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- Joint regression analysis applied to genotype stability evaluation over yearsPublication . Oliveira, Amilcar; Oliveira, Teresa; Mejza, Stanislaw; Mexia, João TiagoMost 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.
- Multiple regression models for lactation curvesPublication . Pereira, Marta S. P.; Oliveira, Teresa; Mexia, João TiagoSeveral methods have been developed in order to study lactation curves. However, the lactation curves are often not well adjusted since several factors affect milk production. The usual model used to describe a lactation curve is Wood’s Model, which generally uses a logarithmic transformation of an incomplete gamma curve to obtain least squares estimates of three constants: a - a scaling factor associated with average daily yield; b - associated with prepeak curvature; and c associated with post-peak curvature (Wood, 1976). Some disadvantages of Wood’s model are strongly connected with the overestimation of milk production at the beginning of lactation, with underestimation of the lactation peak: the self correlated residuals and highly correlated parameter estimates (Scott et al,1996). Fleischmann’s Method is usually used to estimate total milk production. This method generally overestimates actual yields up to peak lactation as well as yield during the period following the last measurement, but underestimates yields for other periods (Norman et al, 1999). The total milk yield estimate according to this method, considers a constant daily milk production between two records and equal to the mean of these two records, which does not describe the true variation of milk secretion during lactation. The mentioned disadvantages led us to consider the milk curve concept as a graphical representation of milk production described by mathematical models. In our work we considered a new approach using polynomial regression, one for each group. Polynomial curves were adjusted to daily milk records for each group and the respective hypo-graphic area was calculated to estimate total yields. An ANOVA to the comparison of these total yiels was carried out and the Scheffémultiple comparison method was applied. This approach greatly increases the power of the test, enabling work with smaller experiments, the reason for this increase being the replacement of classical replicates by time replicates, leading to a great increase in the degrees of freedom. Another advantage of this method is the use of a continuous process instead of an obligatory discrete process conversion. Differences between protein supplements and stocking rate were found using an adaptation of Scheffé's method. We concluded that a lower stocking rate and high protein content in supplement enable higher milk production.
- Analysis of residuals and adjustment in JRAPublication . Oliveira, Amilcar; Oliveira, Teresa; Mexia, João TiagoJoint 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.