Abstract
The objective of this work was to assess the degree of multicollinearity and to identify the variables involved in linear dependence relations in additive-dominant models. Data of birth weight (n=141,567), yearling weight (n=58,124), and scrotal circumference (n=20,371) of Montana Tropical composite cattle were used. Diagnosis of multicollinearity was based on the variance inflation factor (VIF) and on the evaluation of the condition indexes and eigenvalues from the correlation matrix among explanatory variables. The first model studied (RM) included the fixed effect of dam age class at calving and the covariates associated to the direct and maternal additive and non-additive effects. The second model (R) included all the effects of the RM model except the maternal additive effects. Multicollinearity was detected in both models for all traits considered, with VIF values of 1.03 - 70.20 for RM and 1.03 - 60.70 for R. Collinearity increased with the increase of variables in the model and the decrease in the number of observations, and it was classified as weak, with condition index values between 10.00 and 26.77. In general, the variables associated with additive and non-additive effects were involved in multicollinearity, partially due to the natural connection between these covariables as fractions of the biological types in breed composition.
Highlights
In animal breeding studies, an obstacle to obtaining reliable results is the presence of linear correlations between explanatory variables, which is defined as multicollinearity
Considering the RM model for birth weight (Figure 1 A), BTA, BTB, BTC, MBTB, MBTC, NxB, and NxC are probably involved in quasi‐dependence relations, since they presented variance inflation factor (VIF) greater than 10
With the reduction of covariates included in the analysis model, a decrease was observed in the number of covariates involved in multicollinearity and in the VIF values
Summary
An obstacle to obtaining reliable results is the presence of linear correlations between explanatory variables, which is defined as multicollinearity. Roso et al (2005b), working with purebred and crossbred animals from Angus, Blond d’Aquitaine, Charolais, Gelbvieh, Hereford, Limousin, Maine‐Anjou, Salers, Shorthorn, and Simmental breeds, estimated high correlations between maternal dominant and direct epistatic effects as well as between direct and maternal additive effects. In those cases, multicollinearity was responsible for an overestimation of variance components, a bias in estimates of genetic effects, and greater standard errors associated to regression coefficients. The efficiency of selection and crossbreeding strategies based on these results was affected
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