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Sparse Covariance Estimation in Logit Mixture Models

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Document pages: 25 pages

Abstract: This paper introduces a new data-driven methodology for estimating sparsecovariance matrices of the random coefficients in logit mixture models.Researchers typically specify covariance matrices in logit mixture models underone of two extreme assumptions: either an unrestricted full covariance matrix(allowing correlations between all random coefficients), or a restricteddiagonal matrix (allowing no correlations at all). Our objective is to findoptimal 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 thecovariance matrix, corresponding to subsets of correlated coefficients, for anydesired sparsity level using Markov Chain Monte Carlo (MCMC) posterior drawsfrom the unrestricted full covariance matrix. The optimal sparsity level of thecovariance matrix is determined using out-of-sample validation. We demonstratethe ability of MISC to correctly recover the true covariance structure fromsynthetic data. In an empirical illustration using a stated preference surveyon modes of transportation, we use MISC to obtain a sparse covariance matrixindicating how preferences for attributes are related to one another.

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