Joint Regression Analysis and Completed Joint Regression Analysis

Abstract

Joint Regression Analysis (JRA) is a well known technique for the joint analysis of series of cultivar comparison trials. Formerly these trials were usually designed as complete randomized block designs. Now, the -designs are the mostly used. To perform a JRA, a linear regression is adjusted for each cultivar. The dependent variable is continuous (usually the yield) and there is a non observable regressor, the environmental index, which measures the productivity of the plots in which the field trials are divided. An algorithm, the zig-zag, was developed in order to adjust both the regression coefficients and the environmental indexes. Thus the adjusted regression lines, when represented simultaneously, define a convex polygonal, the upper contour, which may be used for cultivar comparison and selection. The cultivars whose adjusted regressions partake in the upper contour will be called dominant. For each dominant cultivar there will be a dominance range and the non dominant cultivars should be compared with the dominant ones within their dominance ranges. In this chapter we intend to apply the JRA to an oat breeding program and introduce the completed JRA which may be used when additional information, besides yields (such as a density measure which represents the economic value), is available for all or for a fraction of plots. When this additional information is available, by applying the completed JRA more accurate results regarding the cultivar selection are obtained.