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• W2139442327 abstract "The field of discrete choice analysis has long wrestled with the question of how best to represent heterogeneity in the decision-making process. In cases where tastes vary systematically with observable variables, heterogeneity in the decision-making process may be captured through interactions between observable characteristics of the decision-maker and observable attributes of the alternatives. However, capturing heterogeneity systematically may be insufficient when tastes vary with unobservable variables or purely randomly, and can result in inconsistent parameter estimates. In such cases, heterogeneity in the decision-making process may be captured through additional interactions between observable variables and the stochastic component. Mixed logit and multinomial probit are two of the more popular models that allow for random taste heterogeneity. Both of these models are parametric mixture models. Numerous functional forms have been employed for the mixing distribution, such as the normal and the lognormal, and attempts have also been made to describe these distributions as functions of covariates to improve fit and ease interpretation. While the use of parametric mixture distributions often provides an excellent fit to the data, it suffers from two major drawbacks. First, it requires the analyst to make a prior assumption about the mixture distribution for each randomly distributed coefficient. A wrongly specified distribution can have deleterious effects on parameter estimates and the attendant model interpretation (Fosgerau, 2005). Since distributional assumptions exert influences of their own on the results, it has been argued that simply knowing that a parameter is distributed randomly across respondents might be of limited utility to policy makers (Hess et al., 2009). Second, parametric distributions are limited by their functional form in the shapes that they can assume. For example, the normal distribution, by far the most commonly employed distribution, is symmetric around the mean and has support on both sides of zero, rendering it inappropriate for parameters that are asymmetric or signed; skew normal distributions are asymmetric, but they too have support on both sides of zero; lognormal distributions are signed, but have thick tails; etc. Efforts to overcome some of the limitations of parametric mixture models have led to interest in the use of nonparametric distributions. Nonparametric distributions do not require the analyst to make prior assumptions about the shape of the distribution and can asymptotically mimic whatever shape best describes the heterogeneity in the data. However, nonparametric distributions require the estimation of a far larger number of parameters than parametric distributions, and the greater computational costs imposed by these distributions has proven to be a stumbling block to their widespread adoption. Recent studies have attempted to develop computationally efficient algorithms for the estimation of discrete choice models with nonparametric distributions. The most recent, Train (2008), uses the Expectation Maximization (EM) algorithm to estimate discrete nonparametric distributions with fixed mass points, such as a grid on the parameter space, where the probability mass at each point is a parameter to be estimated. Though the results have been extremely promising, a major limitation to the approach is that model performance, as measured by both goodness of fit and behavioral interpretation, varies considerably depending upon the predetermined location of the fixed mass points. For example, incorrectly specified boundary points can result in the distribution being concentrated at these points. A possible solution proposed by the study is to determine the fixed mass points exogenously through the estimation of models with different locations for each of the points. The model that outperforms all others in terms of goodness of fit can subsequently be selected as the appropriate model. Though such a method is theoretically possible, it can be impractical since there is no limit to the number of models that the analyst might be required to estimate before she can be suitably confident regarding the nature of her results. A natural and more feasible alternative would be to develop an estimation procedure that allows for the endogenous estimation of the location for each of the fixed mass points. This study builds on the EM algorithm proposed by Bhat (1997) and Train (2008) to develop a computationally tractable method for estimating a fully nonparametric discrete mixture model that can asymptotically mimic any parametric mixture model. The computational performance of the estimation algorithm is tested using multiple synthetic datasets and the behavioral value of the proposed formulation is demonstrated using a case study on travel mode choice behavior. References Bhat, C. (1997), “ An endogenous segmentation mode choice model with an application to intercity travel ,” Transportation Science , Vol. 31, pp. 34-48. Fosgerau, M. (2005), “ Investigating the distribution of the value of travel time savings ,” Transportation Research Part B: Methodological , Vol. 40, No. 8, pp. 688-707. Hess, S., Ben-Akiva, M., Gopinath, D., and Walker, J. (2009), “ Taste heterogeneity, correlation and elasticities in latent class choice models ,” Compendium of Papers, 88th Annual Meeting of the Transportation Research Board. Washington, DC: Transportation Research Board. 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• W2139442327 date "2015-05-11" @default.
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• W2139442327 title "Fully Non-Parametric Discrete Mixture Models for Choice Analysis" @default.
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