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Properties of and Algorithms for Fitting Three-Way Component Models with Offset Terms.

Henk A L Kiers1,2

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This study revisits estimating "offset terms" in three-way component analysis. The proposed successive approach effectively estimates these terms, offering a simple extension to traditional methods for analyzing ratio scale data.

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Area of Science:

  • Multivariate statistics
  • Data analysis

Background:

  • Traditional three-way component analysis preprocesses data by centering and/or rescaling.
  • Offset terms can transform ratio scale measurements into interval scale measurements.

Purpose of the Study:

  • To re-evaluate the estimation of offset terms in three-way component analysis.
  • To develop and compare simultaneous and successive procedures for estimating offset and model parameters.

Main Methods:

  • Investigated unique estimation conditions for offset terms.
  • Developed simultaneous and successive estimation procedures for CANDECOMP/PARAFAC and Tucker3 models with offset terms.
  • Compared performance using simulated data.

Main Results:

  • Both simultaneous and successive procedures perform well when the fitted model includes all underlying offset terms.
  • Simultaneous procedures showed slightly better performance when all offset terms were captured.
  • Successive procedures performed better when fewer offset terms were fitted than present in the data.

Conclusions:

  • The traditional approach for estimating model parameters is robust.
  • Offset terms can be sufficiently estimated using the proposed successive approach, a simple extension of traditional methods.