Application of Principal Component Analysis (PCA) for correcting multicollinearity and dimension reduction of morphological parameters in Bunaji Cows

Abstract

This paper presents the application of Principal Component Analysis (PCA) on the dimension reduction of morphological variables. Sixteen morphological variables were measured from 50 multiparous Bunaji cows. The correlation amongst most of the morphological variables was very high suggesting severe multicollinearity. Therefore, PCA was applied to verify whether the collinear variables could be combined to form composite scores. The application of the PCA effectively reduced the dimensionality of the 16 morphological variables into four artificial composite variables (called principal components) which were uncorrelated and independent of each other with standardized means of zero and standard deviation of one and explained 90.45% of the variation in the original morphological data set. Therefore, PCA can be used to correct the problem of multicollinearity and dimension reduction of morphological data in multiple regression analysis.

Keywords: principal component, correlation, communality, body indices, orthogonal varimax