Testing probabilistic models of choice using column generation

• 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
• ISSN: 0305-0548; 1873-765X; 1873-765X; 0305-0548
• DOI: 10.1016/j.cor.2018.03.001

•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.