To evaluate variety sensitivity, several authors have used the observed environmental mean of crop yield as an explanatory regression variable. This technique enables the performance of varieties to be compared at a given expected environmental yield level. A disadvantage, however, is that it leads to biased estimators of the variety parameters. I therefore propose that the observed environmental mean be replaced by the conditional mean given the environment. In variety trial data, the environments are randomly chosen, so the proposed conditional mean is an unobservable random variable. To estimate its realized values simultaneously with the other unknown elements used in modeling the data, I propose a procedure that combines the EM algorithm for incomplete data with the conventional maximum likelihood estimation of mixed model parameters. Finnish statutory variety trial data on barley are used to show that regression on the observed environmental mean and regression on the conditional mean give significantly different practical results. Because the latter technique yields consistent maximum likelihood estimators, its use is therefore recommended.

Key Words
Adaptation; Conditional expectation; EM algorithm; Maximum likelihood estimation; Mixed model; Regression on conditional mean; Statutory variety trials; Variety testing.

Jukka Öfversten is Head of Data and Information Services, Agricultural Research Centre, Fin-31600 Jokioinen, Finland.