Relational models for contingency tables

JOURNAL OF MULTIVARIATE ANALYSIS

卷:104

Article

Klimova, Anna¹  Rudas, Tamas²  Dobra, Adrian¹ 

[1] Univ Washington, Dept Stat, Seattle, WA 98195 USA

[2] Eotvos Lorand Univ, Dept Stat, H-1117 Budapest, Hungary

关键词: Contingency tables;    Curved exponential family;    Exponential family;    Generalized odds ratios;    Maximum likelihood estimate;    Multiplicative model;   

DOI  :  10.1016/j.jmva.2011.07.006

来源: Elsevier

【 摘 要 】

The paper considers general multiplicative models for complete and incomplete contingency tables that generalize log-linear and several other models and are entirely coordinate free. Sufficient conditions for the existence of maximum likelihood estimates under these models are given, and it is shown that the usual equivalence between multinomial and Poisson likelihoods holds if and only if an overall effect is present in the model. If such an effect is not assumed, the model becomes a curved exponential family and a related mixed parameterization is given that relies on non-homogeneous odds ratios. Several examples are presented to illustrate the properties and use of such models. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free