Unit-Level Models and Discrete Demand
Using this Chapter
This chapter reviews models for discrete data. Much of the disaggregate data collected in marketing has discrete aspects to the quantities of goods purchased. Sections 4.1-4.3 review the latent variable approach to formulating models with discrete dependent variables, while Section 4.4 derives models based on a formal theory of utility maximization. Those interested in multinomial probit or multivariate probit models should focus on Sections 4.2 and 4.3. Section 4.2.1 provides material on understanding the difference between various Gibbs samplers proposed for these models and can be omitted by those seeking a more general appreciation. Section 4.4 forges a link between statistical and economic models and introduces demand models which can be used for more formal economic questions such as welfare analysis and policy simulation.
We define the 'unit-level' as the lowest level of aggregation available in a data set. For example, retail scanner data is available at many levels of aggregation. The researcher might only have regional or market-level aggregate data. Standard regression models can suffice for this sort of highly aggregated data. However, as the level of aggregation declines to the consumer level, sales response becomes more and more discrete. There are a larger number of zeros in this data and often only a few integer-valued points of support. If, for example, we examine the prescribing behavior of a physician over a short period of time, this will be a count variable. Consumers often choose to purchase only a small number of items from a large set of alternatives. The goal of this chapter is to investigate models appropriate for disaggregate data. The common characteristic of these models will be the ability to attach lumps of probability to specific outcomes. It should also be emphasized that even if the goal is to analyze only highly aggregate data, the researcher could properly view this data as arising from individual-level decisions aggregated up to form the data observed. Thus, individual-level demand models and models for the distribution of consumer preferences (the focus of Chapter 5) are important even if the researcher only has access to aggregate data.