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A two-way analysis of variance model with positive definite interaction for homologous factors

Author

Listed:
  • Causeur, David
  • Dhorne, Thierry
  • Antoni, Arlette

Abstract

A special type of modelling of interaction is investigated in the framework of two-way analysis of variance models for homologous factors. Factors are said to be homologous when their levels are in a meaningful one-to-one relationship, which arise in a wide variety of contexts, as recalled by McCullagh (J. Roy. Statist. Soc. B 62 (2000) 209). The classical linear context for analysis of interaction is extended by positive definiteness restrictions on the interaction parameters. These restrictions aim to provide a spatial representation of the interaction. Properties of the maximum likelihood estimators are derived for a given dimensionality of the model. When the dimension is unknown, an alternative procedure is proposed based on a penalty approach. This approach relies heavily on random matrix theory arguments but we focus on their statistical consequences especially on the reduction of over-fitting problems in the maximum likelihood estimation. Confidence ellipses are provided for an illustrative example.

Suggested Citation

  • Causeur, David & Dhorne, Thierry & Antoni, Arlette, 2005. "A two-way analysis of variance model with positive definite interaction for homologous factors," Journal of Multivariate Analysis, Elsevier, vol. 95(2), pages 431-448, August.
    • Handle: RePEc:eee:jmvana:v:95:y:2005:i:2:p:431-448
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    References listed on IDEAS

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    1. P. McCullagh, 2000. "Invariance and factorial models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(2), pages 209-256.
    2. Edelman, Alan, 1997. "The Probability that a Random Real Gaussian Matrix haskReal Eigenvalues, Related Distributions, and the Circular Law," Journal of Multivariate Analysis, Elsevier, vol. 60(2), pages 203-232, February.
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