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The link between multiplicative competitive interaction models and compositional data regression with a total.

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Area of Science:

  • Statistical Modeling
  • Econometrics
  • Marketing Science

Background:

  • Compositional data (CoDa) and multiplicative competitive interaction (MCI) models are distinct approaches for analyzing share data.
  • MCI models have a long-standing tradition in marketing research, grounded in behavioral assumptions.
  • CoDa models offer a rigorous mathematical framework for handling compositional data.

Purpose of the Study:

  • To elucidate the relationship between CoDa regression and MCI models.
  • To demonstrate that MCI models are a special type of CoDa model.
  • To leverage the strengths of each approach for mutual benefit in their respective fields.

Main Methods:

  • Reparameterization to link MCI and CoDa models.
  • Application of CoDa's theoretical guarantees and mathematical tools to enhance MCI model estimation.
  • Analysis of MCI models' elasticity interpretation from a CoDa perspective.

Main Results:

  • MCI models are identified as particular cases of CoDa models with a total.
  • A reparameterization successfully links both modeling frameworks.
  • The CoDa perspective allows for decomposing explanatory variable influence into relative and absolute information contributions.

Conclusions:

  • The integration of CoDa and MCI models offers significant advantages for both statistical and marketing research.
  • CoDa provides enhanced theoretical grounding and estimation techniques for MCI models.
  • MCI's behavioral assumptions and justification for heteroskedasticity can enrich the CoDa literature.