Investigate Household Private Car Ownership and Usage Using Bayesian Dirichlet Mixture Model
Na Wu, School of Transportation Logistics, Faculty of Infrastructure Engineering, Dalian University of Technology, Liaoning, Shengchuan Zhao
In this study, we investigate household private car ownership and usage using Bayesian Dirichlet Mixture model. The model is estimated by Bayesian MCMC (Markov Chain Monte Carlo) method.
In this study, we investigate household private car ownership and usage using Bayesian Dirichlet Mixture model. The model is estimated by Bayesian MCMC (Markov Chain Monte Carlo) method. Moreover, selection rule here is binary. We, therefore, only investigate whether the household owns a private car and annual driving mileage of all private cars for the household if it owns.This is a typical sample selection model. In the traditional sample selection model, bivariate normal distribution of two errors in the selection eqation and outcome equation is assumed. Bayesian Dirichlet Mixture model can relax the strong assumption and can capture flexible error distribution by using mixture of normals approach, which is introduced by a Dirichlet prior. To compare model performance, both of traditional normal model and Dirichlet Mixture model are estimated. Note that normal model here is estimated using Bayesian procedures developed by Van Hasselt in 2011. Data come from a RP (Revealed Preference) survey collected at Dalian city, Liaoning province, China. Variables include household attributes, built environment attributes, and car attributes. The survey was conducted on June 2015 using stratified random sampling. After deleting invalid questionnaires, the total sample size we obtained is 813, in which 60.1% households own at least one private car. Since we do not clearly know which variable only influences ownership rather than usage, the exclusion restriction is not imposed in this study.
For Dirichlet Mixture models, the number of components is ranging from one to six. Firstly, a suitable model with a better goodness of fit and generalization ability is chosen from the six models. Then estimation result of this model is compared with that from the normal model. Here, we employ goodness of fit test and image inspection to infer the most likely number of components. After testing, we find Dirichlet Mixture model with three components performs best in terms of goodness of fit and generalization ability. Bayesian procedure is run for 30,000 iterations. The first 20,000 draws are discarded as burn-in and remaining 10,000 draws are used to compute the estimates and their standard errors. Compared with the normal model, model fit of the Dirichlet mixture model with three components is significantly higher. Log likelihood value is improved from -2285.441 to -1966.017. And log marginal density has been improved from -2294.667 to -2070.011. Obviously, Dirichlet Mixture model with three components explains the data much better than the normal model. Moreover, estimates from the normal model are seriously biased regarding to magnitude, significance level, even the sign.
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