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Title: Analysis of interval data using patterned covariance structures Authors:  Anuradha Roy - The University of Texas at San Antonio (United States) [presenting]
Abstract: Principal component analysis of interval data is proposed by using block compound symmetry (BCS) and doubly block compound symmetry (DBCS) covariance structures. This is deemed by considering each interval as two repeated measurements at the lower and upper bounds of the interval (two-level multivariate data), and then by assuming BCS covariance structure for the data. And, this is accomplished in two stages: first getting eigenblocks and eigenmatrices of the variance-covariance matrix, and then analyzing these eigenblocks and the corresponding principal vectors together to get the adjusted eigenvalues and the corresponding eigenvectors of the interval data. We then work independently with these principal vectors and their corresponding variance-covariance matrices, i.e., the corresponding eigenblocks to get the eigenvalues and eigenvectors of the interval data. If there is some additional information (like brands etc.) in the interval data, the interval data can be considered as three-level multivariate data and can be analyzed by assuming DBCS covariance structure. Results illustrating the appropriateness of the new methods over the existing methods are presented. It is shown that our proposed method of principal component analysis for three-level interval data generalizes the commonly used PCA for multivariate data. The proposed methods is illustrated with a real dataset.