THE BEST LINEAR UNBIASED PREDICTORS (BLUP) FOR DESIGNS TWO AND FOUR OF GRIFFING

Abstract

The parameter estimation in diallel cross experiments is obtained on the basis of a fixed effect model; however, in most applications a mixed effect model should be used, because of the random nature of the general and specific combining abilities; therefore, if such situation is ignored, and if the estimation technique for a fixed effect model is used, unbiased estimators are produced, however, they are not of minimum variance. In this paper, under the treatment designs two and four of Griffing in a completely randomized block design, the best linear unbiased predictors (BLUP) for the effects of general combining ability are obtained, by using the methodology generated for the estimation of random effects in the mixed effect model. A computational algorithm in SAS-IML for obtaining the BLUP is also presented.