Modelo fatorial analítico bayesiano aplicado à experimentos multi-ambiente

Abstract

One of the main challenges in plant breeding programs is the efficient study of the genotypes x environments interaction (GEI). The presence of significant GE interaction hinders the work of the breeder for the recommendation and selection of superior genotypes. Among the various statistical procedures developed for this purpose, special emphasis should be given to those based on mixed models through factor analysis, commonly referred to as factor-analytic model (FA). This consists of a parsimonious approach and presents suggestive advantages when compared with classical methodologies, such as the great flexibility to deal with unbalanced data and heterogeneous variances. However, some problems are related to the factor analytic model: computational cost in analyzes with large number of environments and the Heywood cases, which makes the model unidentifiable. Moreover, the model representation in conventional biplot does not include any measure of uncertainty regarding the scores that describe GEI effect or Genotype (G) + GEI effects, plotted. The present proposal seeks to describe general forms of how heterogeneity of genetic and residual covariance can be modeled from the perspective of factorial analysis in mixed models, using spectral decomposition of the genetic effects within Bayesian approach, different from other procedures present in the literature in which the factor loads are directly sampled. In addition, the objective was to develop a procedure to incorporate inference to the biplot, through the construction of regions of credibility for genotypic and environmental scores. In this study, spherical distributions were assumed as prioris for eigenvectors and truncated normal distribution for singular values, as well as scaled inverse chi-squared distribution for residual variances and non-informative priori for the effect of genotypes. This approach differs from the Bayesian methods presented so far that assume the same constraints present in the mixed effects model. To exemplify the proposed method, we used simulated data and real data which study variable is the yield of spikes in t.ha-1. Samples for the inference process were obtained directly using the Gibbs sampler. Random unbalancing was performed in the data considering levels of 10%, 33% and 50% of losses of the genotype in the environment. According to the results, the FA analysis with two loads presented higher predictive capacity than the competing models. Unbalancing of 10% and 33% had mean values of correlation above 0.40 and with 50%, of 0.46. It was also observed that the performance of the model was better in the order of 50%, 33% and 10% of imbalance. We also verified that the analysis with the Bayesian FA model is robust under large levels of data unbalance. A relevant detail in this study concerns the selection of models, which proved not to be a trivial task in the case of real data, requiring additional criteria. In addition, the model proposed in this work showed greater predictive capacity than the equivalent frequentist model and the parameters were adequately estimated, being identifiable, without the need for rotationality of factor loads or imposition of restrictions, which represents a great advantage of the method proposed here.