{"title":"Multiple discrete choice and quantity with order statistic marginal utilities","authors":"Scott Webster","doi":"10.1016/j.jocm.2022.100395","DOIUrl":null,"url":null,"abstract":"<div><p>This paper presents a random utility maximization model for individuals selecting discrete quantities from a set of <em>n</em> 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.</p><p>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.</p></div>","PeriodicalId":46863,"journal":{"name":"Journal of Choice Modelling","volume":"46 ","pages":"Article 100395"},"PeriodicalIF":2.8000,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Choice Modelling","FirstCategoryId":"96","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1755534522000525","RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ECONOMICS","Score":null,"Total":0}
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.