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

David Causeur, Thierry Dhorne and Arlette Antoni

Journal of Multivariate Analysis, 2005, vol. 95, issue 2, 431-448

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.

Keywords: Biadditive; models; Biplot; Dimensionality; Eigenvalue; distribution; Homologous; factors; Multidimensional; scaling; Random; matrix; theory; Structured; interaction; models (search for similar items in EconPapers)
Date: 2005
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