Conjunctive screening in models of multiple discreteness

Highlights

• Screening model for discrete choice is exteneded to multiple-discreteness data.

• Effects of screening in models for discrete and volumetric demand are compared.

• Screening removes respondents from demand estimates, lowering purchase incidence

• Screening leads to an increase in volumetric demand for consumers who don’t screen.

• Zero-purchases come from screening-out more than from lack of preference.

Abstract

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.

Introduction

Consumer choices among alternatives in any product class involve the screening of alternatives to reduce the cognitive demands of decision making. Some brands available for sale are potentially responsive to the needs of individuals and others are not. Resource conserving decision makers have long been known to rule-out alternatives that are not candidates for purchase. Responsive attributes are those that can potentially serve as instruments in making changes in the state of the individual, and alternatives with these attributes are admitted into a consideration set for further evaluation and potential purchase.

Consideration sets are an example of selection process, where some objects are retained for analysis and others are not. Methods of variable selection (George & McCulloch, 1993) and LASSO estimators (Hans, 2009) identify variables to include in a model and act to filter out the variables with low predictive power. Alternatively, partition models (Müller & Quintana, 2010) are used to identify sets of experimental units (e.g., data points, respondents) that are relevant for analysis. Instead of selecting independently determined variables or observed data on which analysis conditions, our model selects objects and associated error terms (choice alternatives) for removal from the likelihood. In this paper we develop a general model for identifying brands and their characteristics, or attributes, useful for exclusion in an analysis in that their presence improves model fit and prediction. Our method can be easily applied to models of choice and quantity, where objects compete with each other.

Models of a consideration set formation have been successfully developed for discrete choice models (Gilbride & Allenby, 2004) and in this paper we extend their application in models of multiple discreteness or horizontal variety (Kim, Allenby, & Rossi, 2002) where more than one alternative can be simultaneously chosen. Table 1 provides a comparison of extant choice models by demand type (discrete or volumetric) and an implemtation of screening. In discrete choice models, the presence of a screening rule removes a choice alternative from the calculation of the choice probability. In models of multiple discreteness, where Kuhn-Tucker conditions (KT) are used to develop the model likelihood, the screening rule similarly eliminates the choice alternative from the likelihood. The consideration model of Gilbride and Allenby (2004) is based on a probit choice model specification where utilities for non-considered goods can be inferred using the Bayesian technique of data augmentation (Tanner & Wong, 1987). We propose a simplified method for eliminating outcomes from analysis that does not rely on data augmentation technique and can be used with any likelihood specification.

When a choice alternative is included in the consideration set but not chosen, its ratio of marginal utility to price (i.e., its ‘bang for the buck’) serves as a lower bound to the items that are chosen. When it is not part of the consideration set, its ratio does not play this role. This can result in different inferences about the importance of product attributes. Moreover, a specific attribute may be inferred to have a negative effect on marginal utility when its effect is essentially one for consideration set formation for low levels of an attribute (e.g., salt content), where additional amounts of the attribute have no additional effect on demand once the alternative makes it into the choice set. Such “must-have” attribute levels are needed by brands to be competitive and actively considered by individuals. Alternatively, an attribute can be inferred to have a positive effect on marginal utility when it really serves only to screen alternatives for inclusion at higher attribute levels.

We investigate the conjunctive screening occurring during consumers’ decision. Consumers can screen alternatives using a variety of alternative criteria, but empirical evidence favors the conjunctive rule versus others such as a disjunctive rule or the use of a non-compensatory model (Aribarg et al., 2018). The remainder of the paper is organized as follows. Section 2 develops our model of multiple discreteness with a conjunctive screening rule in which acceptable regions of attribute levels can be identified. Section 3 presents two empirical studies of demand for ice cream and frozen pizza in which discrete product attributes are used to construct the consideration set. Section 4 contains the implications of our model including counterfactual experiments, and Section 5 provides concluding remarks.