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- Analysis of residuals and adjustment in JRAPublication . Oliveira, Amilcar; Mexia, João Tiago; Oliveira, Teresa A.Joint Regression Analysis (JRA) is based in linear regression applied to yields, adjusting one linear regression per cultivar. The environmental indexes in JRA correspond to a non observable regressor which measures the productivity of the blocks in the field trials. Usually zig-zag algorithm is used in the adjustment. In this algorithm, minimizations for the regression coefficients alternate with those for the environmental indexes. The algorithm has performed very nicely but a general proof of convergence to the absolute minimum of the sum of squares of residues is still lucking. We now present a model for the residues that may be used to validate the adjustments carried out by the zig-zag algorithm.
- Joint regression analysis applied to genotype stability evaluation over yearsPublication . Oliveira, Amilcar; Mejza, Stanislaw; Mexia, João Tiago; Oliveira, Teresa A.Most genotype differences connected with yield stability are due to genotype environment interaction. The presence and dimension of this interaction are the factors that determine the performance of genotypes in distinct environments. The environmental factors, like annual rainfall, temperature, diseases or soil fertility, can only explain part of this interaction. Many statistical tools have been developed with the aim to explain the information contained in the GE interaction data matrix. In our work we use the Joint Regression Analysis (JRA), the Zig-Zag Algorithm to estimate the regression coefficients and the multiple comparison tests of Scheffé, Tukey and Bonferroni. We point out not just the limitations of the JRA when used year by year, but also genotype selection advantage from general JRA over years. Data of the Portuguese Plant Breeding Board were used to carry the year and over years analyses of yielding stability of 22 different genotypes of oat (Avena sativa L.) at six different locations in the years 2002, 2003 and 2004.