On some results of C. Radhakrishna Rao applied to the analysis of multi-environment variety trials
by
Tadeusz Calinski
Department of Mathematical and Statistical Methods, Agricultural University of Poznan, Poland

The analysis of results of a series of experiments repeated at several environments with the same set of plant varieties (genotypes) is usually based on a mixed effects model. Because of possible different responses of the varieties to variable environmental conditions, the standard mixed model for that analysis becomes questionable. Therefore, a more general mixed model is to be considered. However, in its most general form it involves usually a large number of variance and covariance components to be estimated. This causes computational problems, even when using advanced algorithms, unless some simplifying structures are imposed on the general covariance matrix. It appears, that one can avoid these problems when adopting a classic method proposed by Rao (1972, Section 6). This method has been explored recently by Calinski et al. (2005).

The purpose of the present paper is to show the use of that and some other theoretical results of C. Radhakrishna Rao in detail.

Key words:

Estimation; More general mixed effects model; Series of experiments.

References:

Calinski, T., Czajka, S., Kaczmarek, Z., Krajewski, P., and Pilarczyk, W. (2005). Analyzing multi-environment variety trials using randomization-derived mixed models Biometrics 61, 448-455.

Rao, C. R. (1972). Estimation of variance and covariance components in linear models. Journal of the American Statistical Association 67, 112-115.

Date received: June 30, 2006