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ERIC Number: EJ863076
Record Type: Journal
Publication Date: 2009-Dec
Pages: 17
Abstractor: As Provided
Reference Count: 0
ISSN: ISSN-0033-3123
Joint Procrustes Analysis for Simultaneous Nonsingular Transformation of Component Score and Loading Matrices
Adachi, Kohei
Psychometrika, v74 n4 p667-683 Dec 2009
In component analysis solutions, post-multiplying a component score matrix by a nonsingular matrix can be compensated by applying its inverse to the corresponding loading matrix. To eliminate this indeterminacy on nonsingular transformation, we propose Joint Procrustes Analysis (JPA) in which component score and loading matrices are simultaneously transformed so that the former matrix matches a target score matrix and the latter matches a target loading matrix. The loss function of JPA is a function of the nonsingular transformation matrix and its inverse, and is difficult to minimize straightforwardly. To deal with this difficulty, we reparameterize those matrices by their singular value decomposition, which reduces the minimization to alternately solving quartic equations and performing the existing multivariate procedures. This algorithm is assessed in a simulation study. We further extend JPA for cases where targets are linear functions of unknown parameters. We also discuss how the application of JPA can be extended in different fields.
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Publication Type: Journal Articles; Reports - Research
Education Level: N/A
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A