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. |
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Copyright © The Author(s), 2024. Published by Science Publishing Group |
Interbattery Factor Analysis, STATICO, Common Component and Specific Weight Analysis
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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
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
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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Download@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}
}
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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