The paper introduces a new class of row-column (RC) association models for contingency tables by allowing the user to select both the scale on which interactions are measured as in Kateri and Papaioannou (1994) and the type of logit (local, global, continuation) suitable for the row and column classification variables as in Bartolucci and Forcina (2002). These choices determine the matrix of interactions which is subjected to rank constraints. Examples are provided where the new models fit substantially better than traditional ones; an intuitive explanation for this behavior is outlined and supported by numerical investigations. An extension of the optimality property in Kateri and Papaioannou (1994) is derived, leading to a general representation theorem and reconstruction formulas for the joint probabilities. These results are the key to show that, given marginal logits, the generalized interactions introduced in this paper determine uniquely the bivariate distribution; in addition, for each pair of logit types, we establish which kind of positive association is implied by our extended interactions being non negative. Quick model selection within this wide class can be performed by an efficient algorithm for computing maximum likelihood estimates which allows for additional linear constraints both on marginal logits and interactions.

通过允许用户选择在Kateri和Papaioannou（1994）中测量交互作用的规模以及logit的类型（本地，全局，续）适合行和列的分类变量，如Bartolucci和Forcina（2002）。这些选择确定了受等级约束的相互作用矩阵。提供了一些示例，说明新模型比传统模型更适合；数值研究概述并支持对此行为的直观解释。推导了Kateri和Papaioannou（1994）中最优性属性的扩展，从而得出了联合概率的一般表示定理和重构公式。这些结果是表明在给定边际对数的情况下，本文引入的广义相互作用唯一确定双变量分布的关键。另外，对于每对logit类型，我们都通过扩展的非负扩展交互来暗示哪种正关联。可以通过一种用于计算最大似然估计的有效算法来执行这一广泛类别中的快速模型选择，该算法可以对边际逻辑和交互性进行额外的线性约束。