Multivariate Analysis of a Sequence of Paired Data Matrices: Succesive and Simultaneous Approaches

Rodnellin Onesime Malouata; Chedly G&eacute;lin Louzayadio; Bern&eacute;dy Nel Messie Kodia Banzouzi

doi:doi:10.11648/j.ajtas.20221101.16

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Multivariate Analysis of a Sequence of Paired Data Matrices: Succesive and Simultaneous Approaches

Rodnellin Onesime Malouata, Chedly Gélin Louzayadio, Bernédy Nel Messie Kodia Banzouzi

Published in American Journal of Theoretical and Applied Statistics (Volume 11, Issue 1)

Received: 20 August 2021 Accepted: 7 September 2021 Published: 14 February 2022

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Abstract

The relationship between two data matrices has been studied in the interbattery factor analysis. When two data matrices are partitioned in rows, the relationship between two data matrices has been studied in the STATICO method. The main advantage of this method is the optimality of the compromise of co-structures. It is well known that the weighting coefficients of the compromise may be contrary sign in some cases and make it uninterpretable. Thus, many multivariate data analysis methods have been developed, particularly those designed to tackle the fundamental issue: the description of the relationships between two data matrices. This can be studied by successive modeling approaches as well as by a simultaneous modeling approach. These methods are based on co-inertia and can be reduced to finding the maximum, minimum, or other critical values of a ratio of quadratic forms. However, all these methods are successive. In this paper, we propose two algorithms. The first one called sDO-CCSWA (successive Double-Common Component and Specific Weight Analysis) maximizes the sum of squared covariances, by first finding the best pair-component solution, and repeating that process in the respective residual spaces. The sDO-CCSWA is a new monotonically convergent algorithm obtained by searching for a fixed point of the stationary equations. The second approach is a simultaneous algorithm (DO-CCSWA) which maximizes the sum of squared covariances.

Published in	American Journal of Theoretical and Applied Statistics (Volume 11, Issue 1)
DOI	10.11648/j.ajtas.20221101.16
Page(s)	36-44
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2022. Published by Science Publishing Group

Keywords

Interbattery Factor Analysis, STATICO, Common Component and Specific Weight Analysis

References

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[3]	Hanafi, M., Dolce, P., & Hadri, Z. E. (2021). Generalized properties for Hanafi-Wold’s procedure in partial least squares path modeling. Computational Statistics, 36, 603-614.
[4]	Hanafi, M., Kohler, A., & Qannari, E. M. (2010). Shedding new light on hierarchical principal component analysis. Journal of Chemometrics, 24, 703-709.
[5]	Hanafi, M., & Qannari, E. M. (2008). Nouvelles propriétés de l’analyse en composantes communes et poids spécifiques. Journal de la Société Franc¸aise de Statistique ; tome 149 No 2, 75-97.
[6]	Hanafi, M., & Kiers, H. A. L. (2006). Analysis of K sets of data, with differential emphasis on agreement between and within sets. Computational Statistics & Data Analysis, 51, 1491-1508.
[7]	Kiers, H. A. L., & Giordani, P. (2020). Candecomp/Parafac with zero constraints at arbitrary positions in a loading matrix. Chemometrics and Intelligent Laboratory Systems, 207, 104145.
[8]	Kissita, G. (2003). Les analyses canoniques généralisées avec tableau de référence généralisé: éléents théoriques et appliqués. PhD thesis, University of Paris Dauphine, France.
[9]	Kissita, G., Malouata, R. O., Mizère, D., & Makany, R. A. (2013). Proposition of analyses of links between two vertical multi-tables: methods (sVMA and sOVMA) and (sCIA3 et sOCIA3). Applied mathematical Sciences, Vol. 7, no 131, 6503-6525.
[10]	Lafosse, R., & Ten Berge, J. M. F. (2006). A simultaneous CONCOR algorithm for the analysis of two partitioned matrices. Computational Statistics & Data Analysis, 50, 2529-2535.
[11]	Lafosse, R., & Hanafi, M. (1997). Concordance d’un tableau avec K tableaux: définition de K + 1 uplés synthétiques. Revue de Statistique Appliquée, XLV(4): 111-126.
[12]	Malouata, R. O. (2015). Proposition d’analyse de co- inertie d’une série de couples de tableaux: éléments théoriques et appliqués. PhD thesis, Marien Ngouabi University, Congo.
[13]	Pegaz-Maucet, D. (1980). Impact d’une perturbation d’origine organique sur la dérive des macro-invertébrés bentiques d’un cours d’eau. Comparaison avec le benthos. PhD thesis, University of Lyon I, France.
[14]	Simier, M., Blanc, L., Pellegrin, F., & Nandris, D. (1999). Approche simultanée de k couples de tableaux: Application ` a l’étude des relations pathologie végétale- environnement. Revue de Statistique Appliquée 47 31-46.
[15]	Thioulouse, J. & Chessel, D. (1987). Les analyses multitableaux en ecologie factorielle. i : De la typologie d’etat ` a la typologie de fonctionnement par l’analyse triadique. Acta Oecologica, Oecologia Generalis 8 463- 480.
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Rodnellin Onesime Malouata, Chedly Gélin Louzayadio, Bernédy Nel Messie Kodia Banzouzi. (2022). Multivariate Analysis of a Sequence of Paired Data Matrices: Succesive and Simultaneous Approaches. American Journal of Theoretical and Applied Statistics, 11(1), 36-44. https://doi.org/10.11648/j.ajtas.20221101.16

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ACS Style

Rodnellin Onesime Malouata; Chedly Gélin Louzayadio; Bernédy Nel Messie Kodia Banzouzi. Multivariate Analysis of a Sequence of Paired Data Matrices: Succesive and Simultaneous Approaches. Am. J. Theor. Appl. Stat. 2022, 11(1), 36-44. doi: 10.11648/j.ajtas.20221101.16

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AMA Style

Rodnellin Onesime Malouata, Chedly Gélin Louzayadio, Bernédy Nel Messie Kodia Banzouzi. Multivariate Analysis of a Sequence of Paired Data Matrices: Succesive and Simultaneous Approaches. Am J Theor Appl Stat. 2022;11(1):36-44. doi: 10.11648/j.ajtas.20221101.16

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@article{10.11648/j.ajtas.20221101.16,
  author = {Rodnellin Onesime Malouata and Chedly Gélin Louzayadio and Bernédy Nel Messie Kodia Banzouzi},
  title = {Multivariate Analysis of a Sequence of Paired Data Matrices: Succesive and Simultaneous Approaches},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {11},
  number = {1},
  pages = {36-44},
  doi = {10.11648/j.ajtas.20221101.16},
  url = {https://doi.org/10.11648/j.ajtas.20221101.16},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20221101.16},
  abstract = {The relationship between two data matrices has been studied in the interbattery factor analysis. When two data matrices are partitioned in rows, the relationship between two data matrices has been studied in the STATICO method. The main advantage of this method is the optimality of the compromise of co-structures. It is well known that the weighting coefficients of the compromise may be contrary sign in some cases and make it uninterpretable. Thus, many multivariate data analysis methods have been developed, particularly those designed to tackle the fundamental issue: the description of the relationships between two data matrices. This can be studied by successive modeling approaches as well as by a simultaneous modeling approach. These methods are based on co-inertia and can be reduced to finding the maximum, minimum, or other critical values of a ratio of quadratic forms. However, all these methods are successive. In this paper, we propose two algorithms. The first one called sDO-CCSWA (successive Double-Common Component and Specific Weight Analysis) maximizes the sum of squared covariances, by first finding the best pair-component solution, and repeating that process in the respective residual spaces. The sDO-CCSWA is a new monotonically convergent algorithm obtained by searching for a fixed point of the stationary equations. The second approach is a simultaneous algorithm (DO-CCSWA) which maximizes the sum of squared covariances.},
 year = {2022}
}

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TY - JOUR
T1 - Multivariate Analysis of a Sequence of Paired Data Matrices: Succesive and Simultaneous Approaches
AU - Rodnellin Onesime Malouata
AU - Chedly Gélin Louzayadio
AU - Bernédy Nel Messie Kodia Banzouzi
Y1 - 2022/02/14
PY - 2022
N1 - https://doi.org/10.11648/j.ajtas.20221101.16
DO - 10.11648/j.ajtas.20221101.16
T2 - American Journal of Theoretical and Applied Statistics
JF - American Journal of Theoretical and Applied Statistics
JO - American Journal of Theoretical and Applied Statistics
SP - 36
EP - 44
PB - Science Publishing Group
SN - 2326-9006
UR - https://doi.org/10.11648/j.ajtas.20221101.16
AB - The relationship between two data matrices has been studied in the interbattery factor analysis. When two data matrices are partitioned in rows, the relationship between two data matrices has been studied in the STATICO method. The main advantage of this method is the optimality of the compromise of co-structures. It is well known that the weighting coefficients of the compromise may be contrary sign in some cases and make it uninterpretable. Thus, many multivariate data analysis methods have been developed, particularly those designed to tackle the fundamental issue: the description of the relationships between two data matrices. This can be studied by successive modeling approaches as well as by a simultaneous modeling approach. These methods are based on co-inertia and can be reduced to finding the maximum, minimum, or other critical values of a ratio of quadratic forms. However, all these methods are successive. In this paper, we propose two algorithms. The first one called sDO-CCSWA (successive Double-Common Component and Specific Weight Analysis) maximizes the sum of squared covariances, by first finding the best pair-component solution, and repeating that process in the respective residual spaces. The sDO-CCSWA is a new monotonically convergent algorithm obtained by searching for a fixed point of the stationary equations. The second approach is a simultaneous algorithm (DO-CCSWA) which maximizes the sum of squared covariances.
VL - 11
IS - 1
ER -

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Author Information

Rodnellin Onesime Malouata

Department of Licence, Higher Institute of Management, Marien Ngouabi University, Brazzaville, Congo
Chedly Gélin Louzayadio

Department of Licence, Faculty of Economics, Marien Ngouabi University, Brazzaville, Congo
Bernédy Nel Messie Kodia Banzouzi

Department of Mathematics, Faculty of Science and Technology, Marien Ngouabi University, Brazzaville, Congo

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APA Style

Rodnellin Onesime Malouata, Chedly Gélin Louzayadio, Bernédy Nel Messie Kodia Banzouzi. (2022). Multivariate Analysis of a Sequence of Paired Data Matrices: Succesive and Simultaneous Approaches. American Journal of Theoretical and Applied Statistics, 11(1), 36-44. https://doi.org/10.11648/j.ajtas.20221101.16

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ACS Style

Rodnellin Onesime Malouata; Chedly Gélin Louzayadio; Bernédy Nel Messie Kodia Banzouzi. Multivariate Analysis of a Sequence of Paired Data Matrices: Succesive and Simultaneous Approaches. Am. J. Theor. Appl. Stat. 2022, 11(1), 36-44. doi: 10.11648/j.ajtas.20221101.16

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AMA Style

Rodnellin Onesime Malouata, Chedly Gélin Louzayadio, Bernédy Nel Messie Kodia Banzouzi. Multivariate Analysis of a Sequence of Paired Data Matrices: Succesive and Simultaneous Approaches. Am J Theor Appl Stat. 2022;11(1):36-44. doi: 10.11648/j.ajtas.20221101.16

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@article{10.11648/j.ajtas.20221101.16,
  author = {Rodnellin Onesime Malouata and Chedly Gélin Louzayadio and Bernédy Nel Messie Kodia Banzouzi},
  title = {Multivariate Analysis of a Sequence of Paired Data Matrices: Succesive and Simultaneous Approaches},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {11},
  number = {1},
  pages = {36-44},
  doi = {10.11648/j.ajtas.20221101.16},
  url = {https://doi.org/10.11648/j.ajtas.20221101.16},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20221101.16},
  abstract = {The relationship between two data matrices has been studied in the interbattery factor analysis. When two data matrices are partitioned in rows, the relationship between two data matrices has been studied in the STATICO method. The main advantage of this method is the optimality of the compromise of co-structures. It is well known that the weighting coefficients of the compromise may be contrary sign in some cases and make it uninterpretable. Thus, many multivariate data analysis methods have been developed, particularly those designed to tackle the fundamental issue: the description of the relationships between two data matrices. This can be studied by successive modeling approaches as well as by a simultaneous modeling approach. These methods are based on co-inertia and can be reduced to finding the maximum, minimum, or other critical values of a ratio of quadratic forms. However, all these methods are successive. In this paper, we propose two algorithms. The first one called sDO-CCSWA (successive Double-Common Component and Specific Weight Analysis) maximizes the sum of squared covariances, by first finding the best pair-component solution, and repeating that process in the respective residual spaces. The sDO-CCSWA is a new monotonically convergent algorithm obtained by searching for a fixed point of the stationary equations. The second approach is a simultaneous algorithm (DO-CCSWA) which maximizes the sum of squared covariances.},
 year = {2022}
}

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