摘要
The question of the existence of independent random variables which represent a given set of binary choice data is investigated. It is related to the linear ordering polytope. The subset of it which is independently representable, denoted by ILOn, is characterized for three elements. For the general case, necessary conditions are given and their geometric meaning is discussed. A procedure, called mixture technique, is developed which allows one to construct a new point in ILOn and its independent representation from known points in ILOn. Finally, a few results on parametric representations are derived.
摘要译文
研究了存在表示给定二元选择数据集的独立随机变量的问题。它与线性排序多面体有关。其独立可表示的子集，由I LO n 表示，其特征在于三个元素。对于一般情况，给出了必要的条件并讨论了它们的几何意义。开发了一种称为混合技术的程序，它允许人们在I LO n 中构建一个新点，并从I LO n 中的已知点构建它的独立表示。最后，推导出一些关于参数表示的结果。
ReinhardSuck;. Independent random utility representations[J]. Mathematical Social Sciences, 2002,43(3): 371-389