Testing probabilistic models of choice using column generation

•We describe a Column Generation algorithm for testing models of probabilistic choice.•We investigate the impact of several choices when it comes to implementing the algorithm.•We show the Column Generation algorithm is well-suited for computing Bayes factors. In so-called random preference models o...

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Published in	Computers & operations research Vol. 95; pp. 32 - 43
Main Authors	Smeulders, Bart, Davis-Stober, Clintin, Regenwetter, Michel, Spieksma, Frits C.R.
Format	Journal Article
Language	English
Published	United States Elsevier Ltd 01.07.2018 Pergamon Press Inc Elsevier
Subjects	Algorithms Business & economic sciences Choice Behavior Column Generation Computational mathematics Computer science Decision making Engineering, computing & technology Ingénierie, informatique & technologie Membership Problems Multiple criteria decision making Méthodes quantitatives en économie & gestion Operations research Probabilistic Choice Probabilistic models Probability distribution Quantitative methods in economics & management Sciences informatiques Sciences économiques & de gestion Statistical analysis Studies Probabilistic choice Column generation Membership problems Choice behavior Membership Problems Probabilistic Choice Column Generation Choice Behavior
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ISSN	0305-0548 1873-765X 1873-765X 0305-0548
DOI	10.1016/j.cor.2018.03.001

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Abstract	•We describe a Column Generation algorithm for testing models of probabilistic choice.•We investigate the impact of several choices when it comes to implementing the algorithm.•We show the Column Generation algorithm is well-suited for computing Bayes factors. In so-called random preference models of probabilistic choice, a decision maker chooses according to an unspecified probability distribution over preference states. The most prominent case arises when preference states are linear orders or weak orders of the choice alternatives. The literature has documented that actually evaluating whether decision makers’ observed choices are consistent with such a probabilistic model of choice poses computational difficulties. This severely limits the possible scale of empirical work in behavioral economics and related disciplines. We propose a family of column generation based algorithms for performing such tests. We evaluate our algorithms on various sets of instances. We observe substantial improvements in computation time and conclude that we can efficiently test substantially larger data sets than previously possible.
AbstractList	In so-called random preference models of probabilistic choice, a decision maker chooses according to an unspecified probability distribution over preference states. The most prominent case arises when preference states are linear orders or weak orders of the choice alternatives. The literature has documented that actually evaluating whether decision makers’ observed choices are consistent with such a probabilistic model of choice poses computational difficulties. This severely limits the possible scale of empirical work in behavioral economics and related disciplines. We propose a family of column generation based algorithms for performing such tests. We evaluate our algorithms on various sets of instances. We observe substantial improvements in computation time and conclude that we can efficiently test substantially larger data sets than previously possible. In so-called random preference models of probabilistic choice, a decision maker chooses according to an unspecified probability distribution over preference states. The most prominent case arises when preference states are linear orders or weak orders of the choice alternatives. The literature has documented that actually evaluating whether decision makers’ observed choices are consistent with such a probabilistic model of choice poses computational difficulties. This severely limits the possible scale of empirical work in behavioral economics and related disciplines. We propose a family of column generation based algorithms for performing such tests. We evaluate our algorithms on various sets of instances. We observe substantial improvements in computation time and conclude that we can efficiently test substantially larger data sets than previously possible. In so-called random preference models of probabilistic choice, a decision maker chooses according to an unspecified probability distribution over preference states. The most prominent case arises when preference states are linear orders or weak orders of the choice alternatives. The literature has documented that actually evaluating whether decision makers' observed choices are consistent with such a probabilistic model of choice poses computational difficulties. This severely limits the possible scale of empirical work in behavioral economics and related disciplines. We propose a family of column generation based algorithms for performing such tests. We evaluate our algorithms on various sets of instances. We observe substantial improvements in computation time and conclude that we can efficiently test substantially larger data sets than previously possible.In so-called random preference models of probabilistic choice, a decision maker chooses according to an unspecified probability distribution over preference states. The most prominent case arises when preference states are linear orders or weak orders of the choice alternatives. The literature has documented that actually evaluating whether decision makers' observed choices are consistent with such a probabilistic model of choice poses computational difficulties. This severely limits the possible scale of empirical work in behavioral economics and related disciplines. We propose a family of column generation based algorithms for performing such tests. We evaluate our algorithms on various sets of instances. We observe substantial improvements in computation time and conclude that we can efficiently test substantially larger data sets than previously possible. •We describe a Column Generation algorithm for testing models of probabilistic choice.•We investigate the impact of several choices when it comes to implementing the algorithm.•We show the Column Generation algorithm is well-suited for computing Bayes factors. In so-called random preference models of probabilistic choice, a decision maker chooses according to an unspecified probability distribution over preference states. The most prominent case arises when preference states are linear orders or weak orders of the choice alternatives. The literature has documented that actually evaluating whether decision makers’ observed choices are consistent with such a probabilistic model of choice poses computational difficulties. This severely limits the possible scale of empirical work in behavioral economics and related disciplines. We propose a family of column generation based algorithms for performing such tests. We evaluate our algorithms on various sets of instances. We observe substantial improvements in computation time and conclude that we can efficiently test substantially larger data sets than previously possible.
Author	Spieksma, Frits C.R. Smeulders, Bart Davis-Stober, Clintin Regenwetter, Michel
AuthorAffiliation	c Department of Psychology, University of Illinois at Urbana-Champaign, 603 E. Daniel St., Champaign, IL 61820, USA d Department of Mathematics and Computer Science, TU Eindhoven, 5600 MB Eindhoven, the Netherlands b Department of Psychological Sciences, University of Missouri, 219 McAlester Hall, Columbia, MO 65211, USA a HEC Management School, University of Liège, 4000 Liège, Belgium
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Snippet	•We describe a Column Generation algorithm for testing models of probabilistic choice.•We investigate the impact of several choices when it comes to... In so-called random preference models of probabilistic choice, a decision maker chooses according to an unspecified probability distribution over preference... In so-called random preference models of probabilistic choice, a decision maker chooses according to an unspecified probability distribution over preference...
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SubjectTerms	Algorithms Business & economic sciences Choice Behavior Column Generation Computational mathematics Computer science Decision making Engineering, computing & technology Ingénierie, informatique & technologie Membership Problems Multiple criteria decision making Méthodes quantitatives en économie & gestion Operations research Probabilistic Choice Probabilistic models Probability distribution Quantitative methods in economics & management Sciences informatiques Sciences économiques & de gestion Statistical analysis Studies
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Title	Testing probabilistic models of choice using column generation
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