This paper focuses on studying the relationships among a set of categorical (ordinal) variables collected in a contingency table. Besides the marginal and conditional (in)dependencies, thoroughly analyzed in the literature, we consider the context-specific independencies holding only in a subspace of the outcome space of the conditioning variables. To this purpose we consider the hierarchical multinomial marginal models and we provide several original results about the representation of context-specific independencies through these models. The theoretical results are supported by an application concerning the innovation degree of Italian enterprises.

中文翻译：

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分层多项式边际模型中特定于上下文的独立性

本文着重研究列联表中收集的一组类别（标准）变量之间的关系。除了在文献中全面分析的边际和条件（独立）依赖性之外，我们还考虑了仅在条件变量的结果空间的子空间中持有的特定于上下文的独立性。为此，我们考虑了分层多项式边际模型，并通过这些模型提供了一些有关上下文特定的独立性表示的原始结果。理论结果得到有关意大利企业创新程度的应用的支持。