Collinearity diagnoses and correction in predictive models of Nigerian local chicken of two genotypes using principal component analysis

This paper was aimed at investigating the relationship between body weight and body measurements in normal feathered and naked neck genotypes so as to ascertain the existence or otherwise of collinearity instability. If detected, fix the problem using PCA. Body weight (BW) and seven linear body dimensions; chest circumference (CC), body length (BL), wing span (WS), thigh length (TL), shank length (SL), neck length (NL) and beak length (BkL) were taken from one-hundred and fifty-six matured local chickens comprising 97 normal feathered (57 males and 40 females) and 59 naked necks (24 males and 35 females). GLM was used to study genotype and sex effects. Naked neck birds (NNBs) had higher values for BW, CC, BL and TL compared to their normal feathered (NF) counterparts. Sexual dimorphism was observed in all the traits with higher values recorded for males. Phenotypic correlations among BW and biometric traits were positive and highly significant (r = 0.51-0.95 and 0.52-0.98; <0.01 for NFBs and NNBs). Collinearity diagnosis revealed two severe cases each in NFBs (VIF = 12.60 (CC) and 13.75 (BL)) and NNBs (VIF = 26.39 (CC) and 23.12 (BL)). Collinearity problems were further confirmed from the computations of the eigenvalues of the correlation matrix, condition indexes and variance proportion. Using varimax rotation of the transformation matrix, three Principal Components (PCs) were extracted each for NFB and NNB. The three extracted PCs accounted for 90.913% and 87.086% of the total variance for NFB and NNB respectively. Linear regression of extracted PCs against BW revealed that tolerance (T) = 1 for all the extracted components. This implies that no percentage of the variance in the PC1 of NFBs and NNBs could be explained by the other extracted PCs (PC2 and PC3) included in the model; this clearly shows that the collinearity has been fixed. Further confirmation test with VIF shows that, VIF of PCFS equaled one which neatly shows that the variances of the estimated coefficient were no longer inflated.