EGC: Sparse covariance estimation in logit mixture models
Name
2001.05034.pdf
Description
Submitted version
Size
2.47 MB
Format
Adobe PDF
Checksum (MD5)
a7fd87a5167a7cf181d192cf0b76fd89
Author(s)
Aboutaleb, Youssef M
Danaf, Mazen
Xie, Yifei
Ben-Akiva, Moshe E
Date Issued
March 2021
Journal
Econometrics Journal
Publisher
Oxford University Press (OUP)
Citation
Youssef M Aboutaleb, Mazen Danaf, Yifei Xie, Moshe E Ben-Akiva, Sparse covariance estimation in logit mixture models, The Econometrics Journal, Volume 24, Issue 3, September 2021, Pages 377–398
Version
Original manuscript
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 (mixed integer sparse covariance), 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.
MIT Department
Massachusetts Institute of Technology. Intelligent Transportation Systems Laboratory
Massachusetts Institute of Technology. Department of Civil and Environmental Engineering
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1093/ECTJ/UTAB008
