A Paired Combinatorial Logit Route Choice Model with ProbitBased Equivalent Impedance

Abstract

Abstract:

An improved paired combinatorial Logit route choice model with Probit-based equivalent route impedance is proposed to simplify the calculation and resolve the homoscedasticity problem of the Logit model. The model comprises a twolevel structure: the lower level employs a binary Probit choice model to address the problem of route overlapping. Clark’s approximation for normal distribution is employed to compute the equivalent impendence for each route pair in the upper level. The homoscedasticity problem is resolved through the introduction of the normal distribution. The upper level is a classical multinomial Logit model with relative impedance that reduces the defect of variancehomogeneity in the upper level. The probability of route selection is determined by marginal and conditional probabilities. The proposed model combines the advantages of both Probit and Logit models with closeform formulations, which can be easily calculated. Two numerical tests, which were performed on the wellknown examples, indicate that the proposed model produces more reasonable and stable results.

Key words: integrated transportation, paired combinatorial Logit model, Probit model, stochastic equivalent impendence, relative impedance

摘要：

原有的组合配对Logit模型（Paired Combinatorial Logit, PCL）中相似性系数的确定方法缺乏必要的理论依据，模型的同一分布假设导致它难以表征道路感知误差的异方差特质.为克服这些不足，本文提出了基于Probit等效阻抗的配对组合Logit路径选择模型.模型分上下两层：下层的每一配对采用Probit二元选择法，引入正态分布以表征感知误差的异方差性并提高了计算的准确性；提出随机等效阻抗的概念并以Clark公式计算每一配对的等效阻抗，为相似性系数的计算提供了清晰的理论依据；上层模型采用计算简便的多项Logit模型，利用相对阻抗来缓解Logit模型的长短路缺陷，通过条件概率计算路径的选择概率.新模型综合了Probit模型计算准确及Logit模型计算简便的优点，在两者之间取得了合理的平衡.经典路网的数值计算结果表明，该模型比传统Logit模型更为合理.

关键词: 综合交通运输, 组合配对Logit模型, Probit模型, 随机等效阻抗, 相对阻抗

CLC Number:

U491.1+22

LI Jun, LAI Xin-jun, YU Zhi. A Paired Combinatorial Logit Route Choice Model with ProbitBased Equivalent Impedance[J]. Journal of Transportation Systems Engineering and Information Technology, 2013, 13(4): 100-105.

李军，赖信君，余志. 基于Probit等效阻抗的配对组合Logit路径选择模型[J]. 交通运输系统工程与信息, 2013, 13(4): 100-105.

Add to citation manager EndNote|Ris|BibTeX

URL: http://www.tseit.org.cn/EN/abstract/abstract18619.shtml

http://www.tseit.org.cn/EN/Y2013/V13/I4/100

References

[1]McFadden D.Conditional logit analysis of qualitative choice behavior.Frontiers in econometrics[M].P. Zaremmbka.New York,Academic Press,1973.

[2]BenAkiva M,Meersman H,et al.Recent developments in transport modelling: lessons for the freight sector[M]. Bingley, England, Emerals Group Publishing Limited, 2008.

[3]李聪颖, 马荣国, 等. 基于活动分析法的城市慢行交通出行行为 [J]. 长安大学学报(自然科学版), 2011, 31(2): 86-90. [LI C Y, MA R G, et al. Research on travel behavior of slow traffic based on activity analysis [J]. Journal of Chang’an University (Natural Science Edition), 2011, 32(2): 86-90.]

[4]袁长伟, 吴群琪. 双核都市圈运输通道旅客分担率模型及应用 [J]. 长安大学学报(自然科学版), 2007, 27(6): 80-83. [YUAN C W, WU Q Q. Model of passenger travel shares rate in dual nuclei metropolis transportation corridor [J]. Journal of Chang’an University (Natural Science Edition), 2007, 27(6): 80-83.]

[5]Daganzo C. Multinomial Probit: The theory and its application to demand forecasting [M]. Academic Press, New York, 1979.

[6]Cascetta E, Nuzzolo A, et al. A modified logit route choice model overcoming path overlapping problems: Specification and some calibration results for interurban networks[C]. The Thirteenth International Symposium on Transportation and Traffic Theory, Lyon, France, 1996.

[7]Chu C. A paired combinatorial logit model for travel demand analysis[C]. Proceedings of the Fifth World Conference on Transportation Research, Ventura, CA, 1989.

[8]Frejinger E, Bierlaire M. Capturing correlation with subnetworks in route choice models[J]. Transportation Research Part B: Methodological, 2007, 41 (3): 363-378.

[9]Abbe E,Bierlaire M,et al.Normalization and correlation of crossnested logit models[J]. Transportation Research Part B: Methodological, 2007, 41(7):795-808.

[10]Wen H, Koppelman F S. The generalized nested logit model[J]. Transportation Research Part B: Methodological, 2001, 35(7): 627-641.

[11]Daly A, Bierlaire M. A general and operational representation of generalized extreme value models[J]. Transportation Research Part B: Methodological, 2006, 40(4): 285-305.

[12]Koppelman F S, Wen C H. The paired combinatorial logit model: properties, estimation and application[J]. Transportation Research Part B: Methodological, 2000, 34(3): 75-89.

[13]王卫杰, 王炜. 基于配对组合Logit模型的路线选择[J]. 东南大学学报: 自然科学版, 2010, 40(4): 844-847. [WANG W J, WANG W. Route choice modeling based on paired combinatorial Logit model [J]. Journal of Southeast University: Natural Science Edition, 2010, 40(4): 844-847.]

[14]Pravinvongvuth S, Chen A. Adaption of the paired combinatorial logit model to the route choice problem[J]. Transportmetrica, 2005, 1(3): 223-240.

[15]Chen A, Kasikitwiwat A P, et al. Solving the overlapping problem in route choice with paired combinatorial logit model [J]. Transportation Research Record, 2003, 1857: 65-73.

[16]Prashker J N, Bekhor S. Stochastic userequilibrium formulations for extendedlogit assignment models[J]. Transportation Research Record, 1999, 1676: 145-152.

[17]Chen A, Kasikitwiwat P, Ji Z. Solving the overlapping problem in route choice with paired combinatorial logit model[J]. Transportation Research Record, 2003, 1857: 65-73.

[18]Pravinvongvuth S, Chen A. Adaptation of the paired combinatorial logit model to the route choice peoblem[J]. Transportmetrica, 2005, 1(3): 223-240.

[19]Gliebe J P, Koppleman F S, et al. Route choice using a paired combinatorial logit model[C]. The Annual Meeting of the Transportation Research Board, Washington, DC, USA, 1999.

[20]McFadden D,K Train.Mixed MNL models for discrete response[J]. Journal of Applied Econometrics, 2000, 15(5): 447-470.

[21]Greene W H, D A Hensher, J Rose. Accounting for heterogeneity in the variance of unobserved effects in mixed Logit models[J]. Transportation Research Part B: Methodological, 2006, 40(1): 75-92.

[22]Baibing Li. The multinomial Logit model revisited: A semiparametric approach in discrete choice analysis[J].Transportation Research Part B:Methodological, 2011, 45(3): 461-473. 

[23]LI J, OUYANG J. A modified paired combinatorial Logit route choice model with unified parameter[C]. Proceedings of the 8th International Conference of Chinese Logitstics and Transportation Professionals, Chengdu, China, 2008.

[24]赖信君, 余志, 李军. 相对阻抗 Logit 路径选择模型的推导、应用及验证[J]. 交通运输系统工程与信息, 2012, 12(2): 85-90. [LAI X J, YU Z, LI J. Derivation, implementation and examination of Logit route choice model with relative impedance[J]. Journal of Transportation Systems Engineering and Information Technology, 2012, 12(2): 85-90.]