500 INTRODUCTION The beneft of crossbreeding includes improve- ment in growth and carcass traits (Williams et al., 2010) and has been studied by many researchers over the past decade (Roso et al., 2005a,b; Carvalheiro et al., 2006; Dias et al., 2011). For the purpose of selection for production, the greatest challenge is the nonbiased comparison of breeding bulls and dams of different breed compositions. In crossbred populations, effects that are assumed to be null in pure populations become important and must be taken into account. For a fair comparison, a multibreed genetic evaluation including crossbred and purebred individuals in the same data set is required, as proposed by Arnold et al. (1992). Multibreed analysis requires the inclusion of ef- fects for direct and maternal breed additive, heterosis (Cardoso et al., 2008; Williams et al., 2010), epistatic loss (Dias et al., 2011), and complementarity between different breeds (Carvalheiro et al., 2006; Cardoso et al., 2008) effects. However, this model may be dif- fcult to ft if the data structure does not adequately sample all the genetic relationships. The additive ge- netic effect for each breed involved and their combin- ing ability, general or specifc, should be considered. The nonadditive genetic effects are usually included as covariates (Carvalheiro et al., 2006; Dias et al., 2011). The inclusion of these effects as fxed covariates may Comparing methodologies to estimate fxed genetic effects and to predict genetic values for an Angus × Nellore cattle population C. D. Bertoli,*† 1 J. Braccini,† V. M. Roso‡ *Departamento de Zootecnia, Instituto Federal Catarinense Campus Camboriú (IFC-Camboriu), Camboriú, SC, Brasil; †Departamento de Zootecnia, Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS, Brazil; and ‡GenSys Consultores Associados, Porto Alegre, RS, Brazil ABSTRACT: The study assesses the need for and effectiveness of using ridge regression when estimat- ing regression coeffcients of covariates representing genetic effects due to breed proportion in a crossbreed genetic evaluation. It also compares 2 ways of select- ing the ridge parameters. A large crossbred Angus × Nellore population with 294,045 records for weaning gain and 148,443 records for postweaning gain was used. Phenotypic visual scores varying from 1 to 5 for weaning and postweaning conformation, weaning and postweaning precocity, weaning and postweaning mus- cling, and scrotal circumference were analyzed. Three models were used to assess the need for ridge regres- sion, having 4, 6, and 8 genetic covariates. All 3 models included the fxed contemporary group effect and ran- dom animal, maternal, and permanent environment effects. Model AH included fxed direct and maternal breed additive and the direct and maternal heterosis covariates, model AHE also included direct and mater - nal epistatic loss covariates, and model AHEC further included direct and maternal complementarity effects. The normal approach is to include these covariates as fxed effects in the model. However, being all derived from breed proportions, they are highly collinear and, consequently, may be poorly estimated. Ridge regres- sion has been proposed as a method of reducing the collinearity. We found that collinearity was not a prob- lem for models AH and AHE. We found a high variance infation factor, >20, associated with some maternal covariates in the AHEC model refecting instability of the regression coeffcients and that this instability was well addressed by using ridge regression using a ridge parameter calculated from the variance infation factor. Key words: complementarity, crossbred beef cattle evaluation, epistatic loss, heterosis, nonadditive genetic effects, ridge regression. © 2016 American Society of Animal Science. All rights reserved. J. Anim. Sci. 2016.94:500–513 doi:10.2527/jas2015-9344 1 Correspondig author: cdbertoli@gmail.com Received May 25, 2015. Accepted November 9, 2015. Published February 12, 2016