This study focuses on the menus typically found in the marketplace (e.g., restaurants and Internet vendors), where the consumer may choose one or more from dozens of options or menu items, each at a posted price or fee. We show that modeling choices out of the typical menu leads to the “curse of dimensionality,” which transpires in two ways. First, the choice set (all possible menu selections) grows geometrically with the number of items in the menu. Second, the number of interactions among menu items also grows disproportionately to the number of items in the menu. We propose a menu choice model that circumvents these two problems in a feasible and flexible, but parsimonious way.

We test the proposed model on synthetic data from Monte-Carlo simulations and find that the proposed estimation approach produces consistent parameter estimates while significantly reducing the dimensionality of the problem. We then apply the proposed approach to an actual choice experiment where a sample of consumers made multiple choices from eight different menus, each combining a base system with selections from 25 optional features. Our empirical results show that menu items do interact (positively or negatively) and the proposed approach produces a graphical representation of these interactions. We also perform an optimal pricing policy experiment to further illustrate the practical features of the proposed menu-choice modeling approach.

这项研究的重点是通常在市场（例如，饭店和互联网供应商）中找到的菜单，消费者可以在其中从数十个选项或菜单项中选择一个或多个，每个选项或菜单项均以公布的价格或费用收取。我们表明，从典型菜单中进行建模选择会导致“维数诅咒”，这种情况有两种表现形式。首先，选项集（所有可能的菜单选择）随着菜单项的数量呈几何增长。其次，菜单项之间的交互数量也与菜单中的项目数量不成比例地增长。我们提出了一种菜单选择模型，该模型以可行，灵活，但简单的方式规避了这两个问题。

我们对来自蒙特卡洛模拟的合成数据测试了所提出的模型，发现所提出的估计方法产生了一致的参数估计，同时显着降低了问题的维数。然后，我们将建议的方法应用于实际选择实验，在该实验中，消费者样本从八个不同的菜单中进行了多个选择，每个菜单都将基本系统与来自25个可选功能的选项结合在一起。我们的经验结果表明，菜单项确实发生了交互（正向或负向），并且所提出的方法产生了这些交互的图形表示。我们还将执行最佳定价策略实验，以进一步说明所提出的菜单选择建模方法的实用功能。