Principal Component Analysis of Hierarchical and Multivariate Data

Abstract

Principal component analysis concerned with explaining the variance-covariance structure of a set of variables through a few linear combinations of these variables. To determine how many principal components should be considered, the eigenvalues should first be examined. Investigating whether the processing of numbers depend on the way the numbers were presented, i.e. whether the data could be reduced. Four variables (WordDiff, WordSame, ArabicDiff and ArabicSame) were used. Both covariate and correlation matrix were used to obtain the principal components and compare the results between them. In addition, canonical correlation was used to examine the correlation between the set of Word variables and the set of Arabic variables. To see the correlation between the Word variables and Arabic variables, observing the canonical correlation between the first Word canonical variable and the first Arabic variable is enough. Data was reduced into a single principal component (PC1) as more than 80% of the total variability was explained by this principal component.