Abstract:
ABSTRACT
Multivariate methods such as principal component analysis and factor analysis
have been used to interpret multivariate data. However, these statistical
applications are not able to determine prior to their application whether a
dimension exists within the multivariate data set since it is possible to have a
dimensionless multivariate dataset. In addition, these statistical applications are
method dependent, it is therefore imperative to propose an independent technique
for detecting dimensionality using automated threshold settings which are
thresholds generated based on the structure of the data and not by the judgement
of the researcher so that these statistical applications will be for purposes of
interpretation or giving meaning to the data structure. Also, the formation of
dimensionality in the well-known multivariate techniques is not analytically or
computationally presented. They therefore offer a leave-or-take result with no
understanding of the formation of the dimensions. This study therefore filled this
gap by successfully proposing an independent dimensionality detection method
using three automated threshold settings that generate data specific thresholds by
allowing the data structure to generate the optimal threshold for detecting
dimensionality of the multivariate data set for more accurate results. The study
also established the robustness of the method using Pearson’s correlation which
hinges on the mean and another correlation profile that does not hinge on a
statistic which is affected by extreme values, in this case order statistic which
hinges on the median. The algorithm converged in all cases. Confirmatory factor
analysis are carried out for confirmation of results. The proposed method
completely removes the challenge of subjectivity associated with dimensionality
detection, and hence is highly recommended
