Mixed models and experimental design for variety trials
by
G. Peter Clarke
Department of Agriculture, Western Australia

Typically, a mixed model contains unknown parameters associated with fixed effects, and also those associated with random effects (for example variance components). The general problem is to find a design with optimal properties for estimation of both parameter sets. This paper focuses on the more restricted problem commonly faced in variety trials, where genetic effects may be fixed or random and spatial effects are measured by auto-regressive correlations and maybe trend terms. A popular approach historically has been to use designs with good neighbourhood balance or to use incomplete blocking, in one or two directions. This paper presents a brief historical review and a comparison among some designs using uniformity trial data. Difficult issues of the joint modelling of random model terms and distributions induced by randomization are examined.

Date received: September 3, 2001