Fixing collinearity instability using principal component and ridge regression analyses in the relationship between body measurements and body weight in Japanese black cattle
Malau Aduli, A.E.O.; Aziz, M.A.; Kojima, T.; Niibayashi, T.; Oshima, K.; Komatsu, M.
Journal of Animal and Veterinary Advances 3(12): 856-863
Monthly measurements of withers height (WHT), hip height (HIPHT), body length (BL), chest width (CHWD), shoulder width (SHWD), chest depth (CHDP), hip width (HIPWD), lumbar vertebrae width (LUVWD), thurl width (THWD), pin bone width (PINWD), rump length (RUMPLN), cannon circumference (CANNCIR) and chest circumference (CHCIR) from birth to yearling age, were utilized in principal component and ridge regression analyses to study their relationship with body weight in Japanese Black cattle with an objective of fixing the problem of collinearity instability. The data comprised of a total of 10 543 records on calves born between 1937 and 2002 within the same herd under the same management. Simple pairwise correlation coefficients between the body measurements revealed positive, highly significant (P<0.001) values (0.98) between WHT and HIPHT and between HIPWD and LUVWD. The lowest correlation (0.50) was found between CHDP and SHWD. Severe collinearity problems as portrayed by variance inflation factors (VIF) above 10 were evident in all body measurements ranging from 11.25 in PINWD to 46.94 in LUVWD, except for SHWD (1.80), CHDP (3.70), CHWD (7.11) and CANNCIR (7.33). Principal component and ridge regression analyses allowed the derivation of new and more stable regression coefficients that overcame the problem of collinearity. Of all the body measurements studied, hip height was shown to be the least important for predicting the body weight of Japanese Black cattle, whereas SHWD and CHWD were the most important.