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Canonical Correlation Analysis of Longitudinal Data

Jayesh Srivastava, Dayanand N. Naik

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Abstract

Studying the relationship between two sets of variables is an important multivariate statistical analysis problem in statistics. Canonical correlation coe‐cients are used to study these relationships. Canonical correlation analysis (CCA) is a general multivariate method that is mainly used to study relationships when both sets of variables are quantitative. In this paper, we have generalized CCA to analyze the relationships between two sets of repeatedly or longitudinally observed data using a block Kronecker product matrix to model dependency of the variables over time. We then apply canonical correlation analysis on this matrix to obtain canonical correlations and canonical variables.

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What this paper is about

Studying the relationship between two sets of variables is an important multivariate statistical analysis problem in statistics. Canonical correlation coe‐cients are used to study these relationships. Canonical correlation analysis (CCA) is a general multivariate method that is mainly used to study relationships when both sets of variables are quantitative. In this paper, we have generalized CCA to analyze the relationships between two sets of repeatedly or longitudinally observed data using a block Kronecker product matrix to model dependency of the variables over time. We then apply canonical correlation analysis on this matrix to obtain canonical correlations and canonical variables.

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Available abstract

Studying the relationship between two sets of variables is an important multivariate statistical analysis problem in statistics. Canonical correlation coe‐cients are used to study these relationships. Canonical correlation analysis (CCA) is a general multivariate method that is mainly used to study relationships when both sets of variables are quantitative. In this paper, we have generalized CCA to analyze the relationships between two sets of repeatedly or longitudinally observed data using a block Kronecker product matrix to model dependency of the variables over time. We then apply canonical correlation analysis on this matrix to obtain canonical correlations and canonical variables.

Key concepts: Canonical correlation, Canonical analysis, Canonical correspondence analysis, Mathematics, Kronecker product, Dependency (UML), Correspondence analysis, Statistics

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