Bayesian mixture modeling approach to account for heterogeneity in speed data

Speed is one of the most important parameters describing the condition of the traffic flow. Many analytical models related to traffic flow either produce speed as a performance measure, or use speed to determine other measures such as travel time, delay, and the level of service. Mathematical models or distributions used to describe speed characteristics are very useful, especially when they are utilized in the context of simulation and theoretical derivations. Traditionally, normal, log-normal and composite distributions have been the usual mathematical distributions to characterize speed data. These traditional distributions, however, often fail to produce an adequate goodness-of-fit when the empirical distribution of speed data exhibits bimodality (or multimodality), skewness, or excess kurtosis (peakness). This often occurs when the speed data are generated from several different sub-populations, for example, mixed traffic flow conditions or mixed vehicle compositions. The traditional modeling approach also lacks the ability to explain the underlying factors that lead to different speed distribution curves. The objective of this paper is to explore the applicability of the finite mixture of normal (Gaussian) distributions to capture the heterogeneity in vehicle speed data, and thereby explaining the aforementioned special characteristics. For the parameter estimation, Bayesian estimation method via Markov Chain Monte Carlo (MCMC) sampling is adopted. The field data collected on IH-35 in Texas is used to evaluate the proposed models. The results of this study show that the finite mixture of normal distributions can very effectively describe the heterogeneous speed data, and provide richer information usually not available from the traditional models. The finite mixture modeling produces an excellent fit to the multimodal speed distribution curve. Moreover, the causes of different speed distributions can be identified through investigating the components.

[1]  Jerry Nedelman,et al.  Book review: “Bayesian Data Analysis,” Second Edition by A. Gelman, J.B. Carlin, H.S. Stern, and D.B. Rubin Chapman & Hall/CRC, 2004 , 2005, Comput. Stat..

[2]  H J Leong,et al.  The distribution and trend of free speeds on two lane two way rural highways in New South Wales , 1968 .

[3]  P. Deb.  Finite Mixture Models , 2008 .

[4]  Adolf D. May,et al.  Traffic Flow Fundamentals , 1989 .

[5]  Walter R. Gilks,et al.  Hypothesis testing and model selection , 1995 .

[6]  Sylvia Frühwirth-Schnatter,et al.  Finite Mixture and Markov Switching Models , 2006 .

[7]  Sylvia Richardson,et al.  Markov Chain Monte Carlo in Practice , 1997 .

[8]  M. Aitkin.  Likelihood and Bayesian analysis of mixtures , 2001 .

[9]  L. Wasserman,et al.  Computing Bayes Factors by Combining Simulation and Asymptotic Approximations , 1997 .

[10]  P. Green,et al.  On Bayesian Analysis of Mixtures with an Unknown Number of Components (with discussion) , 1997 .

[11]  M. Stephens.  Dealing with label switching in mixture models , 2000 .

[12]  Robert Fildes,et al.  Journal of business and economic statistics 5: Garcia-Ferrer, A. et al., Macroeconomic forecasting using pooled international data, (1987), 53-67 , 1988 .

[13]  P. Dey,et al.  Speed Distribution Curves under Mixed Traffic Conditions , 2006 .

[14]  Pravin K. Trivedi,et al.  Flexible Parametric Models for Long-Tailed Patent Count Distributions , 2002 .

[15]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .

[16]  Bradley P. Carlin,et al.  Bayesian measures of model complexity and fit , 2002 .

[17]  J H Wyman,et al.  FIELD EVALUATION OF FHWA VEHICLE CLASSIFICATION CATEGORIES--MDOT. EXECUTIVE SUMMARY , 1984 .

[18]  Ajay Jasra,et al.  Markov Chain Monte Carlo Methods and the Label Switching Problem in Bayesian Mixture Modeling , 2005 .

[19]  Wayne S. DeSarbo,et al.  Bayesian inference for finite mixtures of generalized linear models with random effects , 2000 .

[20]  D. L. Gerlough,et al.  Traffic flow theory : a monograph , 1975 .

[21]  David B. Dunson,et al.  Bayesian Data Analysis , 2010 .

[22]  C. Holmes,et al.  MCMC and the Label Switching Problem in Bayesian Mixture Modelling 1 Markov Chain Monte Carlo Methods and the Label Switching Problem in Bayesian Mixture Modelling , 2004 .

[23]  C. Robert,et al.  Estimation of Finite Mixture Distributions Through Bayesian Sampling , 1994 .

[24]  J Lindner.  A CONTRIBUTION TO THE STATISTICAL ANALYSIS OF SPEED DISTRIBUTIONS. IN VEHICULAR TRAFFIC SCIENCE , 1967 .

[25]  J R McLean.  OBSERVED SPEED DISTRIBUTIONS AND RURAL ROAD TRAFFIC OPERATIONS , 1979 .

[26]  D. L. Gerlough,et al.  Traffic flow theory : a monograph , 1975 .

[27]  Martin L. Puterman,et al.  Analysis of Patent Data—A Mixed-Poisson-Regression-Model Approach , 1998 .

[28]  Randall Guensler,et al.  Characterization of Congestion Based on Speed Distribution: A Statistical Approach Using Gaussian Mixture Model , 2005 .

[29]  David R. Anderson,et al.  Model selection and multimodel inference : a practical information-theoretic approach , 2003 .

[30]  P. Green,et al.  Corrigendum: On Bayesian analysis of mixtures with an unknown number of components , 1997 .