Computation of partial correlation coefficient: Variance-covariance matrix approach

Abstract

This thesis examined variance-covariance matrix approach of computing orders of partial correlation coefficients. The main objective of this thesis is to explore further if the partial correlation coefficients beyond the first order can be computed using the method of variance-covariance matrix approach. Statistical tests were performed on the datasets used for the fundamental partial correlation assumptions, namely linearity, normality, and the lack of outliers. In order to account for the effects of one or more extra random variables, the thesis provided a logical investigation into the linear connection between two random variables. To achieve this, the study determines the appropriate dataset structure and partitioning, as well as the key matrices that allow us to acquire the theoretical conclusion. Practical examples and R syntax were used to clearly illustrate the computation of higher order partial correlation coefficients. It was found that the orders of partial correlation coefficient may be achieved by normalizing the conditional variance-covariance matrix results. The study demonstrates that, if the partial correlation assumptions are met, the variance covariance matrix technique may compute partial correlation coefficients of any order. Finally, the study recommends that future researchers adopt the method of variance-covariance matrix technique to generate higher orders of partial correlation coefficients since the method is trustworthy, and comprehensible.