Vol: 32 Page: 141

Authors:
Wiesław Mądry

Title:
 A mixed joint regression model with unequal residual variances

Language: Polish

Keywords:
mixed models of joint regression
model of Eberhart-Russel-Shukla
stability analysis
minimum least square method
REML method
comparison of statistical tools

Summary:
The objective of the paper is to present theoretical backgrounds and statistical tools for a mixed joint regression model with unequal residual variances called model of Eberhart-Russell-Shukla (E-R-S model). Estimators and tests, obtained using both ordinary approximate minimum least squares method (OALS) for balanced (complete) data of two-way genotype*environment classification, for stability measures (parameters) in the model are considered. Some general remarks on REML tools in this model is presented. Comparable evaluating statistical efficiency of the tools obtained by each of the methods is discussed. In the discussion knowledge on known statistical properties of the tools and empirical knowledge on planning series of variety trials and variation of considered effects in the model were taken into account. OALS method enables us to obtain relatively simple estimators and tests for all stability measures in the model E-R-S. These statistical tools have rather good properties if the number of genotypes I would be large and environmental variance σe2 would substantially dominate variances all other random effects in the model. In such situations and when the number of environments J would be small (especially if J<≈10), properties of the OALS tools in the model E-R-S could be better than ones of REML tools. REML estimators and tests are known to have asymptotically optimal properties for the large number of environments. Thus, in the model E-R-S under large number of environments, especially if J>I (these occur rather rarely in practice), properties of the REML tools could be better then properties of the OALS ones. Theoretically proved advantages and disadvantages of the OALS and REML tools in the model E-R-S and their usefulness in different experimental situations are based in the paper on asymptotic properties of them. Then, sufficient evaluation of their behaviour in practice, showing practical preferences of OALS and REML tools, needs both simulation and experimental studies.