A study on AMMI model and its biplots

AMMI model has been shown to be a useful technique to capture the non-linear interactions, when Joint Regression technique fails to perceive important effects in studies of G x E interaction. The application of biplots to draw reliable stability conclusions is subject to great interest when significant proportion of interaction explained is by the first or first two PCA axes. In the present study some stability measures are proposed which are equivalent to biplot with first PCA axis and biplot with first two PCA axes for rankingpurposes. The reliability of stability conclusions improves with increase in thenumber of PCA axes, which has been exploited while proposing the new measure of stability. The proposed stability measure Wi(AMMI) which accomodates all possible PCA axes is shown equivalent to Wrick's ecovalence. The proposed stability measures are precise in the order in which amount of information increases. The ranking ability of Wi(AMMI) is found to be superior to other measures when there are missing cells in the data; showing some kind of robustness to the missing data. the ranking abilities of different stability measures are found to be better in the proposed EM-AMMI with random environments as compared to EM-AMMI of Gauch and Zobel [6] and Modified EM-AMMI of Bajpai [1] revealing its superiority over the other two methodologies. Thus, the stability measure Wi(AMMI) using EM-AMMI with random environments methodology may be recommended and may be employed toderive stability conclusions from AMMI model when some cells in two-way table are missing. EM-AMMI enriched technique has been proposed for Joint Regression to deal with incomplete data. This technique enables us to fit not only the main effects but also the interactions for the missing cells.