交通统计与分析同济课件.doc

Tongji UniversitySchool of Transportation EngineeringHomework 2Discrete Choice ModelYou are asked to develop a mode choice model for work trips in the City of Toronto, Canada. For this purpose, a one-day travel diary survey A subset of the data in the 1986 Transportation Tomorrow Survey (TTS) for the Greater Toronto Area was conducted for a sample of 49 workers. The survey includes the workers socio-economic characteristics, mode characteristics and the workers mode choice among the four modes of travel (auto-drive, auto-passenger, local transit, and commuter rail). This survey data is stored in Homework 2.txt in the following format:tmodechoiceivttovtttcnvehIncfemaleagehhsize110578.237.78238132221578.233.8923813223064.8118.471.4223813224033.9918.540.22381322210:20:30:41:Note: t= worker number mode = 1 auto-drive, 2 auto-passenger, 3 local transit, 4 commuter railchoice= 1 selected mode, 0 unselected modes ivtt= in-vehicle travel time for each mode (min) Same travel time for auto-drive and auto-passenger ovtt= out-of-vehicle travel time for each mode (min)2 tc= travel cost (dollars) Travel cost for auto-passenger is assumed to be a half of the travel cost for auto-drive. nveh= number of vehicles in the workers household inc= workers income (thousand dollars)female= workers gender (1 female, 0 male) age= workers agehhsize= number of persons in the workers householdThe following multinomial logit model was used to estimate the workers mode choice: Where Pit= probability that worker t chooses mode i Vit= utility of mode i for worker tV1t,V2t,V3t,V4t= utilities of auto-drive, auto-passenger, local transit and commuter rail, respectively, for worker tFor four travel modes, four different systematic (observable) utility functions were specified as follows:Auto-drive:Auto-passenger:Local transit:Commuter rail:Coefficients of the variables in the above utility functions were estimated using the LIMDEP 7.0 software (Greene, 1998). The coefficients are summarized as follows:Estimated parametersVariableCoefficientt-statisticsq1 (constant)10.172.04q2 (constant)5.721.25q3 (constant)5.611.87a1 (auto drive in-vehicle travel time)-0.07-1.65a2 (auto passenger in-vehicle travel time)-0.07-1.20a3 (local transit in-vehicle travel time)-0.14-3.00a4 (commuter rail in-vehicle travel time)0.050.68b (out-of-vehicle travel time)-0.06-1.69c (travel cost) -1.60-2.60d (household size)0.982.47e (female worker)1.631.76The goodness-of-fit of the logit model is as follows:Goodness of fit statistics:Number of observations= 49 Log-likelihood at convergence = -46.4632Log-likelihood at b=0= -67.9284Log-likelihood ratio index (r2)= 0.32t23 = t32 = 2t13 = t31 = 4Question 1:Discuss the results of the above logit model estimation in terms of(a) statistical significance of variables at a 90% confidence level;(b) the signs of the coefficients (e.g. why is the sign of out-of-vehicle travel time negative or the sign of household size positive?, etc.);(c) model fit; and(d) additional data (not included in TDS_sample.txt) which you would have liked to have had for inclusion in the utility functions.Question 2:Using the logit model, calculate the following:(a) Calculate the probabilities of choosing the four modes for each worker.(b) Calculate the average probabilities for all workers using the results in (a). (c) Calculate the averages of variables in utility functions for all workers. Use these average values to estimate the probabilities of choosing the four modes for all workers (i.e. naive aggregation). (d) Describe the characteristics of the mode with the highest probability compared to the other modes in terms of the averages of variables obtained in part (c).(e) Classify the workers into 10 homogeneous worker groups according to the number of persons in the workers household and the workers gender. For instance, let the first group be a male worker whose household size is 1 (i.e. female = 0, hhsize = 1), the second group be a male worker whose household size is 2 (i.e. female = 0, hhsize =2), and so on. Calculate the averages of variables in utility functions for each worker group. Use these average values to estimate the probabilities of choosing the four modes for each worker group. Finally, calculate the “weighted” average probabilities using these probabilities for groups (i.e. classification with naive aggregation).(f) Compare the results in (b), (c) and (e) with the “observed” percentages of mode choice from the original survey data. Evaluate the accuracy based on the root-mean-square errors as follows: where Pi = observed percentage of mode i, and Pi = predicted average probability of choosing mode i for all workers. Which level of aggregation is the most accurate? Why?(g) The local transit company