Youssef M Aboutaleb, Mazen Danaf, Yifei Xie, Moshe Ben-Akiva
arXiv 14 Jan 2020 · Statistics — Methodology · publishedEconometrics Journal (2021)
arXiv:2001.05034 · PDF · DOI · OpenAlex · Extracted main text
This paper introduces a new data-driven methodology for estimating sparse covariance matrices of the random coefficients in logit mixture models. Researchers typically specify covariance matrices in logit mixture models under one of two extreme assumptions: either an unrestricted full covariance matrix (allowing correlations between all random coefficients), or a restricted diagonal matrix (allowing no correlations at all). Our objective is to find optimal subsets of correlated coefficients for which we estimate covariances. We propose a new estimator, called MISC, that uses a mixed-integer optimization (MIO) program to find an optimal block diagonal structure specification for the covariance matrix, corresponding to subsets of correlated coefficients, for any desired sparsity level using Markov Chain Monte Carlo (MCMC) posterior draws from the unrestricted full covariance matrix. The optimal sparsity level of the covariance matrix is determined using out-of-sample validation. We demonstrate the ability of MISC to correctly recover the true covariance structure from synthetic data. In an empirical illustration using a stated preference survey on modes of transportation, we use MISC to obtain a sparse covariance matrix indicating how preferences for attributes are related to one another.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Becker, F (2016) Bayesian estimation of mixed logit models with inter-and intra-personal heterogeneity | 1.000 | 5 | 3 | 100% |
| 2 | Khondker, Z. S., H. Zhu, H. Chu, W. Lin, and J. G. Ibrahim (2013) The bayesian covariance lasso | 0.811 | 4 | 2 | 100% |
| 3 | Bertsimas, D., A. King, R. Mazumder, et al (2016) Best subset selection via a modern optimization lens | 0.737 | 3 | 2 | 100% |
| 4 | Train, K. E (2009) Discrete choice methods with simulation | 0.737 | 3 | 2 | 100% |
| 5 | Allenby, G (1997) An introduction to hierarchical bayesian modeling | 0.644 | 2 | 2 | 100% |
| 6 | Allenby, G. M. and P. E. Rossi (1998) Marketing models of consumer heterogeneity | 0.644 | 2 | 2 | 100% |
| 7 | Hess, S. and K. Train (2017) Correlation and scale in mixed logit models | 0.644 | 2 | 2 | 100% |
| 8 | Keane, M. and N. Wasi (2013) Comparing alternative models of heterogeneity in consumer choice behavior | 0.644 | 2 | 2 | 100% |
| 9 | Revelt, D. and K. Train (1998) Mixed logit with repeated choices: households' choices of appliance efficiency level | 0.644 | 2 | 2 | 100% |
| 10 | Wang, H. et al (2012) Bayesian graphical lasso models and efficient posterior computation | 0.585 | 3 | 1 | 100% |
Showing the top 10 of 56 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Discrete Choice Analysis with Machine Learning Capabilities | 0.737 | 3 | 2 |
| 2 | Learning Structure in Nested Logit Models | 0.405 | 1 | 1 |