Consumer demand for products often result in the purchase of multiple goods at the same time. Corner solutions, or the non-purchase of items, occur when consumers have strong preference for some goods that do not satiate and weak preference for other goods. However, if non-purchase arises because a consumer finds particular brands and attributes unacceptable, leading to the formation of consideration sets, then estimates of preference will be too extreme and biased. In this paper, we extend the work on consideration sets and discrete choices to a wider class of models, and develop a model of multiple discreteness with conjunctive screening of the alternatives that remove offerings from consideration. We propose a method for consideration set formation that does not require one to specify a partitioned space of the augmented variable, and that can be adapted into the class of choice models in which an outcome variable is removed. We explore implications for disentangling non-purchase due to consideration set formation using two data sets of ice cream and frozen pizza purchases. The ice cream data, in which responses are both discrete and volumetric, allow us to compare differences in how screening affect purchase incidence versus volumetric demand per incidence. Screening reduces the estimated number of customers with positive demand but leads to an increase in demand for those not screened. In the frozen pizza data, we find that conjunctive screening accounts for many of the observed corner solutions and leads to estimates of preference and satiation that differs from traditional models of multiple-discreteness without screening.

消费者对产品的需求往往会导致同时购买多种商品。当消费者对某些不满意的商品有强烈偏好而对其他商品的偏好较弱时，就会出现角落解决方案或不购买商品。然而，如果由于消费者发现特定品牌和属性不可接受而导致不购买，从而导致考虑集的形成，那么对偏好的估计将过于极端和有偏见。在本文中，我们将关于考虑集和离散选择的工作扩展到更广泛的模型类别，并开发了一个多重离散模型，对备选方案进行联合筛选，将产品从考虑中移除。我们提出了一种考虑集形成方法，不需要指定增广变量的分区空间，并且可以将其改编为选择模型类，其中删除了结果变量。我们使用冰激凌和冷冻比萨饼购买的两个数据集探索了由于考虑集形成而导致的非购买的分离意义。冰激凌数据，其中响应既是离散的又是体积的，使我们能够比较筛选如何影响购买发生率与每次发生的体积需求之间的差异。筛选减少了具有积极需求的客户的估计数量，但导致对未筛选的客户的需求增加。在冷冻披萨数据中，我们发现联合筛选解释了许多观察到的角解，并导致对偏好和饱腹感的估计，这与没有筛选的传统多重离散模型不同。