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 variancecovariance
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.
