Mixed linear models in the research agriculture and livestock

Abstract

The mixed models have been traditionally studied by means of variance analysis in which variance components are estimated by a linear model solution. For mixed model analysis some points are relevant: the prediction of random effects, tests upon and estimation of variance components, and estimation and tests of hypothesis upon fixed effects. In the analysis of unbalanced linear mixed models the problem is not that simple and the use of the SAS program (SAS System Inc., Cary, NC, USA) is preferable, which demand a proper understanding of the theoretical background because of a proper modeling of the structure of the variance-covariance matrix and the choice of the estimation method is required. In the MIXED procedure are available the ML (Maximum Likelihood), REML (Restricted Maximum Likelihood), and MIVQUE (Minimum Variance Quadratic Unbiased) as described respectively by Hartley e Rao (1967), Rao (1971a), and Patterson e Thompson (1971). For an optimized use of SAS it is rather necessary to define the appropriate type of sum of squares: SS1, SS2, SS3, or SS4. Because of its properties the use of REML is recommended and for unbalanced data the SS3 type is the appropriate choice. With balanced data the four types of sum of squares yield the same results.