Otimização de fatores para a clonagem em coffea arábica utilizando correlação canônica em experimentos rotacionais subdivisíveis em blocos

Abstract

The blocking of rotational designs depending on the number of factors and repetitions, can result in almost orthogonal designs and in this situation, there is an alternative to the use of optimal designs, which minimizes the variance of the estimates of the parameters of the model to be adopted. In a multivariate approach, the consideration of the experimental structure becomes more complex, since covariance matrices between factor levels must be analyzed. Following these arguments, this work aims to evaluate the efficiency of equiradial subdivisible designs in blocks, with and analysis of redundancy indices description of the percentage of variability in the first canonical pair of variables. For this, Monte Carlo simulations were used in different scenarios, involving sample sizes (N), heterogeneity between the covariance matrices and specification of polar and spherical coordinates. It was concluded that for the equiradial design in the shape of a hexagon, it presented better efficiency indices. Regarding the percentage of variation explained by the first to canonical and the redundancy indices, the results were similar in relation to the use of polar and spherical coordinates, for all situations involving degree of heterogeneity between the covariance matrices and sample sizes. Finally, perform an application on data from stem segments of an arabica coffea progeny.