Overview of Joint Regression Analysis

Abstract

Joint Regression Analysis (JRA) has been widely used to compare cultivars. In this technique a linear regression is adjusted per cultivar. The slope of each regression measures the ability of the corresponding cultivar to answer to variations in productivity. Presently we are manly interested in cultivars with better responses to high productivity. To extend the application range of JRA to connected series of designs in incomplete blocks, thus going beyond the classic case of series of randomized blocks, we introduced the L2 environmental indexes. Nowadays, comparison trials for cultivars are mainly ®-designs, which have in- complete blocks. Moreover, the introduction of these indexes: enables the inte- gration of JRA into the statistical inference for normal models; allows a better approach to the study of speci¯c interactions. These interactions occur when a cultivar behaves abnormally well or abnormally badly, for a (location , year) pair. We will also, use JRA to obtain and update of lists of recommended cultivars. Appropriate algorithms have been developed for the adjustments: the zig zag algorithm and the double minimization algorithm.