Conjunctive screening in models of multiple discreteness

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.