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Maximum likelihood inference for log-linear models subject to constraints of double monotone dependence

机译:对数线性模型受双单调相关性约束的最大似然推断

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摘要

To model an hypothesis of double monotone dependence between two ordinal categorical variables A and B usually a set of symmetric odds ratios defined on the joint probability function is subject to linear inequality constraints. Conversely in this paper two sets of asymmetric odds ratios defined, respectively, on the conditional distributions of A given B and on the conditional distributions of B given A are subject to linear inequality constraints. If the joint probabilities are parameterized by a saturated log-linear model, these constraints are nonlinear inequality constraints on the log-linear parameters. The problem here considered is a non-standard one both for the presence of nonlinear inequality constraints and for the fact that the number of these constraints is greater than the number of the parameters of the saturated log-linear model.
机译:为了对两个有序分类变量A和B之间的双单调依赖关系的假设进行建模,通常在联合概率函数上定义的一组对称优势比受线性不等式约束。相反,在本文中,分别在A给定B的条件分布和B给定A的条件分布上定义的两组非对称比值受到线性不等式约束。如果通过饱和对数线性模型对联合概率进行参数化,则这些约束是对数线性参数的非线性不等式约束。对于非线性不等式约束的存在以及这些约束的数量大于饱和对数线性模型的参数数量的事实,此处考虑的问题是非标准的。

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