Fixing Collinearity Instability Using Principal Component and Ridge Regression Analyses in the Relationship Between Body Measurements and Body Weight in Japanese Black Cattle

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 utilised 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 pair wise correlation coefficients between the body measurements revealed positive, highly significant (P<0.001) values of 0.98 between WHT and HIPHT, HIPWD and LUVWD, while the lowest correlation of 0.50 was 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, while SHWD and CHWD were the most important.