Although somewhat complex, the formation of composite animals represents an alternative for the solution of several problems found in the production of beef cattle in Brazil, given the diversity of climates and regions present in our country, the creation of these composite animals helps in the quality of herds in terms of productive, reproductive and subsistence aspects. In view of so many races, combinations and parameters in the models of genetic evaluation of composite animals, a mathematical problem arises: multicollinearity, it occurs when the independent variables have a high correlation, leading then to a confusion of the estimators of the regression coefficients. The main objectives of this study are: to evaluate the population structure and genetic diversity throughout the creation and selection process of Composite Montana Tropical ® beef cattle. Detect the presence of multicollinearity in growth traits. Obtain estimates of direct and maternal additive genetic effects, non-additive genetic effects, as well as fixed effects, by methods without correction (WC), maximum restricted likelihood (REML), ordinary least squares (OLS), ridge regression (RR), factor analysis (FA) and principal component regression (ACP). The diagnosis for multicollinearity for these traits was large enough to prove that this phenomenon exists and deserves special attention in the analysis of estimation of the components of variance by the method of least squares and in the prediction of genetic values for these traits. The corrections for multicollinearity performed were efficient to adjust the β of the covariates, for all methods. The FA and ACP presented results consistent with the correction of the problem of this study, these analyzes have a high potential for inclusion in the genetic evaluations of databases with a multicollinearity problem. The prediction of the genetic values of the animals for the traits of this study was benefited by the analysis that consisted of the use of the original phenotype, with the components adjusted for the analysis of the OLS (QMP). Ridge regression in this study may not have brought great benefits, possibly due to the empirical estimation of the "k" parameter. As much as the methods showed differences in the model comparison analyzes, as the adjustment of the β of the covariates does not interfere in the prediction of genetic values, it is recommended to apply the correction to estimate the variance components and genetic parameters, it is up to the the researcher then gave more details to his database to choose the most appropriate and parsimonious model.