Modelos mistos na experimentação animal - Ferro, Mariane Moreno (2018)
The aim was of this work was to consider several variance and covariance structures for the matrices associated with the random part and the residual, trying to emphasize those inserted in the random part, and based on this modeling, we intend to question and compare the different forms proposed for a given experiment. A dataset was simulated to represent different measures of the covariance matrix repeated measures in animals, representing a 5x5 Latin square delineation. Structures such as diagonal homogeneous, diagonal heterogeneous, correlated with homogeneous variances, correlated with heterogeneous variances, correlated between periods sequences with homogeneous variances, correlated between periods sequences with heterogeneous variances. For the analyzes of the 5x5 Latin square, the simulated data were evaluated under the mixed models approach considering the effect of the animal as the experimental and random unit, considering the period as repeated measurements of the same experimental unit, adjusting the covariance structures as measures taken in the same animal. The treatment effect and period were considered as fixed. Five models of covariance structures, component of variance, first order auto regressive, composite symmetry, heterogeneous composite symmetry and Toeptiz were used to fit the data. The Akaike and Bayesian Schwars information criteria were used to compare the models. The results were quite similar when using the homogeneous diagonal and heterogeneous diagonal covariance structure, where F values for treatment effect differed substantially between the models tested, leading to different significant effects of the models tested. Similar values were observed when the covariance structures of component type of variance and composite symmetry were used. When the covariates were correlated and maintained the variances on the main homogeneous diagonal, the structure that best fit was the first order auto regressive. The use of the structure of variance correlated with heterogeneous variance led to different results where the first-order autoregressive structure was the one that best fit the model for the AIC criterion, but not for the BIC criterion, while the autoregressive heterogeneity of the first order presented a better fit for BIC, but not for AIC, pointing out that the choice of the selection criterion presents total importance as to the final result of the test. The analysis of the correlated structure between sequential periods with homogeneous variances pointed out that the best structure to use was the component of variance. The component structure of variance showed the best fit in most of the covariance matrices tested. The use of different covariance structures led to similar values for the minimum mean square, however, it is observed that the standard error tends to change according to the chosen structure.