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    Area of Science:

    • Multivariate statistics
    • Psychometrics
    • Data analysis

    Background:

    • Three-mode component analysis is applicable to longitudinal multivariate data.
    • Millsap and Meredith (1988) proposed a component analysis method using stationary compositing weights for such data.

    Purpose of the Study:

    • To present theorems defining constraints for equivalency between component representations.
    • To compare three-mode component analysis with methods using stationary compositing weights.

    Main Methods:

    • Mathematical theorem derivation.
    • Comparative analysis of component representation methods.

    Main Results:

    • Theorems establish specific constraints for the equivalency of component representations.
    • In general, the two approaches (three-mode component analysis and stationary compositing weights) produce mathematically distinct representations.

    Conclusions:

    • Equivalency between component representations from three-mode component analysis and stationary compositing weights is not generally guaranteed.
    • Understanding the constraints for equivalency is crucial for accurate longitudinal data analysis.