Heterogeneidade entre estruturas de matrizes de (co) variâncias

Abstract

: The evaluation about the existence of variance heterogeneity can be done individually for each variance component. However, when the estimated components are correlated, the presence of heterocedasticity must be evaluated by the application of a method which verifies differences in the whole (co)variance structure. To test the existence of heterogeneity of genetic and residual variance in multivariate structures, three methodologies were used for comparison of (co)variance structures, in which the matrices in each source of heterogeneity were confronted by the natural logarithm of the ratio between their determinants and by analysis of the principal components. An evaluation of change among structures by frequentist procedures was also carried out. This methodologies were applied to matrices of genetic and residual (co)variance of the parameters A, B and K of Von Bertalanffy?s growth curves, adjusted for quails of three different strains, fed with two different energy dietary levels. Estimations of (co)variance components were made through Bayesian procedures, using the animal model. These analysis were made in a way that, to take into account the heterogeneity between strains, tricaracter analyses were made involving the parameters A, B and K, for each strain. Supposing heterogeneity between environments, the parameters A, B and K were considered distinct characteristics in each environment, yielding an hexacaracter analysis for each strain. For the matrix of phenotypic correlations of those parameters, the principal components were obtained. The coefficient values of the first principal component, in two environments or in each two strains, were combined with the original variables and, in a new bicaracter analysis, resulted in samples of the (co)variance components of this set of transformed variables. As the first principal component did not accumulate enough variance, this result made the heterocedasticity detection difficult. There was also a problem with the application of the logarithm of the ratio between determinants for some samples because of ill conditioned matrices. The frequentist methodology, given by the M-Box criterion, was not capable of detecting the presence of heterogeneity among the (co)variance structures. The distribution of the logarithm values of the ratio between determinants indicated heterogeneity only in residual (co)variance structures, while the evaluation through the differences among the transformed variables of the principal components indicated both genetic and residual (co)variance structure divergence. Although the first principal component has not accumulated enough variation, its utilization seemed more capable of detecting the presence of heterogeneity in (co)variance structures.