Hierarchical Aitchison-Silvey models for incomplete binary sample spaces

JOURNAL OF MULTIVARIATE ANALYSIS

卷:187

Article

Klimova, Anna^1,3  Rudas, Tamas² 

[1] Natl Ctr Tumor Dis NCT, Partner Site Dresden, Dresden, Germany

[2] Eotvos Lorand Univ, Dept Stat, Budapest, Hungary

[3] Tech Univ, Inst Med Informat & Biometry, Dresden, Germany

关键词: Algebraic variety;    Contingency table;    Generalized odds ratio;    Overall effect;    Relational model;   

DOI  :  10.1016/j.jmva.2021.104808

来源: Elsevier

【 摘 要 】

Multivariate sample spaces may be incomplete Cartesian products, when certain combi-nations of the categories of the variables are not possible. Traditional log-linear models, which generalize independence and conditional independence, do not apply in such cases, as they may associate positive probabilities with the non-existing cells. To describe the association structure in incomplete sample spaces, this paper develops a class of hi-erarchical multiplicative models which are defined by setting certain non-homogeneous generalized odds ratios equal to one and are named after Aitchison and Silvey who were among the first to consider such ratios. These models are curved exponential families that do not contain an overall effect and, from an algebraic perspective, are non-homogeneous toric ideals. The relationship of this model class with log-linear models and quasi log-linear models is studied in detail in terms of both statistics and algebraic geometry. The existence of maximum likelihood estimates and their properties, as well as the relevant algorithms are also discussed. (c) 2021 Elsevier Inc. All rights reserved.

【 授权许可】

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