Estimating Random Coefficient Logit Models with Full Covariance Matrix

2009 ◽  
Vol 2132 (1) ◽  
pp. 87-94 ◽  
Author(s):  
Cristian Angelo Guevara ◽  
Elisabetta Cherchi ◽  
Matias Moreno
Keyword(s):  
Covariance Matrix ◽  
Random Coefficient ◽  
Logit Models ◽  
Random Coefficient Logit ◽  
Full Covariance Matrix

scholarly journals Monte Carlo Simulation in Random Coefficient Logit Models Involving Large Sums

2013 ◽  
Vol 1 (1) ◽  
pp. 85-108
Author(s):  
Zsolt Sándor
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Monte Carlo Methods ◽  
Mean Squared Error ◽  
Mixed Logit ◽  
Random Coefficient ◽  
Consumer Information ◽  
Logit Models ◽  
Quasi Monte Carlo ◽  
Random Coefficient Logit

Abstract We study Monte Carlo simulation in some recent versions of random coefficient logit models that contain large sums of expressions involving multivariate integrals. Such large sums occur in the random coefficient logit with demographic characteristics, the random coefficient logit with limited consumer information and the design of choice experiments for the panel mixed logit. We show that certain quasi-Monte Carlo methods, that is, so-called (t, m, s)-nets, provide improved performance over pseudo-Monte Carlo methods in terms of bias, standard deviation and root mean squared error.

Bayesian analysis of random coefficient logit models using aggregate data

2009 ◽  
Vol 149 (2) ◽  
pp. 136-148 ◽  
Author(s):  
Renna Jiang ◽  
Puneet Manchanda ◽  
Peter E. Rossi
Keyword(s):  
Bayesian Analysis ◽  
Aggregate Data ◽  
Random Coefficient ◽  
Logit Models ◽  
Random Coefficient Logit

scholarly journals Multivariate Ensemble Sensitivity Analysis for Super Typhoon Haiyan (2013)

2019 ◽  
Vol 147 (9) ◽  
pp. 3467-3480 ◽  
Author(s):  
Sijing Ren ◽  
Lili Lei ◽  
Zhe-Min Tan ◽  
Yi Zhang
Keyword(s):  
Sensitivity Analysis ◽  
High Resolution ◽  
Covariance Matrix ◽  
Multivariate Regression ◽  
Ensemble Forecast ◽  
Initial Condition ◽  
Maximum Wind ◽  
Diagonal Approximation ◽  
Low Levels ◽  
Full Covariance Matrix

Abstract Ensemble sensitivity is often a diagonal approximation to the multivariate regression, leading to a simple univariate regression. Comparatively, the multivariate ensemble sensitivity retains the full covariance matrix when computing the multivariate regression. The performances of both univariate and multivariate ensemble sensitivities in multiscale flows have not been thoroughly examined, and the demonstration of the latter in realistic applications has been sparse. A high-resolution ensemble forecast of Typhoon Haiyan (2013) is used to examine the performances of the two ensemble sensitivities. Compared to the multivariate sensitivity, the univariate sensitivity overestimates the forecast metric, especially at higher levels. To increase the predicted Haiyan’s intensity, multivariate ensemble sensitivity gives initial perturbations characterized by a warming area around the center of the storm, an increased moisture area around the eyewall, a stronger primary circulation around the radius of maximum wind, and stronger inflow at low levels and stronger outflow at high levels. Perturbed initial condition experiments verify that the predicted response from the multivariate sensitivity is more accurate than that from the univariate sensitivity. Therefore, the ability of multivariate sensitivity to provide more accurate predicted responses than the univariate sensitivity has been demonstrated in a realistic multiscale flow application.

scholarly journals Sparse covariance estimation in logit mixture models

2021 ◽  
Author(s):  
Youssef M Aboutaleb ◽  
Mazen Danaf ◽  
Yifei Xie ◽  
Moshe E Ben-Akiva
Keyword(s):  
Covariance Matrix ◽  
Mixture Models ◽  
Stated Preference ◽  
Synthetic Data ◽  
Covariance Matrices ◽  
Random Coefficients ◽  
Mixed Integer ◽  
Integer Optimization ◽  
Sparsity Level ◽  
Full Covariance Matrix

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.

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