The State of the Art and the State of Practice
Edited by Stephane Hess and Andrew Daly
Chapter 3: Workshop report: recent advances on modeling multiple discrete-continuous choices
Many consumer choice situations involve making a selection (or selections) from among a set of competing (discrete) alternatives, along with a set of corresponding (continuous) quantity decisions. An important, widely studied special case is the discrete choice of a single alternative (assuming all consumption is confined to the single chosen alternative). However, situations involving multiple discrete-continuous (MDC) choices are pervasive in the social sciences, including transportation, economics and marketing. Examples include individuals’ time-use choices (decisions to engage in different types of activities and time allocation to each activity), investment portfolios (where and how much to invest), and grocery purchases (brand choice and purchase quantity). A number of different approaches have been used in the literature to handle “multiple discreteness.” One approach is to enumerate all possible bundles of the elemental choice alternatives and treat each bundle as a “composite” alternative within a traditional, single discrete choice framework. A problem with this approach is that the number of composite alternatives explodes as the number of elemental alternatives increases. A second approach is to use a multivariate statistical system, with several univariate discrete choice model equations linked to each other through statistical correlations. This reduced-form method is based on a rather mechanical statistical “stitching” of multiple univariate model equations rather than a unified, underlying theoretical framework.
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