[Paper Review] A Customer Choice Model with HALO Effect

Reza Yousefi Maragheh, Alexandra Chronopoulou+1 more|arXiv (Cornell University)|May 4, 2018

Consumer Market Behavior and PricingBusiness, Management and Accounting18 references4 citations

TL;DR

This paper proposes the Halo MNL model, an extension of the multinomial logit (MNL) choice model that incorporates pairwise interaction effects between products to capture positive or negative halo effects in customer choice behavior. By modeling how the presence or absence of one product influences the choice probabilities of others, the model improves fit over standard MNL, especially with rich datasets, while establishing sufficient identifiability conditions for robust parameter estimation via maximum likelihood with closed-form solutions.

ABSTRACT

In this paper, we propose an extension to the multinomial logit (MNL) model, the Halo MNL, that takes into account the interaction effects among products in an assortment. In particular, this model incorporates pairwise interactions of items in an effort to describe positive/negative effects among products that are present/absent in the assortment. Furthermore, we are interested in establishing sufficient conditions for identifiability, in order to build robust estimation methods. Under strict identifiability conditions, we use maximum likelihood to estimate the model parameters for which we derive closed formulas. We also perform simulation experiments, in order to numerically evaluate our method, study the accuracy of the estimators and compare it with the MNL. Last, we fit our model in the Hotel Chain dataset in Bodea et al., and we compare it with MNL in terms of efficiency, accuracy and robustness. We conclude that for rich enough datasets the model that includes interaction effects performs better in terms of how well it fits the data.

Motivation & Objective

• To develop a customer choice model that captures positive and negative interaction effects between products in an assortment, moving beyond the Independence of Irrelevant Alternatives (IIA) assumption of the MNL model.
• To establish sufficient identifiability conditions for the model parameters to ensure robust and valid parameter estimation under the proposed framework.
• To derive closed-form maximum likelihood estimators for the model parameters under specific conditions, enabling efficient estimation.
• To evaluate the model's performance numerically through simulations and on real-world data, particularly the Hotel Chain dataset.
• To compare the Halo-MNL model’s fit, accuracy, and robustness against the standard MNL model in terms of likelihood, AIC, and BIC metrics.

Proposed method

• Extends the multinomial logit (MNL) model by introducing pairwise interaction terms between products in the linear utility function to model halo effects.
• Derives sufficient identifiability and partial identifiability conditions to ensure unique and stable parameter estimation despite the increased number of parameters.
• Applies maximum likelihood estimation (MLE) with closed-form solutions for model parameters under specific structural assumptions.
• Performs simulation experiments with two sets of true parameters to evaluate estimator accuracy and convergence behavior.
• Employs real data from the Hotel Chain dataset to compare model performance using log-likelihood, AIC, and BIC scores.
• Uses Baron optimization software to compute maximum likelihood estimates and compares computational runtime and model fit across models.

Experimental results

Research questions

• RQ1 Can a customer choice model that incorporates pairwise interaction effects between products better capture real-world choice behavior than the standard MNL model?
• RQ2 What sufficient conditions on the model structure ensure identifiability of parameters in the presence of interaction terms?
• RQ3 How do the proposed closed-form estimators perform in terms of accuracy and convergence compared to standard MLE in simulated settings?
• RQ4 Does the Halo-MNL model outperform the MNL model in terms of fit and predictive accuracy on real-world data, especially when data richness is sufficient?
• RQ5 How do information criteria like AIC and BIC balance model fit and complexity when comparing Halo-MNL and MNL on real data?

Key findings

• In the full dataset, the Halo-MNL model achieves a significantly better fit than MNL, with a higher log-likelihood score (-1192.10 vs. -1259.91) and lower AIC (2404.20 vs. 2535.82) and BIC (2454.64 vs. 2576.17).
• Despite having more parameters, the Halo-MNL model outperforms MNL on the full dataset across all metrics, indicating superior fit and robustness.
• On the testing set, the Halo-MNL model has a higher log-likelihood (-301.34 vs. -304.43), but MNL performs better on AIC and BIC, suggesting a trade-off that depends on data size.
• Simulation results show that as the number of offer sets in the training data increases, the Halo-MNL model's AIC and BIC performance improves relative to MNL.
• The model estimation process took 20.48 seconds for Halo-MNL versus 6.4 seconds for MNL, indicating a reasonable computational cost for the added complexity.
• The results confirm that for sufficiently rich datasets, the Halo-MNL model provides a better fit than MNL, even after penalizing for model complexity.