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Sparse Covariance Estimation in Logit Mixture Models

Youssef M Aboutaleb, Mazen Danaf, Yifei Xie and Moshe Ben-Akiva

Papers from arXiv.org

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.

Date: 2020-01
New Economics Papers: this item is included in nep-dcm and nep-ecm
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