Maximum Likelihood and L₂ Environmental Indices in Joint Regression Analysis

This paper describes an iterative analysis of incomplete genotype × environment data. L₂ environmental indices were introduced to enable the use of Joint Regression Analysis (JRA) in analyzing experiments with incomplete blocks. We now show how, once normality of yields is assumed, the introduction of L2 environmental indices provides a theoretical framework for Joint Regression Analysis. Using this framework, maximum likelihood estimators are obtained and likelihood ratio tests are derived. It is noted that the technique allows unequal weighting of data, and the special case of complete blocks is discussed.