Use of ridge regression for the prediction of early growth performance in crossbred calves

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

The problem of multicollinearity in regression analysis was studied. Ridge regression (RR) techniques were used to estimate parameters affecting the performance of crossbred calves raised in tropical and subtropical regions by a model including additive, dominance, joint additive or profit heterosis and epistatic effects and their interactions with latitude in an attempt to model genotype by environment interactions. A software was developed in Fortran 77 to perform five variant types of RR: the originally proposed method; the method implemented by SAS; and three methods of weighting the RR parameter lambda. Three mathematical criteria were tested with the aim of choosing a value for the lambda coefficient: the sum and the harmonic mean of the absolute Student t-values and the value of lambda at which all variance inflation factors (VIF) became lower than 300. Prediction surfaces obtained from estimated coefficients were used to compare the five methods and three criteria. It was concluded that RR could be a good alternative to overcome multicollinearity problems. For all the methods tested, acceptable prediction surfaces could be obtained when the VIF criterion was employed. This mathematical criterion is thus recommended as an auxiliary tool for choosing lambda.