Multiple discrete choice and quantity with order statistic marginal utilities

IF 2.8 3区 经济学 Q1 ECONOMICS Journal of Choice Modelling Pub Date : 2023-03-01 DOI:10.1016/j.jocm.2022.100395
Scott Webster
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引用次数: 1

Abstract

This paper presents a random utility maximization model for individuals selecting discrete quantities from a set of n alternatives. Multiple alternatives with positive quantities may be selected. Diminishing marginal utility to quantity of each alternative is modeled via order statistics of independent Gumbel random variables. The model is parsimonious and tractable, admitting closed-form expressions for choice probabilities. As such, the model is amenable to maximum likelihood estimation of structural parameters from observed choices.

Probability functions recover binary logit probabilities under binary choice and a maximum quantity of one unit, and probability is monotonic in the quantity of each alternative. The monotonic property likely restricts the application of the model to a narrow range of settings. The property is a manifestation of a recursive relationship among Gumbel order statistic probabilities. This relationship and related properties may lead to new models for capturing important complexities in a tractable manner.

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具有订单统计边际效用的多重离散选择与数量
本文提出了一个随机效用最大化模型,用于个体从一组n个备选方案中选择离散量。可以选择多个具有正数量的备选方案。边际效用对每个备选方案数量的递减是通过独立Gumbel随机变量的顺序统计建模的。该模型简洁易处理,允许选择概率的闭式表达式。因此,该模型适用于根据观察到的选择对结构参数进行最大似然估计。概率函数在二元选择和一个单位的最大数量下恢复二元logit概率,并且概率在每个备选的数量上是单调的。单调特性可能会将模型的应用限制在较窄的设置范围内。该性质是Gumbel阶统计概率之间递归关系的表现。这种关系和相关属性可能会导致以可处理的方式捕捉重要复杂性的新模型。
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来源期刊
CiteScore
4.10
自引率
12.50%
发文量
31
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