Measures of fit in principal component and canonical variate analysis

Lubbe-Gardner, Sugnet; le Roux, Niël J. and Gower, John C. (2008). Measures of fit in principal component and canonical variate analysis. Journal of Applied Statistics, 35(9) pp. 947–965.

DOI: https://doi.org/10.1080/02664760802185399

Abstract

Treating principal component analysis (PCA) and canonical variate analysis (CVA) as methods for approximating tables, we develop measures, collectively termed predictivity, that assess the quality of fit independently for each variable and for all dimensionalities. We illustrate their use with data from aircraft development, the African timber industry and copper froth measurements from the mining industry. Similar measures are described for assessing the predictivity associated with the individual samples (in the case of PCA and CVA) or group means (in the case of CVA). For these measures to be meaningful, certain essential orthogonality conditions must hold that are shown to be satisfied by predictivity.

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About

• Item ORO ID
• 22530
• Item Type
• Journal Item
• ISSN
• 1360-0532
• Extra Information
• Winner of the Gopal Kanji Prize 2008
• Keywords
• biplots; canonical variate analysis; measures of fit; prediction; principal component analysis
• Academic Unit or School
• Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
  Faculty of Science, Technology, Engineering and Mathematics (STEM)
• Copyright Holders
• © 2008 Taylor & Francis
• Depositing User
• Sarah Frain