Estimation of General Linear-Bilinear Models for two-way tables

Journal of Statistical Computation and Simulation

Volumn 58, Issue 4, 1997, Pages 287-322

  Cornelius, P L ^a   Seyedsadr, M S ^b  

^a UNIVERSITY OF KENTUCKY   (United States)

^b AMGEN INC   (United States)

Author keywords

Bilinear models; Genotype x environment interaction; Least squares estimates; Multiplicative models; Newton Raphson algorithm; Principal components; Singular value decomposition

Indexed keywords

EID: 0038867591     PISSN: 00949655     EISSN: None     Source Type: Journal    
DOI: 10.1080/00949659708811837     Document Type: Article

References (32)

1. Allen, D. M. (1971) Mean square error of prediction as a criterion for selecting variables. Technometrics, 13, 469-475.
2. Bartlett, M. S. (1937) Some examples of statistical methods of reasearch in agriculture and applied biology. Journal of the Royal Statistical Society Supplement. 4, 153-170.
3. Boik, R. J. (1986) Testing the rank of a matrix with applications to the analysis of interaction in ANOVA. Journal of the American Statistical Association, 81, 243-248.
4. Bradu, D. and Gabriel, K. R. (1978) The biplot as a diagnostic tool for models of two-way tables. Technometrics, 20, 47-68.
5. Corsten, L. C. A. and Van Eijnsbergen, A. C. (1972) Multiplicative effects in two-way analysis of variance. Statistica Neerlandica, 26, 61-68.
6. Cornelius, P. L. (1978) Empirical models for the analysis of unreplicated lattice-split-plot cultivar trials. Crop Science, 18, 627-633.
7. Cornelius, P. L. and Byars, J. (1976) Lattice designs for unreplicated yield trials of maize varieties at several plant densities. Crop Science, 16, 42-49.
8. Cornelius, P. L., Crossa, J. and Seyedsadr, M. S. (1996) Statistical tests and estimators of multiplicative models for genotype-by-environment interaction. In : Kang, M. S. and H. G. Gauch, Jr.(eds.), Genotype-by Environment Interaction. CRC Press, Boca Raton, FL, pp. 199-234.
9. Cornelius, P. L., Seyedsadr, M. and Crossa, J. (1992) Using the shifted multiplicative model to search for "separability" in crop cultivar trials. Theoretical and Applied Genetics, 84, 161-172.
10. Denis, J. B. and Gower, J. C. (1994) Asymptotic covariances for the parameters of biadditive models. Utilitas Mathematika, 46, 193-205.
11. Denis, J. B. and Gower, J. C. (1996) Asymptotic confidence regions for biadditive models: Interpreting genotype-environment interactions. Applied Statistics, 45, 479-493.
12. Gabriel, K. R (1978) Least squares approximation of matrices by additive and multiplicative models. Journal of the Royal Statistical Society, Series B, 40, 186-196.
13. Gauch, H. G., Jr. (1988) Model selection and validation for yield trials with interaction. Biometrics, 44, 705-715.
14. Gauch, H. G., Jr. and Zobel, R. W. (1988) Predictive and postdictive success of statistical analyses of yield trials. Theoretical and Applied Genetics, 76, 1-10.
15. Gollob, H. F. (1968) A statistical model which combines features of factor analytic and analysis of variance techniques. Psychometrika, 33, 73-115.
16. Goodman, L. A. and Haberman, S. J. (1990) The analysis of nonadditivity in two-way analysis of variance. Journal of the American Statistical Association, 85, 139-145.
17. Greenstadt, J. (1967) On the relative efficiencies of gradient methods. Mathematics of Computation, 21, 360-367.
18. Hegemann, V. and Johnson, D. E. (1976) Analyzing two-way data with interaction. Technometrics, 18, 273-281.
19. Johnson, D. E. and Graybill, F. A. (1972) An analysis of a two-way model with interaction and no replication. Journal of the American Statistical Association, 67, 862-868.
20. Mandel, J. (1961) Nonadditivity in two-way analysis of variance. Journal of the American Statistical Association, 56, 878-888.
21. Mandel, J. (1971) A new analysis of variance model for non-additive data. Technometrics, 13, 1-18.
22. Marasinghe, M. G. (1985) Asymptotic tests and Monte Carlo studies associated with the multiplicative interaction model. Communications in Statistics, A. Theory and Methods, 14, 2219-2231.
23. Marasinghe, M. G. and Johnson, D. E. (1981) Testing subhypotheses in the multiplicative interaction model. Technometrics, 23, 385-393.
24. Marasinghe, M. G. and Johnson, D. E. (1982) A test of incomplete additivity in the multiplicative interaction model. Journal of the American Statistical Association, 77, 869-877.
25. Rao, C. R. (1973) Linear Statistical Inference and Its Applications, Second ed. New York: John Wiley and Sons.
26. Schott, J. R. (1986) A note on the critical values in stepwise tests for multiplicative components of interaction. Communications in Statistics, A. Theory and Methods, 15, 1561-1570.
27. Seber, G. A. F. and Wild, C. J. (1989) Nonlinear Regression. New York: John Wiley and Sons.
28. Seyedsadr, M. and Cornelius, P. L. (1992) Shifted multiplicative models for nonadditive two-way tables. Communications in Statistics, B. Simulation and Computation, 21, 807-822.
29. Seyedsadr, M. S. and Cornelius, P. L. (1993) Hypothesis testing for components of the shifted multiplicative model for a nonadditive two-way table. Communications in Statistics, B. Simulation and Compilation, 22, 1065-1078.
30. Steel, R. G. D. and Torrie, J. H. (1980) Principles and Procedures of Statistics. Second ed. New York: McGraw Hill Book Co.
31. Yochmowitz, M. G. and Cornell, R. G. (1978) Stepwise tests for multiplicative components of interaction. Technometrics, 20, 79-84.
32. Zobel, R. W., Wright, M. J. and Gauch, H. G., Jr. (1988) Statistical analysis of a yield trial. Agronomy Journal, 80, 388-393.