After more then 50 years of probabilistic choice modeling in Economics, Marketing, Political Science, Psychology, and related disciplines, theoretical and computational advances give scholars access to a sophisticated array of modeling and inference resources. We review some important, but perhaps often overlooked, properties of major classes of probabilistic choice models. For within-respondent applications, we discuss which models require repeated choices by an individual to be independent and response probabilities to be stationary. We show how some model classes, but not others, are invariant over variable preferences, variable utilities, or variable choice probabilities. These models, but not others, accommodate pooling of responses or averaging of choice proportions within participant when underlying parameters vary across observations. These, but not others, permit pooling/averaging across respondents in the presence of individual differences. We also review the role of independence and stationarity in statistical inference, including for probabilistic choice models that, themselves, do not require those properties.

中文翻译：

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独立性和平稳性在二元选择概率模型中的作用

在经济学、市场营销、政治学、心理学和相关学科中进行了 50 多年的概率选择建模之后，理论和计算的进步使学者们能够获得一系列复杂的建模和推理资源。我们回顾了一些主要类别的概率选择模型的一些重要但可能经常被忽视的属性。对于内部响应应用程序，我们讨论哪些模型需要个人重复选择才能独立，而响应概率是平稳的。我们展示了一些模型类（而不是其他模型类）如何在可变偏好、可变效用或可变选择概率上保持不变。当基本参数随观察而变化时，这些模型（而不是其他模型）可容纳参与者内的反应汇总或平均选择比例。这些（但不是其他）允许在存在个体差异的情况下对受访者进行汇总/平均。我们还回顾了独立性和平稳性在统计推断中的作用，包括对于本身不需要这些属性的概率选择模型。