Canonical STATIS: Biplot analysis of multi-table group structured data based on STATIS-ACT methodology

• Published in: Computational statistics & data analysis Vol. 51; no. 9; pp. 4193 - 4205
• Main Authors: Vallejo-Arboleda, Amparo, Vicente-Villardón, José L., Galindo-Villardón, M.P.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 15-05-2007; Elsevier Science; Elsevier
• Series: Computational Statistics & Data Analysis
• Subjects: Biplot; Canonical variate analysis; Exact sciences and technology; General topics; Group theory; Group theory and generalizations; MANOVA; Mathematics; Multivariate analysis; Numerical analysis; Numerical analysis. Scientific computation; Numerical methods in probability and statistics; Probability and statistics; Sciences and techniques of general use; STATIS-ACT; Statistics; Canonical variate analysis; Biplot; MANOVA; STATIS-ACT; Canonical analysis; Data analysis; Experimental data; Statistical computation; Grouped data; Data table; Multivariate analysis; Data structure
• ISSN: 0167-9473; 1872-7352
• DOI: 10.1016/j.csda.2006.04.032

Frequently multivariate experimental data taken over multiple occasions is found to produce a multivariate multi-table experiment. Neither the separate analysis of each occasion, using MANOVA or canonical variate analysis, nor the joint analysis using the STATIS-ACT methodology for multiple tables, are adequate to capture the real structure of the data matrices, since the first account for group structure but not time evolution and the second confuses the “between” and “within” group variabilities. A method baptized Canonical STATIS, based on STATIS-ACT methodology, is proposed. The method permits to account for data group structure as well as time evolution on the various occasions by obtaining common or stable canonical variates across multiple occasions or data sets. A simultaneous representation of groups, variables and occasions (biplot) is obtained, thereby widening the capabilities of classical methods.