Dealing with Multicollinearity in Predicting Egg Components from Egg Weight and Egg Dimension

Abstract

Measurements of 174 eggs from meat-type breeder flock (Ross) at 36 weeks of age were used to study the problem of multicollinearity (MC) instability in the estimation of egg components of yolk weight (YKWT), albumen weight (ALBWT) and eggshell weight (SHWT). Egg weight (EGWT), egg shape index (ESI)=egg width (EGWD)*100/egg length (EGL) and their interaction (EGWTESI) were used in the context of un-centred vs centred data and principal components regression (PCR) models. The pairwise phenotypic correlations, variance inflation factor (VIF), eigenvalues, condition index (CI), and variance proportions were examined. Egg weight had positive correlations with EGWD and EGL (r=0.56 and 0.50, respectively; P<0.0001) and EGL had a negative correlation with ESI (r=-0.79; P<0.0001). The highest correlation was observed between EGWT and ALBWT (r=0.94; P<0.0001), while the lowest was between EGWD and SHWT (r=0.33; P<0.0001). Multicollinearity problems were found in EGWT, ESI and their interaction as shown by VIF (>10), eigenvalues (near zero), CI (>30) and high corresponding proportions of variance of EGWT, ESI and EGWTESI with respect to EGWTESI. Results from this study suggest that mean centring and PCR were appropriate to overcome the MC instability in the estimation of egg components from EGWT and ESI. These methods improved the meaning of intercept values and produced much lower standard error values for regression coefficients than those from un-centred data.