A note on multivariate logistic: Models for contingency tables
A note on multivariate logistic: Models for contingency tables
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DOI：
10.1111/j.1467-842x.1997.tb00691.x
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发表时间：
1997-12-01
期刊：
影响因子：
--
通讯作者：
Kauermann, G
中科院分区：
文献类型：
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作者：
Kauermann, G
对数线性模型是一种广泛接受的工具，用于模拟列联表中的离散数据。虽然它的参数反映了所有变量联合分布中的相互作用结构，但它并没有给出有关出现在表格边缘的结构的信息。这与Glonek & McCullagh（1995）最近引入的多变量logistic参数形成对比，多变量logistic参数具有从联合表和每个边缘表导出的最高阶对数优势比作为参数。Glonek; & McCullagh以代数的方式给出了细胞概率和多变量逻辑参数之间的联系。本文着重于这一环节，表明它是由一般参数变换指数家庭。特别是，自然之间的连接，期望和混合参数化指数家庭（Barndorff-Nielsen，1978）被使用;这也产生的衍生物的似然方程，并显示属性的Fisher矩阵。本文着重分析列联表边际中的独立性假设。
The log-linear model is a tool widely accepted for modelling discrete data given in a contingency table. Although its parameters reflect the interaction structure in the joint distribution of all variables, it does not give information about structures appearing in the margins of the table. This is in contrast to multivariate logistic parameters, recently introduced by Glonek & McCullagh (1995), which have as parameters the highest order log odds ratios derived from the joint table and from each marginal table. Glonek; & McCullagh give the link between the cell probabilities and the multivariate logistic parameters, in an algebraic fashion. The present paper focuses on this link, showing that it is derived by general parameter transformations in exponential families. In particular, the connection between the natural, the expectation and the mixed parameterization in exponential families (Barndorff-Nielsen, 1978) is used; this also yields the derivatives of the likelihood equation and shows properties of the Fisher matrix. The paper emphasises the analysis of independence hypotheses in margins of a contingency table.