analysis. Theor. Appl. Genet. 89:647-654.
32. Piepho, H.P. 1995. Robustness of statistical test for multiplicative terms in additive main effects and multiplicative interaction model for cultivar trial. Theor. Appl. Genet. 90:438-443.
33. Seyedsadr, M., and P.L. Cornelius. 1992. Shifted multiplicative models for nonadditive two-way tables. Commun. Stat. B Simul. Comp. 21:807-832.
34. Stone, M. 1974. Cross-validatory choice and assessment of statistical predictions (with Discussion). J. Roy. Stat. Soc. Series B 36:111-148.
35. Tukey, J.W. 1949. One degree of freedom for non-additivity. Biometrics 5:232-242.
36. Vargas, M.V., and J. Crossa. 2000. The AMMI analysis and graphing the biplot. CIMMYT, INT., Mexico.
37. Venter, J.H., and S.J. Steel. 1993. Simultaneous selection and estimation for the some zeros family of normal models. J. Statist. Computation Simulation. 45:129-146.
38. Weber, W.E., G. Wricke, and T. Westermann. 1996. Selection of genotypes and predictions performance and analysing genotype-by-environment interactions. p. 353-371. In M.S. Kang and H.G. Gauch (ed.) Genotype by environment interaction. CRC Press, Boca Raton, FL.
39. Wold, S. 1976. Pattern recognition by means of disjoint principal component models. Pattern Recognition 8:127-139.
40. Wold, S. 1978. Cross-validatory estimation of the number of components in factor and principal component models. Technometrics 20:397-405.
41. Yates, F., and W.G. Cochran. 1938. The analysis of groups of experiments. J. Agric. Sci. 28:556-580.
42. Zobel, R.W., M.J. Wright, and H.G. Gauch, Jr. 1988. Statistical analysis of a yield trial. Agron. J. 80:388-393.