Abstract
Principal component analysis (PCA) is one of the powerful statistical tools to transform a large
number of original variables into a smaller set of variables that still contains most of the correlation
information in statistical data. However, note that the principal components are formulated as the
linear combinations of all the original variables. Thus, when we wish to evaluate the principal components
for individuals of interest, it is necessary to observe all the original variables of the individuals.
To solve the problem, McCabe (1984) proposed the principal variable (PV) selection criteria from the
perspective of principal component analysis, and de Falguerolles and Jmel (1993) reviewed the PV
selection problems from the viewpoint of Gaussian graphical modeling. However, McCabe (1984) or
de Falguerolles and Jmel (1993) did not discuss the mathematical properties of their proposed PV
selection criteria. Taking it into account, this paper proposes novel PV selection criteria based on the
inverse partial correlation matrix from the perspective of McCabe (1984) and de Falguerolles and
Jmel (1993), and clarifies the mathematical properties in terms of the undirected independence graph.
