Preference and choice models
Research In Progress
My research focuses on developing quantitative methods to understand consumer behavior and guide firms’ decisions. Currently, I work on models that account for consumer psychological biases, consumer learning, and decision processes (e.g., lexicographic) with applications in e-commerce, big data and branding.
A generalized-means choice model for regularity violations
We introduce a multi-attribute choice model that allows violations of regularity, as well as violations of the weak order independence and IIA conditions. The proposed model generalizes the multinomial logit model, and can accommodate a non-compensatory choice process in which an alternative is evaluated by its best or worst features.
- Randomized algorithm for lexicographic inference
The inference of a lexicographic rule from paired comparisons, ranking or choice data is a discrete optimization problem that generalizes the linear ordering problem. We develop an approach to its solution using randomized algorithms. First, we show that maximizing the expected value of a randomized solution is equivalent to solving the lexicographic inference problem. As a result, the discrete problem is transformed into a continuous and unconstrained nonlinear program that can be solved, possible to a local optimum, using standard nonlinear optimization methods. Second, we show that a maximum likelihood procedure, which runs in polynomial time, can be used to implement the randomized algorithm. The maximum likelihood value determines a lower bound on the performance ratio of the randomized algorithm. We employ the proposed approach to infer lexicographic rules for individuals using data from a choice experiment for electronic tablets. These rules obtain substantially better fit and predictions than a previously described greedy algorithm and a multinomial logit model.
- Linking continuous and discrete linear ordering problems
Inferring a lexicographic rule from preference or choice data is an NP hard problem. We propose a randomized algorithm for solving the problem. The expected value of its solution is expressed as a function of the parameters of independent, extreme value distributions. The parameter estimates needed to implement the algorithm are obtained in polynomial time by maximizing a likelihood function. The maximum likelihood value is used to obtain a lower bound on the performance ratio of the randomized algorithm. This lower bound can be computed for each problem instance, and cannot be smaller than 1/2. The linear ordering problem can be solved as a special case of the lexicographic inference problem.
- Fit or hit in choice models
We examine and illustrate conditions under which a choice model with a higher likelihood value may obtain a lower hit rate. We also show that the solution obtained by maximizing a likelihood function can be different from the solution obtained by maximizing the hit rate. The analysis and results suggest that the hit rate should not be overly emphasized when the objective is testing a theory and/or statistical inference.
- Simulated hierarchical EBA
We develop a model of consumer inter-temporal learning about uncertain aspects for a non-compensatory choice rules, specifically elimination by aspect. We show that the model allows for inference about learning with latent consumption outcomes. We calibrate the model on panel data using Bayesian estimation techniques.
- A mean-field model of brand association formation
We develop a model of brand association where the long run brand perception is a Nash-equilibrium of a continuous time stochastic differential game. The large number of consumers is incorporated in the model through mean-field approximation techniques. Results indicate that brand association is a mutual outcome of the intrinsic aspect of the brand and the social consensus around it.
Quantitative Marketing and Structural Econometrics Workshop Fellow, 2015
INFORMS Doctoral Consortium Fellow, 2015
Graduate Student Fellowship, Columbia University, 2013
Laureate Fellowship, Tunisian Government, 2006