EconBase
← All papers

Sparse Covariance Estimation in Logit Mixture Models

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

Abstract

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.

Citation extraction

56
references
80
in-text mentions
56
distinct cited
4
self-citations
9,884
main-text words

appendix boundary found by none_found · 100% of the source is main text. Read the extracted text to check this.

Most heavily cited references

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.

ReferenceIntensityMentionsSectionsMain text
1Becker, F (2016) Bayesian estimation of mixed logit models with inter-and intra-personal heterogeneity1.00053100%
2Khondker, Z. S., H. Zhu, H. Chu, W. Lin, and J. G. Ibrahim (2013) The bayesian covariance lasso0.81142100%
3Bertsimas, D., A. King, R. Mazumder, et al (2016) Best subset selection via a modern optimization lens0.73732100%
4Train, K. E (2009) Discrete choice methods with simulation0.73732100%
5Allenby, G (1997) An introduction to hierarchical bayesian modeling0.64422100%
6Allenby, G. M. and P. E. Rossi (1998) Marketing models of consumer heterogeneity0.64422100%
7Hess, S. and K. Train (2017) Correlation and scale in mixed logit models0.64422100%
8Keane, M. and N. Wasi (2013) Comparing alternative models of heterogeneity in consumer choice behavior0.64422100%
9Revelt, D. and K. Train (1998) Mixed logit with repeated choices: households' choices of appliance efficiency level0.64422100%
10Wang, H. et al (2012) Bayesian graphical lasso models and efficient posterior computation0.58531100%

Showing the top 10 of 56 scored citations.

Cited by, within the corpus

arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.

Citing paperIntensityMentionsSections
1Discrete Choice Analysis with Machine Learning Capabilities0.73732
2Learning Structure in Nested Logit Models0.40511