Browsing by Subject "discrete choice models"
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Item The MACML Estimation of the Normally-Mixed Multinomial Logit Model(2011-01-18) Bhat, Chandra R.The focus of this paper is to develop a procedure for the Maximum Composite Marginal Likelihood (MACML) estimation of multinomial logit models with normally mixed terms, as would be the case with normally-mixed random coefficient and/or error-component structures.Item The maximum approximate composite marginal likelihood (MACML) estimation of multinomial probit-based unordered response choice models(Elsevier, 2011) Bhat, Chandra R.The likelihood functions of multinomial probit (MNP)-based choice models entail the evaluation of analytically-intractable integrals. As a result, such models are usually estimated using maximum simulated likelihood (MSL) techniques. Unfortunately, for many practical situations, the computational cost to ensure good asymptotic MSL estimator properties can be prohibitive and practically infeasible as the number of dimensions of integration rises. In this paper, we introduce a maximum approximate composite marginal likelihood (MACML) estimation approach for MNP models that can be applied using simple optimization software for likelihood estimation. It also represents a conceptually and pedagogically simpler procedure relative to simulation techniques, and has the advantage of substantial computational time efficiency relative to the MSL approach. The paper provide s a “blueprint” for the MACML estimation for a wide variety of MNP models.Item Numerical Analysis of Effect of Sampling of Alternatives in Discrete Choice Models(National Academy of Sciences, 2004) Nerella, Sriharsha; Bhat, Chandra R.A large number of alternatives characterize the choice set in many activity and travel choice contexts. Analysts generally sample alternatives from the choice set in such situations because estimating models from the full choice set can be very expensive or even prohibitive. This paper undertakes numerical experiments to examine the effect of the sample size of alternatives on model performance for both an MNL model (for which consistency with a subset of alternatives is guaranteed) and a mixed multinomial logit model (for which no consistency result holds).Item On modeling departure time choice for home-based social/recreational and shopping trips(Transportation Research Board of the National Academies, 2000) Steed, Jennifer L.; Bhat, Chandra R.The existing literature on departure time choice has primarily focused on work trips. In this paper, we examine departure time choice for non-work trips, which constitute an increasingly large proportion of urban trips. Discrete choice models are estimated for home-based social/recreational and home-based shopping trips using the 1996 activity survey data collected in the Dallas-Fort Worth metropolitan area. The effects of individual and household socio-demographics, employment attributes, and trip characteristics on departure time choice are presented and discussed. The results indicate that departure time choice for social/recreational trips and shopping trips are determined for the most part by individual/household socio-demographics and employment characteristics, and to a lesser extent by trip level-of-service characteristics. This suggests that departure time for social/recreational and shopping trips are not as flexible as one might expect and are confined to certain times of day because of overall scheduling constraints. The paper concludes by identifying future methodological and empirical extensions of the current research.Item Simulation Estimation of Mixed Discrete Choice Models with the Use of Randomized Quasi-Monte Carlo Sequences: A Comparative Study(National Academy of Sciences, 2005) Sivakumar, Aruna; Bhat, Chandra R.; Okten, GirayThis paper numerically compares the overall performance of the quasi-Monte Carlo (QMC) sequences proposed by Halton and Faure, and their scrambled versions, against each other and against the Latin Hypercube Sampling sequence in the context of the simulated likelihood estimation of a Mixed Multinomial Logit model of choice. In addition, the efficiency of the QMC sequences generated with and without scrambling across observations is compared, and the performance of the Box-Muller and Inverse Normal transform procedures is tested. The numerical experiments were performed in 5 dimensions with 25, 125 and 625 draws, and in 10 dimensions with 100 draws. The results of our analysis indicate that the Faure sequence consistently outperforms the Halton sequence, and the scrambled versions of the Faure sequence show the best performances overall.Item A Simulation Evaluation of the Maximum Approximate Composite Marginal Likelihood (MACML) Estimator for Mixed Multinomial Probit Models(Elsevier, 2011) Bhat, Chandra R.; Sidharthan, RaghuprasadThis paper evaluates the ability of the maximum approximate composite marginal likelihood (MACML) estimation approach to recover parameters from finite samples in mixed cross-sectional and panel multinomial probit models. Comparisons with the maximum simulated likelihood (MSL) estimation approach are also undertaken. The results indicate that the MACML approach recovers parameters much more accurately than the MSL approach in all model structures and covariance specifications. The MACML inference approach also estimates the parameters efficiently, with the asymptotic standard errors being, in general, only a small proportion of the true values. As importantly, the MACML inference approach takes only a very small fraction of the time needed for MSL estimation. In particular, the results suggest that, for the case of five random coefficients, the MACML approach is about 50 times faster than the MSL for the cross-sectional random coefficients case, about 15 times faster than the MSL for the panel inter-individual random coefficients case, and about 350 times or more faster than the MSL for the panel intra- and inter-individual random coefficients case. As the number of alternatives in the unordered-response model increases, one can expect even higher computational efficiency factors for the MACML over the MSL approach. Further, as should be evident in the panel intra- and inter-individual random coefficients case, the MSL is all but practically infeasible when the mixing structure leads to an explosion in the dimensionality of integration in the likelihood function, but these situations are handled with ease in the MACML approach. It is hoped that the MACML procedure will spawn empirical research into rich model specifications within the context of unordered multinomial choice modeling, including autoregressive random coefficients, dynamics in coefficients, space-time effects, and spatial/social interactions.