Summary
The shifted multiplicative model (SHMM) is used in an exploratory step-down method for identifying subsets of environments in which genotypic effects are “separable” from environmental effects. Subsets of environments are chosen on the basis of a SHMM analysis of the entire data set. SHMM analyses of the subsets may indicate a need for further subdivision and/or suggest that a different subdivision at the previous stage should be tried. The process continues until SHMM analysis indicates that a SHMM with only one multiplicative term and its “point of concurrence” outside (left or right) of the cluster of data points adequately fits the data in all subsets. The method is first illustrated with a simple example using a small data set from the statistical literature. Then results obtained in an international maize (Zea mays L.) yield trial with 20 sites and nine cultivars is presented and discussed.
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References
Azzalini A, Cox DR (1984) Two new tests associated with analysis of variance. J R Statist Soc B 46:335–343
Baker RJ (1988) Tests for crossover genotype-environmental interactions. Can J Plant Sci 68:405–410
Baker RJ (1990) Crossover genotype-environmental interaction in spring wheat. In: Kang MS (ed) Genotype-by-environment interaction and plant breeding. Department of Agronomy, Louisiana Agric Exp Stn, LSU Agric Center, Baton Rouge, La.
Boik RJ (1985) A new approximation to the distribution function of the studentized maximum root. Commun in Stat B Simul Comput 14:759–767
Gauch HG Jr (1988) Model selection and validation for yield trials with interaction. Biometrics 44:705–715
Gauch HG Jr, Zobel RW (1988) Predictive and postdictive success of statistical analyses of yield trials. Theor Appl Genet 76:1–40
Gregorius H-R, Namkoong G (1986) Joint analysis of genotypic and environmental effects. Theor Appl Genet 12:413–422
Goodman LA, Haberman ST (1990) The analysis of nonadditivity in two-way analysis of variance. J Am Stat Assoc 85:139–145
Johnson DE (1976) Some new multiple comparison procedures for the two-way AOV model with interaction. Biometrics 32:929–934
Johnson DE, Graybill FA (1972) An analysis of a two-way model with interaction and no replication. J Am Stat Assoc 67:862–868
Mandel J (1961) Nonadditivity in two-way analysis of variance. J Am Stat Assoc 56:878–888
Mandel J (1971) A new analysis of variance model for nonadditive data. Technometrics 13:1–8
Marasinghe MG (1985) Asymptotic tests and Monte Carlo studies associated with the multiplicative interaction model. Commun Stat A Theory Methods 14:2219–2231
Schott JR (1986) A note on the critical values used in stepwise tests for multiplicative components of interaction. Commun Stat A Theory Methods 15:1561–1570
Seyedsadr SM (1987) Statistical and computational procedures for estimation and hypothesis testing with respect to the shifted multiplicative model. Ph.D thesis, University of Kentucky
Seyedsadr M, Cornelius PL (1991a) Functions approximating the expectations and standard deviations of sequential sums of squates in the shifted multiplicative model for a two-way table. University of Kentucky. Department of Statistics Technical Report 322
Seyedsadr M, Cornelius PL (1991b) Hypothesis testing for components of the shifted multiplicative model for a nonadditive two-way table. University of Kentucky. Department of Statistics Technical Report 315
Seyedsadr M, Cornelius PL (1991c) Shifted multiplicative models for nonadditive two-way tables. Commun Stat B Simul Comput 2/(3): (in press)
Snee RD (1982) Nonadditivity in a two-way classification: Is it interaction or nonhomogeneous variance? J Am Stat Assoc 77:515–518
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Communicated by A. R. Hallauer
Journal Article No. 91-3-171 of the Kentucky Agricultural Experiment Station published with the approval of the Director
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Cornelius, P.L., Seyedsadr, M. & Crossa, J. Using the shifted multiplicative model to search for “separability” in crop cultivar trials. Theoret. Appl. Genetics 84, 161–172 (1992). https://doi.org/10.1007/BF00223996
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DOI: https://doi.org/10.1007/BF00223996