# Modeling Intercity Travel Mode Choice with Data Balance Changes: A Comparative Analysis of Bayesian Logit Model and Artificial Neural Networks

Authors: Xiaowei Li; Yuting Wang; Yao Wu; Jun Chen; Jibiao Zhou
Journal: Journal of Advanced Transportation
 (2021)

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## Abstract

This study conducts a comprehensive comparative analysis of regression-based multinomial models and artificial neural network models in intercity travel mode choices. The four intercity travel modes of airplane, high-speed rail (HSR), train, and express bus were used for analysis. Passengers’ activity data over the process of intercity travel were collected to develop the models. The standard multinomial logit (MNL) regression and Bayesian multinomial logit (BMNL) regression were compared with the radial basis function (RBF) and multilayer perceptron (MLP). The results show that MLP performs best in terms of predictive accuracy, followed by BMNL and MNL, and RBF is the least accurate. The performances of all models were examined against changes in data balance, and it was found that rebalancing can improve fitting performance while slightly reducing the predictive performance. This comparative study and its parameter estimation shed new light on the comparison of traditional and emerging models in travel behavior studies, and the findings can be used as heuristic guidance for all stakeholders.


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## Body

## 1. Introduction

To model passengers’ travel behaviors is of value to better understand mobility modes in the complex travel environment [1]. Policies and managerial strategies rely on the accurate estimation of travel mode choices of passengers. In 2020, COVID-19 has profoundly influenced passengers’ travel behaviors, causing a dramatic shift in intracity and intercity mobility modes, inevitably affecting society, production, and the global economy. Scholars have investigated contextual factors that influence travel modes, aiming to better understand passengers’ choices and develop suitable models.Previous studies have shown that travel mode choice can be affected by social and demographic factors, including gender [2–4], age [4–6], occupation [3], income [2, 4, 7, 8], and car ownership [4]. Miskeen et al. [4] found that males were more likely to use public transportation than cars, while females were less likely to shift to public transportation. Cheng et al. [6] indicated that age was the most significant individual-related attribute. Tourists were more likely to choose a plane or train than a coach [3]. Forinash et al. [7] found that high- and low-income groups preferred air travel and bus, respectively. It was similarly reported that an increase in passengers’ incomes decreased their use of buses [4]. Lower-income individuals were found to be more sensitive to cost and less sensitive to out-of-vehicle time than middle- and high-income individuals [8]. Related attributes, such as travel demand, service quality of transport modes, and accessibility of transportation hubs, have been found to influence travel mode choices [1, 3, 9, 10].The most widely used modeling techniques in travel mode choice are discrete choice models, such as the binomial logit (BL) [11], multinomial logit (MNL) [4, 12], multinomial probit (MNP) [3], nested logit (NL) [13, 14], and mixed logit (ML) models [15–17], which have high interpretability of estimation results on input variables, as well as high transferability and validity. Regression-based models form maximum likelihood estimates of parameters [4, 5, 11, 12, 17, 18]. Apart from the popular logit model, Bayesian parameter estimation methods have shown good accuracy and performance [19–22]. For example, Wong and Farooq [23] developed an algorithm based on the restricted Boltzmann machine, which has multiple discrete-continuous layers and can be expressed as a variational Bayesian inference optimization problem.Emerging machine learning techniques have been studied for travel mode choice [24–34]. Lindner et al. [33] found an artificial neural network (ANN) and classification tree (CT) to outperform binary logit regression in motorized travel mode choice. Cheng et al. [6] found the random forest (RF) to have significantly better prediction accuracy than support vector machine (SVM), adaptive boosting (AdaBoost), and MNL in modeling travel mode choice. Zhao et al. [24] compared the model development, evaluation, and behavior interpretation of MNL and ML with that of the naive Bayes, CT, AdaBoost, bag fruit tree, RF, SVM, and ANN machine learning classifiers. Among machine learning approaches, the multilayer perceptron (MLP) and radial basis function (RBF) have been widely applied due to their better classification accuracy compared to naive Bayes, K-nearest neighbors, and backpropagation neural networks [35–37]. Hence, they have potential use in the study of travel mode choice.The influence of data balance on the accuracy of multimode choice models has not been widely reported. Imbalanced sample data can influence the accuracy of estimation in multiclass discrete choice prediction [38, 39], and methods such as oversampling and undersampling have been proposed to address this issue [40, 41]. However, there is no commonly agreed best method to resolve this issue in multiclass classification. This is a well-known issue in travel mode choice, and the effectiveness of rebalancing methods when using different regression-based and neural network models in empirical studies of modeling travel mode choice requires study.This study has three objectives: (1) to investigate the predictive performance of modeling techniques including Bayesian multinomial logit (BMNL), MNL, MLP, and RBF for intercity travel mode choice; (2) to assess the predictive performance of the above techniques after data balancing; and (3) to evaluate the factors affecting intercity travel mode choice and their relative importance using a comprehensive dataset. Passengers’ activity data over the whole process of intercity travel were collected. The travel modes of airplane, HSR, train, and express bus were investigated. The BMNL, MNL, MLP, and RBF models were developed and validated. A receiver operating characteristic (ROC) curve and confusion matrix were employed to evaluate the models’ predictive performance.The remainder of this paper is organized as follows. Section2 introduces the methodological background of the selected models, followed by a description of the dataset in Section 3. Section 4 presents the results and findings. We summarize our conclusions and propose future work in Section 5.


## 2. Methodology

### 2.1. Bayesian Multinomial Logit Model

MNL regression generalizes logistic regression into multiclass problems that consist of more than two possible discrete groups [1, 19]. It can be expressed as [19](1)PZj=i=expβ0i+β1ixj1+β2ixj2+⋯+βkixjk∑i=1Iexpβ0i+β1ixj1+β2ixj2+⋯+βkixjk,where X=xj1,xj2,…,xjk is a vector of independent variables xjk, β=β0i,β1i,β2i,…,βkiT is the corresponding coefficient vector, and Zj=i is the choice of travel mode i for the jth observation.The likelihood function can be expressed as(2)fZ|β=∏j=1N∏i=1Iεji×PZj=i=∏j=1N∏i=1Iεji×expβ0i+β1ixj1+β2ixj2+⋯+βkixjk∑m=1Iexpβ0i+β1ixj1+β2ixj2+⋯+βkixjk,where N is the number of samples, I is the number of outcomes, and εij equals 1 when the discrete outcome of sample j is i and is 0 otherwise.The Bayesian approach using Markov chain Monte Carlo (MCMC) was utilized for model estimation. Based on Bayesian inference, the posterior joint distribution of parametersβ conditional on dataset Z can be estimated as [19](3)fβ|Z=fZ,βfZ=fZ|βπβfZ|βπβdβ∝fZ|βπβ,where fZ,β is the joint probability distribution of Z and β, fZ|β is the likelihood of the conditional function based on β, and πβ is the prior distribution of β. Due to lack of information on the random parameters, we used the noninformative prior distributions [1]:(4)β∼N0k,106Mk,where 0k is a vector of zeros and Mk is the k×k identity matrix.The posterior joint distribution can be derived as [42] (5)fβ|Z∝fZ|βπβ=∏j=1N∏i=1Iεji×expβ0i+β1ixj1+β2ixj2+⋯+βkixjk∑m=1Iexpβ0i+β1ixj1+β2ixj2+⋯+βkixjk×∏j=1N∏i=1I12π103exp−12βki2106∝exp∑j=1N∑i=1Iεij×expβ0i+β1ixj1+β2ixj2+⋯+βkixjk∑m=1Iexpβ0i+β1ixj1+β2ixj2+⋯+βkixjk−∑j=1N∑i=1I12βki2106.


### 2.2. Radial Basis Function (RBF) Neural Network

An RBF neural network is a typical three-layer neural network model with input, hidden, and output layers, as shown in Figure1, where k is the number of input variables, H is the number of hidden neurons, I is the number of output neurons (travel modes), X=x1,x2,…,xkT is the input, Y=y1,y2,…,yIT is the output, and whi is the connection weight of the hth hidden layer neuron to the ith output layer neuron.Figure 1
RBF network.A Gaussian function is generally used as the hidden layer excitation function. The output of thehth hidden layer neuron is(6)Ghx=e−X−ch2/2σh2,h=1,2,…,H,and the linear mapping relationship between Ghx and the ith output layer neuron is(7)Ghx=yi=∑h=1HwhiGhx,i=1,2,…,I,where ch and σh are, respectively, the center vector of the Gaussian function and the base width of the hth hidden neuron.RBF has been criticized as a “black box” that lacks interpretability [43]. Various tools have been developed to address this issue, the most common being variable importance analysis [44–46], which measures the relative importance of each independent variable in predicting dependent variables.


### 2.3. Multilayer Perceptron (MLP) Neural Network

MLP is a commonly used supervised ANN model that can be used for both pattern recognition and function approximation. Compared to RBF, MLP can have multiple hidden layers (shown in Figure2) [47]. The hyperbolic tangent function is selected as the activation function of MLP hidden neurons. The output from a hidden neuron is(8)y=eu−e−ueu+e−u,and the connection weight is the output of the net function,(9)u=b+∑p=1kwpxp,where k is the number of inputs, xp is the input, wp is the weight of the corresponding input (wp;1≤p≤k), b is the bias weight, and the Levenberg–Marquardt training algorithm is selected [28].Figure 2
General topology of MLP.


### 2.4. Model Comparison and Validation

The multiclassification confusion matrix (see Table1) is used to calculate the accuracy of each model [48], where sim is the number of samples in which mode i is predicted as mode m. The recall and precision of mode i are(10)Recalli=Sii∑m=1Isim,Precisioni=Sii∑m=1ISmi,and the accuracy of the model can be calculated as [1](11)accuracy=∑i=1ISiiN.Table 1
Multiclassification confusion matrix.
Predictive classMode123…IRecallActual class1s11s12s13…s1IRecall12s21s22s23…s2IRecall23s31s32s33…s3IRecall3………………IsI1sI2sI3sIIRecallIPrecisionPrecision1Precision2Precision3PrecisionIAccuracyThe ROC curve and area under the curve (AUC) were also used to measure the predictive ability. A higher AUC value indicates better predictive accuracy [42, 49].


## 2.1. Bayesian Multinomial Logit Model

MNL regression generalizes logistic regression into multiclass problems that consist of more than two possible discrete groups [1, 19]. It can be expressed as [19](1)PZj=i=expβ0i+β1ixj1+β2ixj2+⋯+βkixjk∑i=1Iexpβ0i+β1ixj1+β2ixj2+⋯+βkixjk,where X=xj1,xj2,…,xjk is a vector of independent variables xjk, β=β0i,β1i,β2i,…,βkiT is the corresponding coefficient vector, and Zj=i is the choice of travel mode i for the jth observation.The likelihood function can be expressed as(2)fZ|β=∏j=1N∏i=1Iεji×PZj=i=∏j=1N∏i=1Iεji×expβ0i+β1ixj1+β2ixj2+⋯+βkixjk∑m=1Iexpβ0i+β1ixj1+β2ixj2+⋯+βkixjk,where N is the number of samples, I is the number of outcomes, and εij equals 1 when the discrete outcome of sample j is i and is 0 otherwise.The Bayesian approach using Markov chain Monte Carlo (MCMC) was utilized for model estimation. Based on Bayesian inference, the posterior joint distribution of parametersβ conditional on dataset Z can be estimated as [19](3)fβ|Z=fZ,βfZ=fZ|βπβfZ|βπβdβ∝fZ|βπβ,where fZ,β is the joint probability distribution of Z and β, fZ|β is the likelihood of the conditional function based on β, and πβ is the prior distribution of β. Due to lack of information on the random parameters, we used the noninformative prior distributions [1]:(4)β∼N0k,106Mk,where 0k is a vector of zeros and Mk is the k×k identity matrix.The posterior joint distribution can be derived as [42] (5)fβ|Z∝fZ|βπβ=∏j=1N∏i=1Iεji×expβ0i+β1ixj1+β2ixj2+⋯+βkixjk∑m=1Iexpβ0i+β1ixj1+β2ixj2+⋯+βkixjk×∏j=1N∏i=1I12π103exp−12βki2106∝exp∑j=1N∑i=1Iεij×expβ0i+β1ixj1+β2ixj2+⋯+βkixjk∑m=1Iexpβ0i+β1ixj1+β2ixj2+⋯+βkixjk−∑j=1N∑i=1I12βki2106.


## 2.2. Radial Basis Function (RBF) Neural Network

An RBF neural network is a typical three-layer neural network model with input, hidden, and output layers, as shown in Figure1, where k is the number of input variables, H is the number of hidden neurons, I is the number of output neurons (travel modes), X=x1,x2,…,xkT is the input, Y=y1,y2,…,yIT is the output, and whi is the connection weight of the hth hidden layer neuron to the ith output layer neuron.Figure 1
RBF network.A Gaussian function is generally used as the hidden layer excitation function. The output of thehth hidden layer neuron is(6)Ghx=e−X−ch2/2σh2,h=1,2,…,H,and the linear mapping relationship between Ghx and the ith output layer neuron is(7)Ghx=yi=∑h=1HwhiGhx,i=1,2,…,I,where ch and σh are, respectively, the center vector of the Gaussian function and the base width of the hth hidden neuron.RBF has been criticized as a “black box” that lacks interpretability [43]. Various tools have been developed to address this issue, the most common being variable importance analysis [44–46], which measures the relative importance of each independent variable in predicting dependent variables.


## 2.3. Multilayer Perceptron (MLP) Neural Network

MLP is a commonly used supervised ANN model that can be used for both pattern recognition and function approximation. Compared to RBF, MLP can have multiple hidden layers (shown in Figure2) [47]. The hyperbolic tangent function is selected as the activation function of MLP hidden neurons. The output from a hidden neuron is(8)y=eu−e−ueu+e−u,and the connection weight is the output of the net function,(9)u=b+∑p=1kwpxp,where k is the number of inputs, xp is the input, wp is the weight of the corresponding input (wp;1≤p≤k), b is the bias weight, and the Levenberg–Marquardt training algorithm is selected [28].Figure 2
General topology of MLP.


## 2.4. Model Comparison and Validation

The multiclassification confusion matrix (see Table1) is used to calculate the accuracy of each model [48], where sim is the number of samples in which mode i is predicted as mode m. The recall and precision of mode i are(10)Recalli=Sii∑m=1Isim,Precisioni=Sii∑m=1ISmi,and the accuracy of the model can be calculated as [1](11)accuracy=∑i=1ISiiN.Table 1
Multiclassification confusion matrix.
Predictive classMode123…IRecallActual class1s11s12s13…s1IRecall12s21s22s23…s2IRecall23s31s32s33…s3IRecall3………………IsI1sI2sI3sIIRecallIPrecisionPrecision1Precision2Precision3PrecisionIAccuracyThe ROC curve and area under the curve (AUC) were also used to measure the predictive ability. A higher AUC value indicates better predictive accuracy [42, 49].


## 3. Data Collection

Data from Li et al.’s work [42] were used in this study. A total of 985 random samples collected in Xi’an from March 1–10, 2018, were used for analysis, where 161 samples reported the choice of airplane, accounting for 16.3% of intercity travel records, and 369 (37.5%) were reported as HSR, 299 (30.4%) as train, and 156 (15.8%) as express bus. Among them, 80% were randomly selected for training, and the remaining 20% were used for prediction. In addition to the original information included in the database, the travel distance was calculated by Baidu Maps using the real route between the cities of origin and destination. The intercity travel time was obtained according to the identification number of the carrier, transportation schedule, and origin and destination cities.Undersampling and oversampling are the most frequently used techniques to balance data for machine learning and pattern recognition [38–41]. Undersampling achieves relative equilibrium among classes by reducing the number of samples of classes with more samples. Using this method, the number of samples of each travel mode was 156, with 80% randomly selected for training, and the remaining 20% selected for prediction. Oversampling is to add samples of classes with fewer samples to equal the number of samples in a class with more samples. Through oversampling, the sample size of each transportation mode became 369; 80% of samples were randomly selected for training, and the remaining 20% were selected for prediction.Tables2 and 3 describe the categories and continuous variables for imbalanced and rebalanced data, respectively.Table 2
Description of categorical variables.
VariableDescriptionValueImbalanced dataOversampling balanced dataUndersampling balanced dataTraining setPredictive setTraining setPredictive setTraining setPredictive setFrequencyProportion (%)FrequencyProportion (%)FrequencyProportion (%)FrequencyProportion (%)FrequencyProportion (%)FrequencyProportion (%)DependentTravel modesAirplane112916.393216.16295257425125253125HSR229537.487437.37295257425125253125Train323930.376030.31295257425125253125Express bus412415.763216.16295257425125253125IndependentGenderFemale033542.578140.9147540.2512542.2321342.65846.77Male145257.4311759.0970559.7517157.7728757.46653.23Age<191182.2952.53262.241.3591.810.8120–29232441.178341.9250142.4613144.2621142.25443.5530–39326133.165829.2937731.958328.0415731.43729.8440–49411614.743819.1919116.194314.538316.62318.5550–595546.86115.56635.34289.4630675.6560 and above6141.7831.51221.8672.3610221.60OccupationEnterprise unit116821.354522.7324520.766622.310220.42923.39Personnel of institutions213417.034020.2019716.694816.229418.81915.32Student322528.595326.7736631.029231.0815230.43326.61Farmer4506.3573.54655.51186.08285.6108.06Self-employed511314.363015.1517114.493712.56713.42116.94Other69712.332311.6113611.533511.825711.4129.68Monthly income<3K yuan124931.645929.8039333.319933.4516633.23729.843-4K yuan214718.684120.7119816.785317.919819.62016.134-5K yuan320025.415427.2730125.516421.6212324.63729.845-6K yuan411214.232914.65177155016.896813.62116.946-7K yuan5293.6842.02383.2262.03112.221.61>7K yuan6506.35115.55736.19248.11346.875.65Travel purposeMandatory138048.289447.4758449.4915953.7225150.26653.23Leisure040751.7210452.5359650.5113746.2824949.85846.77Access modePublic transit154869.6312965.1580868.4720067.5735871.67459.68Private car or taxi023930.376934.8537231.539632.4314228.45040.32Access time0–30 min125232.026633.3338332.4610435.1416633.24435.4830–60 min228335.968040.4141435.089732.77165334233.8760–90 min325232.025226.2638332.469532.0916933.83830.65SafetyVery unsafe1000000000000Unsafe281.0221.01171.4431.0161.221.61General314518.423015.1521618.316722.649218.43125Safe439049.5610553.0359450.3414448.6525150.25544.35Very safe5244316130.8135329.918227.715130.23629.03ComfortVery uncomfortable150.6431.52151.2720.6861.221.61Uncomfortable2405.08126.06705.93279.12326.4108.06General319825.164723.7430125.51742511923.83225.81Comfortable441152.2210553.0360951.6114047.326252.45947.58Very comfortable513316.93115.6518515.685317.918116.22116.94PunctualityVery unpunctual1000000000000Unpunctual2303.8194.54463.9227.43244.854.03General320425.924723.7434028.817625.6814128.23729.84Punctual441452.611156.0662452.8816054.0524849.67056.45Very punctual513917.663115.6617014.413812.848717.4129.68Departure modePublic transit157172.5514271.7281669.1522074.3235671.29072.58Private car or taxi021627.455628.2836430.857625.6814428.83427.42Departure time0–30 min138749.2410251.5259450.4213445.2726052.14536.2930–60 min225432.316834.3436931.3210033.7815130.265141.1360–90 min314518.452814.1421518.256220.958817.642822.58Table 3
Description of continuous variables.
DataVariableUnitTraining setPredictive setMinMaxMeanSDMinMaxMeanSDImbalanced dataIntercity travel distancekm16.002831.00797.54579.8616.002540.00792.66632.00Intercity travel costYuan7.002600.00310.46319.447.001400.00283.07288.70Intercity travel timeHour0.2252.006.486.490.2533.006.005.87Access costYuan1.00300.0011.5922.891.00100.0010.1916.36Departure costYuan1.00150.0013.5220.721.00150.0013.2321.89Oversampling balanced dataIntercity travel distanceKm16.002831.00807.54621.3516.002801.00808.45617.20Intercity travel costYuan7.002600.00321.23343.357.002600.00324.57344.48Intercity travel timeHour0.2252.005.926.330.2537.005.856.50Access costYuan1.00300.0013.0325.511.00150.0011.5720.38Departure costYuan1.00150.0015.1923.361.00150.0014.2422.69Undersampling balanced dataIntercity travel distanceKm17.002831.00823.55616.2127.002500.00731.52597.32Intercity travel costYuan7.002600.00330.79360.5413.501200.00277.20275.22Intercity travel timeHour0.2237.005.926.140.2528.005.225.90Access costYuan1.00300.0012.7725.431.00120.0012.4919.88Departure costYuan1.00150.0014.6823.111.00120.0014.5122.79


## 4. Results

Stata 15.0 software was used for parameter estimation of the BMNL and MNL models, confusion matrix, and ROCs. SPSS 25.0 was used for relative importance analysis of variables by the RBF and MLP models.


### 4.1. Model Results

Table4 presents the estimated means of variables from the BMNL model, and Tables 5–7 show their parameter estimates. The frequently used train was considered as the reference in the model. The typical variables including gender, age, occupation, travel purpose, monthly income, intercity travel distance, intercity travel cost, intercity travel time, safety, comfort, punctuality, access time, and departure time were selected for modeling after collinearity testing. The MCMC simulation-based full Bayesian approach was employed to estimate the posterior distributions of parameters. Variables with confidence intervals not including zero were regarded as significant [19]. As shown in Table 4, we found that the parameter estimates of certain variables differed slightly between the imbalanced and balanced data. For example, the intercity travel distance is significantly related to the choice of express bus when using balanced data, but not when using imbalanced data. The signs of variables were found to be consistent between balanced and imbalanced data.Table 4
Parameter estimation in BMNL.
VariableImbalanced dataOversampling balanced dataUndersampling balanced dataAirplaneHSRExpress busAirplaneHSRExpress busAirplaneHSRExpress busMeanMeanMeanMeanMeanMeanMeanMeanMeanGenderMale vs. female0.5550.1860.3680.6830.1970.7131.2310.3840.733Age0.2820.3500.2470.4160.3570.3460.396—0.380OccupationPersonnel of institutions vs. enterprise unit0.7100.4080.6510.3440.1430.313———Student vs. enterprise unit—−0.3001.3480.316−0.3491.930——1.454Farmer vs. enterprise unit−0.473——−0.898−0.561−0.333−2.097−0.584−0.574Self-employed vs. enterprise unit——0.686−1.157−0.3840.558−2.540−1.114—Others vs. enterprise unit−0.844−0.1930.679−1.480−0.4750.616−2.160−0.7040.473Monthly income—−0.273——−0.221—−0.163−0.222—Travel purposeMandatory travel vs. leisure travel−0.477−0.284−0.425−0.341−0.388——−0.2300.138Intercity travel distance0.0040.001—0.002—−0.0020.003—−0.002Intercity travel cost0.0180.015—0.0270.0220.0010.0260.023—Intercity travel time−1.239−0.397—−1.265−0.4170.002−1.255−0.4820.036Safety0.5660.609—0.8180.685—−0.0980.621—Comfort—0.314−0.4330.1950.369−0.4630.6390.312−0.480Punctuality−0.3350.319−0.574−0.3770.317−0.525−0.4960.323−0.817Access time0.390—−0.2680.455—−0.2840.351−0.220—Departure time0.694——1.0260.264—0.796—−0.427Constant−7.703−5.8033.089−9.503−6.7982.328−5.985−5.5893.884Note: parameters that were significant at the 95% confidence level are shown in the table.Table 5
Parameter estimation in BMNL using imbalanced data.
VariableAirplaneHSRExpress busMeanSDCredit intervalMeanSDCredit intervalMeanSDCredit interval2.50%97.50%2.50%97.50%2.50%97.50%GenderMale vs. female0.5550.1430.2750.8330.1860.0570.0670.2950.3680.1670.0400.677Age0.2820.0890.1140.4540.3500.0910.1800.5380.2470.0840.0720.407OccupationPersonnel of institution vs. enterprise unit0.7100.1730.3771.0510.4080.0590.2950.5270.6510.1290.4030.913Student vs. enterprise unit0.1140.171−0.2170.435−0.3000.068−0.440−0.1671.3480.1811.0021.727Farmer vs. enterprise unit−0.4730.226−0.930−0.027−0.0780.063−0.2050.423−0.0310.158−0.3210.288Self-employed vs. enterprise unit−0.1470.187−0.5220.2280.0740.082−0.0830.2350.6860.1390.4090.967Others vs. enterprise unit−0.8440.161−1.173−0.526−0.1930.066−0.316−0.0590.6790.1440.3960.953Monthly income−0.0980.090−0.2700.089−0.2730.062−0.394−0.154−0.1210.070−0.2510.016Travel purposeMandatory travel vs. leisure travel−0.4770.196−0.871−0.096−0.2840.053−0.384−0.185−0.4250.130−0.699−0.192Intercity travel distance0.0040.0010.0030.0050.0010.0010.0010.002−0.0010.001−0.0020.001Intercity travel cost0.0180.0020.0140.0220.0150.0020.0110.1860.0010.002−0.0050.004Intercity travel time−1.2390.096−1.433−1.059−0.3970.044−0.485−0.311−0.0090.029−0.0640.048Safety0.5660.1490.2680.8470.6090.0860.4400.7820.0390.065−0.0790.173Comfort0.2450.124−0.0170.4740.3140.0530.2110.427−0.4330.099−0.634−0.254Punctuality−0.3350.13−0.586−0.0890.3190.0660.1890.440−0.5740.04−0.655−0.498Access time0.3900.1510.0740.677−0.080.056−0.1890.034−0.2680.106−0.472−0.066Departure time0.6940.1420.4280.9810.0290.060−0.0800.151−0.1610.132−0.4190.094Constant−7.7030.081−7.863−7.537−5.8030.098−5.997−5.623.0890.1242.8573.342Table 6
Parameter estimation in BMNL using oversampling of balanced data.
VariableAirplaneHSRExpress busMeanSDCredit intervalMeanSDCredit intervalMeanSDCredit interval2.50%97.50%2.50%97.50%2.50%97.50%GenderMale vs. female0.6830.1180.4740.9470.1970.0750.0520.3390.7130.0850.5560.872Age0.4160.1060.1900.6150.3570.0280.2980.4100.3460.0540.2410.452OccupationPersonnel of institution vs. enterprise unit0.3440.0760.2180.5100.1430.0540.0410.2560.3130.1070.0500.491Student vs. enterprise unit0.3160.0780.1260.436−0.3490.050−0.444−0.2561.9300.0601.8172.041Farmer vs. enterprise unit−0.8980.058−1.014−0.787−0.5610.077−0.712−0.417−0.3330.054−0.438−0.229Self-employed vs. enterprise unit−1.1570.120−1.398−0.928−0.3840.075−0.531−0.2320.5580.1420.2690.818Others vs. enterprise unit−1.4800.072−1.643−1.348−0.4750.116−0.695−0.2490.6160.1010.4230.794Monthly income−0.0440.061−0.1920.058−0.2210.047−0.315−0.1290.0150.052−0.0790.128Travel purposeMandatory travel vs. leisure travel−0.3410.033−0.396−0.264−0.3880.086−0.556−0.216−0.1270.064−0.2430.004Intercity travel distance0.0020.0010.0010.004−0.0010.001−0.0020.001−0.0020.001−0.003−0.001Intercity travel cost0.0270.0020.0230.0310.0220.0020.0180.0260.0010.002−0.0020.005Intercity travel time−1.2650.075−1.426−1.128−0.4170.022−0.459−0.3730.0020.024−0.0470.045Safety0.8180.0690.6710.9470.6850.0470.5940.7800.1550.104−0.0420.359Comfort0.1950.1200.0070.4900.3690.0330.3030.434−0.4630.094−0.644−0.284Punctuality−0.3770.116−0.602−0.1640.3170.0410.2420.399−0.5250.080−0.680−0.370Access time0.4550.0810.2550.587−0.1360.110−0.3570.066−0.2840.058−0.409−0.175Departure time1.0260.1710.7171.3560.2640.0330.2010.329−0.2020.111−0.4180.012Constant−9.5030.080−9.678−9.362−6.7980.092−6.976−6.6052.3280.0672.1642.433Table 7
Parameter estimation in BMNL using undersampling of balanced data.
VariableAirplaneHSRExpress busMeanSDCredit intervalMeanSDCredit intervalMeanSDCredit interval2.50%97.50%2.50%97.50%2.50%97.50%GenderMale vs. female1.2310.2660.7191.7640.3840.1140.1670.6200.7330.1650.4351.075Age0.3960.1020.2060.5950.2320.143−0.0800.5060.3800.0830.2200.541OccupationPersonnel of institution vs. enterprise unit−0.1620.130−0.4030.081−0.1760.106−0.3930.0350.1390.171−0.2350.444Student vs. enterprise unit0.0410.170−0.2740.366−0.1210.210−0.5290.2881.4540.1311.1981.718Farmer vs. enterprise unit−2.0970.191−2.450−1.722−0.5840.061−0.709−0.458−0.5740.223−1.017−0.128Self-employed vs. enterprise unit−2.5400.232−3.011−2.105−1.1140.081−1.280−0.9540.0210.231−0.4490.485Others vs. enterprise unit−2.1600.211−2.563−1.735−0.7040.085−0.906−0.5740.4730.1340.2170.740Monthly income−0.1630.067−0.305−0.031−0.2220.101−0.418−0.027−0.1280.075−0.2840.020Travel purposeMandatory travel vs. leisure travel−0.0380.215−0.4700.352−0.2300.113−0.471−0.0130.1380.205−0.2530.554Intercity travel distance0.0030.0010.0010.0050.0000.001−0.0020.002−0.0020.001−0.004−0.001Intercity travel cost0.0260.0040.0200.0350.0230.0030.0160.0310.0000.003−0.0060.006Intercity travel time−1.2550.062−1.378−1.146−0.4820.056−0.598−0.3880.0360.043−0.0490.126Safety−0.0980.133−0.3570.1510.6210.0990.4320.8240.0770.096−0.1130.274Comfort0.6390.0350.5740.7060.3120.1200.0560.526−0.4800.134−0.753−0.223Punctuality−0.4960.158−0.800−0.1900.3230.0180.2900.363−0.8170.118−1.065−0.582Access time0.3510.0730.2160.490−0.2200.030−0.278−0.1590.0420.070−0.0980.178Departure time0.7960.1090.5841.029−0.0500.063−0.1780.064−0.4270.115−0.641−0.200Constant−5.9850.135−6.242−5.731−5.5890.207−6.001−5.2003.8840.1733.5404.203Table8 shows the estimated coefficients of variables from the MNL model using the same variables. Parameter estimates of variables are shown in Tables 9–11. Similar to the BMNL model, the parameter estimates differ to some extent between imbalanced and balanced data, and the signs of significant variables are consistent. The symbols of significant variables in the MNL model were consistent with those in the BMNL model. However, the significant variables in MNL were not completely consistent with those in the BMNL model. For example, the travel purpose is significant in the BMNL model but not in the MNL model. Gender was significantly related to the choice of HSR in the BMNL model, but not in the MNL model.Table 8
Parameter estimation in MNL.
VariableImbalanced dataOversampling balanced dataUndersampling balanced dataAirplaneHSRExpress busAirplaneHSRExpress busAirplaneHSRExpress busCoefficientCoefficientCoefficientCoefficientCoefficientCoefficientCoefficientCoefficientCoefficientGenderMale vs. female—————0.681——0.723Age—0.349——0.3660.360———OccupationPersonnel of institutions vs. enterprise unit—————————Student vs. enterprise unit——1.298—−0.3521.856——1.642Farmer vs. enterprise unit—————————Self-employed vs. enterprise unit—————————Others vs. enterprise unit—————————Monthly income−0.128−0.289——−0.226————Travel purposeMandatory travel vs. leisure travel—————————Intercity travel distance0.0040.001—0.002—−0.0020.003——Intercity travel cost0.0170.014—0.0260.022—0.0310.027—Intercity travel time−1.211−0.380—−1.242−0.421—−1.395−0.638—Safety—0.585—0.8010.678————Comfort——−0.458——−0.461——−0.418Punctuality—0.299−0.575——−0.513——−0.617Access time—————————Departure time0.731——1.030—−0.185———Constant−7.673−5.8213.058−9.522−6.7982.303—−5.2973.420Note: parameters that were significant at the 95% confidence level are shown in the table.Table 9
Parameter estimation in MNL using imbalanced data.
VariableAirplaneHSRExpress busCoefficientP>zCredit intervalCoefficientP>zCredit intervalCoefficientP>zCredit interval2.50%97.50%2.50%97.50%2.50%97.50%GenderMale vs. female0.4740.321−0.4621.4100.1600.543−0.3550.6740.4090.121−0.1070.926Age0.3260.269−0.2520.9040.3490.0350.0240.6750.2530.128−0.0730.579OccupationPersonnel of institution vs. enterprise unit0.7250.290−0.6182.0690.4100.316−0.3911.2100.6420.191−0.3201.604Student vs. enterprise unit0.1160.885−1.4531.685−0.3620.390−1.1890.4641.2980.0020.4642.132Farmer vs. enterprise unit−0.4250.658−2.3071.458−0.0800.892−1.2341.074−0.0590.929−1.3591.241Self-employed vs. enterprise unit−0.2070.789−1.7201.3060.0810.849−0.7540.9160.6110.195−0.3141.537Others vs. enterprise unit−0.8240.366−2.6100.962−0.1730.732−1.1610.8160.7050.178−0.321.730Monthly income−0.1280.565−0.5630.307−0.2890.013−0.516−0.062−0.1060.329−0.3180.106Travel purposeMandatory travel vs. leisure travel−0.4430.340−1.3520.466−0.3020.256−0.8230.219−0.4120.112−0.9210.096Intercity travel distance0.0040.0010.0020.0050.0010.278−0.0010.002−0.0010.009−0.0030.001Intercity travel cost0.0170.0010.0130.0210.0140.0010.0100.0180.0010.828−0.0050.004Intercity travel time−1.2110.001−1.444−0.978−0.3800.001−0.483−0.276−0.0030.917−0.0610.055Safety0.4910.137−0.1561.1380.5850.0040.1880.9820.0590.760−0.3190.437Comfort0.2510.410−0.3450.8460.3580.056−0.010.725−0.4580.011−0.811−0.105Punctuality−0.2780.356−0.8660.3110.2990.104−0.0610.660−0.5750.002−0.936−0.213Access time0.4040.180−0.1870.994−0.0350.841−0.3740.304−0.2210.172−0.5390.096Departure time0.7310.0170.1311.3310.0470.791−0.3040.398−0.2100.269−0.5840.163Constant−7.6730.002−12.518−2.828−5.8210.001−8.592−3.0513.0580.0120.6675.450Table 10
Parameter estimation in MNL using oversampling of balanced data.
VariableAirplaneHSRExpress busCoefficientP>zCredit intervalCoefficientP>zCredit intervalCoefficientP>zCredit interval2.50%97.50%2.50%97.50%2.50%97.50%GenderMale vs. female0.6610.118−0.1671.4900.1960.443−0.3050.6970.6810.0010.2751.087Age0.3860.126−0.1080.8800.3660.0200.0580.6730.3600.0070.0970.624OccupationPersonnel of institution vs. enterprise unit0.3430.564−0.8241.5100.1380.723−0.6270.9030.3180.401−0.4241.061Student vs. enterprise unit0.2980.672−1.0821.679−0.3520.399−1.1710.4661.8560.0011.1932.519Farmer vs. enterprise unit−0.8980.309−2.6270.831−0.5460.376−1.7570.664−0.3380.488−1.2910.616Self-employed vs. enterprise unit−1.1070.126−2.5250.312−0.3870.376−1.2430.4690.5540.119−0.1421.250Others vs. enterprise unit−1.5180.055−3.0670.030−0.4790.305−1.3940.4370.5450.179−0.2501.340Monthly income−0.0400.836−0.4160.336−0.2260.043−0.445−0.007−0.0170.840−0.1820.148Travel purposeMandatory travel vs. leisure travel−0.3430.413−1.1660.479−0.3840.140−0.8950.126−0.1340.506−0.5290.261Intercity travel distance0.0020.0010.0010.004−0.0010.264−0.0020.001−0.0020.001−0.003−0.001Intercity travel cost0.0260.0010.0210.0310.0220.0010.0170.0260.0010.580−0.0030.005Intercity travel time−1.2420.001−1.432−1.053−0.4210.001−0.524−0.3180.0010.964−0.0500.052Safety0.8010.0060.2251.3780.6780.0010.2791.0770.1460.333−0.1490.440Comfort0.2360.404−0.3180.7910.3710.051−0.0010.743−0.4610.001−0.737−0.185Punctuality−0.3530.194−0.8860.1790.3210.082−0.0400.682−0.5130.001−0.808−0.219Access time0.4560.076−0.0480.959−0.1220.462−0.4470.203−0.2440.060−0.4990.010Departure time1.0300.0010.5061.5540.2710.130−0.0800.621−0.1850.232−0.4870.118Constant−9.5220.001−13.873−5.170−6.7980.001−9.530−4.0662.3030.0200.3564.250Table 11
Parameter estimation in MNL using undersampling of balanced data.
VariableAirplaneHSRExpress busCoefficientP>zCredit intervalCoefficientP>zCredit intervalCoefficientP>zCredit interval2.50%97.50%2.50%97.50%2.50%97.50%GenderMale vs. female0.8470.137−0.2681.9620.1750.637−0.5520.9010.7230.0100.1761.271Age0.4390.213−0.2521.1300.3050.183−0.1440.7540.2590.135−0.0800.598OccupationPersonnel of institution vs. enterprise unit0.2520.748−1.2841.787−0.0570.916−1.1130.9990.2200.657−0.7511.191Student vs. enterprise unit0.3170.742−1.5652.199−0.1280.831−1.3041.0481.6420.0010.7742.510Farmer vs. enterprise unit−1.6000.179−3.9310.732−0.7040.399−2.3390.931−0.5180.420−1.7770.741Self-employed vs. enterprise unit−1.9390.059−3.9530.076−0.8280.200−2.0960.4390.6460.176−0.2911.584Others vs. enterprise unit−1.8600.093−4.0280.307−0.7820.289−2.2290.6640.6320.256−0.4581.721Monthly income−0.1390.612−0.6760.398−0.2230.180−0.5500.103−0.0480.671−0.2710.175Travel purposeMandatory travel vs. leisure travel−0.3370.549−1.4390.764−0.3130.408−1.0550.428−0.2830.300−0.8190.252Intercity travel distance0.0030.0060.0010.0050.0010.960−0.0020.002−0.0020.008−0.0030.001Intercity travel cost0.0310.0010.0230.0400.0270.0010.0190.0360.0010.875−0.0060.005Intercity travel time−1.3950.001−1.686−1.105−0.6380.001−0.837−0.439−0.0130.763−0.0950.070Safety0.0840.838−0.7270.8960.5140.074−0.0501.0770.0140.945−0.3920.421Comfort0.3010.424−0.4371.0390.4660.074−0.0440.976−0.4180.023−0.780−0.057Punctuality−0.3890.256−1.0610.2830.1890.448−0.2980.675−0.6170.002−1.003−0.230Access time0.4220.237−0.2771.120−0.1940.430−0.6760.288−0.1350.434−0.4750.204Departure time0.6550.073−0.0611.371−0.0340.892−0.5300.461−0.2260.259−0.6170.166Constant−5.6960.050−11.3960.004−5.2970.006−9.039−1.5553.4200.0080.9125.928Figures3 and 4 show the relative importance of the factors obtained by RBF and MLP, respectively. There is a slight difference in the order of relative importance of factors. For example, using imbalanced data, intercity travel cost is most important in the RBF model, but second in importance in the MLP model, after intercity travel time. Slight differences exist in the relative importance of factors between imbalanced and balanced data in the same model. For example, in the MLP model, gender is the least important using imbalanced data, and travel purpose is the least important using balanced data. Overall, intercity travel cost, intercity travel time, intercity travel distance, comfort, safety, and punctuality are the most important factors in the intercity travel mode choice, followed by the monthly income, age, and occupation. Access and departure times, which reflect the accessibility of a transport hub, show moderate importance. Travel purpose and gender are the least important.Figure 3
Relative importance of each variable using RBF. (a) Imbalanced data. (b) Oversampling balanced data. (c) Undersampling balanced data.
(a)(b)(c)Figure 4
Relative importance of each variable using MLP. (a) Imbalanced data. (b) Oversampling balanced data. (c) Undersampling balanced data.
(a)(b)(c)


### 4.2. Model Comparison and Validation

#### 4.2.1. Model Performance for Imbalanced Data

AUCs and confusion matrices were employed to compare the fitting and predictive performance of the MNL, BMNL, MLP, and RBF models. The confusion matrix of the four models using imbalanced data is shown in Table12. Through the analysis of the accuracy, it can be found that MLP has the best fitting performance (80.70%), and RBF is the worst (67.30%). BMNL (76.36%) and MNL (76.10%) have similar fitting performance. For the predictive set, the predictive performance of MLP (78.70%) is the best, followed by MNL (75.76%), BMNL (75.25%), and RBF (65.50%).Table 12
Confusion matrix and recall, precision, and accuracy of each model for imbalanced data.
ModelTraining setPredictive setPredictive classPredictive classModeAirplaneHSRTrainExpress busRecallAirplaneHSRTrainExpress busRecallMNLActual classAirplane109182084.50%3020093.80%HSR1624627683.40%35711377.00%Train3251812876.40%3544873.30%Express bus08545948.80%01121959.40%Precision85.16%82.83%68.56%63.44%76.10%83.33%87.69%65.67%63.33%75.76%BMNLActual classAirplane113142087.60%3020093.80%HSR1824328682.40%35513374.30%Train5241842677.00%3545775.00%Express bus37536149.20%00131959.40%Precision81.29%84.38%68.91%65.59%76.36%83.33%88.71%63.38%65.52%75.25%MLPActual classAirplane11892091.50%2930090.60%HSR1226813290.80%3646186.50%Train1301832377.20%0745776.30%Express bus05546251.20%02131753.10%Precision90.08%85.90%72.62%71.26%80.70%90.63%84.21%70.31%68.00%78.70%RBFActual classAirplane80416262.00%21110065.60%HSR17216451773.20%45312571.60%Train0391811776.40%19381164.40%Express bus018544940.50%01141753.10%Precision82.47%68.79%63.29%57.65%67.30%80.77%71.62%59.38%51.52%65.50%The bold values represent the accuracy of models.The ROC curves of the four models are shown in Figures5 and 6. For the training set, the AUC of the MLP for the airplane is 0.9857, which indicates that its fitting performance is better than that of BMNL (0.9732), MNL (0.9731), and RBF (0.9443). The MLP model is almost perfect, as its ROC curve rises rapidly toward the upper-left corner of the graph. Similarly, the AUCs of MLP for HSR and train are the largest, followed by BMNL, MNL, and RBF. These findings confirm that the MLP model outperforms BMNL and MNL, followed by RBF.Figure 5
ROC curves of models for imbalanced data training set. (a) Airplane. (b) HSR. (c) Train. (d) Express bus.
(a)(b)(c)(d)Figure 6
ROC curves of models for imbalanced data predictive set. (a) Airplane. (b) HSR. (c) Train. (d) Express bus.
(a)(b)(c)(d)For the predictive set, the AUC of MLP for airplane is 0.9905, which is better than RBF (0.9823), BMNL (0.9784), and MNL (0.9767). Similarly, MLP is almost perfect, as its ROC curve rises rapidly toward the upper-left corner of the graph. The AUC of MLP for HSR is also the largest, followed by BMNL, MNL, and RBF. The AUC of MLP for train is 0.9054, which indicates that its predictive performance is significantly better than that of MNL (0.8637), BMNL (0.8624), and RBF (0.8280). However, the AUC of BMNL for express bus is the largest, followed by MNL, MLP, and RBF.


#### 4.2.2. Model Performance for Rebalanced Data

MNL, BMNL, MLP, and RBF were used to train and verify the balanced data with the same variables used for the imbalanced data. The confusion matrices of each model for undersampled and oversampled balanced data are shown in Tables13 and 14. The ROC curves for the undersampled training and predictive set are presented in Figures 7 and 8. The ROC curves for the oversampled training and predictive sets are presented in Figures 9 and 10.Table 13
Confusion matrix and recall, precision, and accuracy of each model for undersampling of balanced data.
ModelTraining setPredictive setPredictive classPredictive classModeAirplaneHSRTrainExpress busRecallAirplaneHSRTrainExpress busRecallMNLActual classAirplane11581192.00%2740087.10%HSR81027881.60%5211467.74%Train315792863.20%04151248.39%Express bus33259475.20%0182270.97%Precision89.15%79.69%70.54%71.76%78.00%84.38%70.00%62.50%57.89%68.55%BMNLActual classAirplane11671192.80%2830090.32%HSR1288141170.40%5183558.06%Train36813564.80%02171254.84%Express bus30289475.20%0182270.97%Precision86.57%87.13%65.32%66.67%75.80%84.85%75.00%60.71%56.41%68.55%MLPActual classAirplane12121196.80%2830090.30%HSR61077585.60%2251380.60%Train113921774.80%0419861.30%Express bus03308973.00%02101961.30%Precision94.53%85.60%70.77%79.46%81.80%93.33%73.53%63.33%63.33%73.40%RBFActual classAirplane105123584.00%2550180.60%HSR2079151163.20%3203564.50%Train112832767.50%0222771.00%Express bus19288468.90%0282167.70%Precision82.68%70.54%64.34%66.14%70.20%89.29%68.97%66.67%61.76%71.00%The bold values represent the accuracy of models.Table 14
Confusion matrix of each model for oversampling of balanced data.
ModelTraining setPredictive setPredictive classPredictive classModeAirplaneHSRTrainExpress busRecallAirplaneHSRTrainExpress busRecallMNLActual classAirplane275181193.22%7111195.95%HSR18235231979.66%9555574.32%Train6231907664.41%110402354.05%Express bus786321773.56%01274662.16%Precision89.87%82.75%68.59%69.33%77.71%87.65%82.09%54.79%61.33%71.62%BMNLActual classAirplane276171193.56%7111195.95%HSR18235222079.66%9546572.97%Train6231947265.76%110412255.41%Express bus757321071.19%00284662.16%Precision89.90%83.93%66.90%69.31%77.54%87.65%83.08%53.95%62.16%71.62%MLPActual classAirplane277161193.90%7201197.30%HSR13241212081.70%6555874.30%Train3212095871.80%113421856.80%Express bus0133124484.70%02155777.00%Precision94.54%82.82%79.77%75.54%83.10%91.14%78.57%66.67%67.86%76.40%RBFActual classAirplane2443361282.70%58103378.40%HSR51176373159.70%14438958.10%Train2371886464.60%215411655.40%Express bus2187219668.10%03185371.60%Precision81.61%66.67%62.05%64.69%68.14%78.38%60.56%58.57%65.43%65.90%The bold values represent the accuracy of models.Figure 7
ROC curves for undersampled balanced data training set. (a) Airplane. (b) HSR. (c) Train. (d) Express bus.
(a)(b)(c)(d)Figure 8
ROC curves for undersampled balanced data predictive set. (a) Airplane. (b) HSR. (c) Train. (d) Express bus.
(a)(b)(c)(d)Figure 9
ROC curves for oversampled balanced data training set. (a) Airplane. (b) HSR. (c) Train. (d) Express bus.
(a)(b)(c)(d)Figure 10
ROC curves for oversampled balanced data training set. (a) Airplane. (b) HSR. (c) Train. (d) Express bus.
(a)(b)(c)(d)The results show that MLP provides the best fitting for both oversampled and undersampled data, followed by BMNL and MNL, and RBF has the poorest fitting performance. The results are consistent with those of the four models using imbalanced data. Hence, whether the data are balanced will not affect the relative fitting performance of the models.For the predictive performance of the models, we found that MLP performs best regardless of oversampling or undersampling balanced data. More importantly, BMNL and MNL show the same predictive performance when using oversampling balanced data, and RBF models have the worst predictive performance. Similarly, BMNL and MNL have the same predictive performance using undersampled data, but their performance is lower than that of RBF.The fitting performance of models based on balanced data is a slight improvement over using imbalanced data. For example, the fitting performance of MLP model is 80.70% using imbalanced data, and 81.80% and 83.10%, respectively, with undersampled and oversampled data. However, except for the RBF model, the predictive performance of these models based on balanced data is slightly lower than that when using imbalanced data.The ROC curve was also used to intuitively judge the predictive performance of each model, and AUCs were used to quantitatively compare their predictive accuracy under different modeling techniques. We found that the results from AUCs are consistent with those from the confusion matrices for each model.


### 4.3. Model Interpretation

We use the results of the BMNL with better statistical performance and MLP models with better predictive performance to explain the effects of factors on intercity travel mode choice.From Table4 and Figure 4, it is found that gender was positively correlated with the choice of HSR and express bus, indicating that men were prone to traveling by HSR or express bus, and women by train. This finding is consistent with a previous study [2], which revealed that women preferred using train more than men. The models show that personnel of government-sponsored institutions were more likely than enterprise personnel to choose an airplane. Farmers and the self-employed were less likely than enterprise personnel to travel by airplane. Similarly, students and farmers were not prone to choosing HSR, and farmers were prone to using an express bus [2, 8]. These results are supported by a previous study [1, 3] that found that passengers working in the state sector are likely to choose airplane over coach. Monthly income was found to be positively associated with airplane choice, and negatively with express bus choice. This result agrees with the result of a study [4, 7] that found that higher- and lower-income individuals favor air and bus travel, respectively.The variable of travel purpose had a significant positive effect on HSR choice and was ranked 11th in the relative importance of all variables. This finding is similar to that of a past study [1] and reveals that, compared to the train, leisure passengers prefer HSRs or airplanes more than passengers for mandatory travel. It is possible that leisure passengers can afford the higher travel cost and are more willing to travel in a comfortable mode. The modeling results also show the significant impact of travel distance on intercity travel mode choice, which is third most important. This result implies that, compared to the train, the longer travel distance favors airplane and HSR, and the shorter distance favors express bus, which is consistent with previous studies [3, 10]. Intercity travel cost is the most important variable and is a positive sign for the airplane or HSR choice, indicating that passengers incurring higher travel costs are more likely to travel by airplane or HSR. Intercity travel time is the second most important factor, showing a negative association with the choice of airplane and HSR, indicating that passengers spending less travel time are more likely to select airplane or HSR. This finding is intuitive because airplanes and HSRs are faster than trains.Safety ranked fourth, and this variable affects the choice of airplane and HSR, showing that passengers with a higher safety demand are more likely to travel by airplane or HSR. Comfort is the fifth most important factor; it positively influences the choice of airplane and HSR and is negatively associated with express bus. This result is expected, as airplanes and HSRs have better service facilities and environments than trains [1]. Punctuality ranked ninth and is positively related to HSR choice and negatively associated with airplane and express bus. This shows that a higher punctuality demand favors HSR and does not favor airplane and express bus. This result is expected, as external conditions such as bad weather can easily affect the operation of airplanes and express buses, but its impact on HSRs and trains is relatively small [1].Access time ranked seventh in relative importance and is found to have a positive effect on airplane choice and a negative effect on express bus compared to train, indicating that passengers spending longer access time prefer traveling by airplane and are less likely to travel by express bus. The finding is straightforward because the airport is generally farther than the railway station from the city center, and the highway passenger station is closer [10]. A similar result was found for the effect of departure time.


## 4.1. Model Results

Table4 presents the estimated means of variables from the BMNL model, and Tables 5–7 show their parameter estimates. The frequently used train was considered as the reference in the model. The typical variables including gender, age, occupation, travel purpose, monthly income, intercity travel distance, intercity travel cost, intercity travel time, safety, comfort, punctuality, access time, and departure time were selected for modeling after collinearity testing. The MCMC simulation-based full Bayesian approach was employed to estimate the posterior distributions of parameters. Variables with confidence intervals not including zero were regarded as significant [19]. As shown in Table 4, we found that the parameter estimates of certain variables differed slightly between the imbalanced and balanced data. For example, the intercity travel distance is significantly related to the choice of express bus when using balanced data, but not when using imbalanced data. The signs of variables were found to be consistent between balanced and imbalanced data.Table 4
Parameter estimation in BMNL.
VariableImbalanced dataOversampling balanced dataUndersampling balanced dataAirplaneHSRExpress busAirplaneHSRExpress busAirplaneHSRExpress busMeanMeanMeanMeanMeanMeanMeanMeanMeanGenderMale vs. female0.5550.1860.3680.6830.1970.7131.2310.3840.733Age0.2820.3500.2470.4160.3570.3460.396—0.380OccupationPersonnel of institutions vs. enterprise unit0.7100.4080.6510.3440.1430.313———Student vs. enterprise unit—−0.3001.3480.316−0.3491.930——1.454Farmer vs. enterprise unit−0.473——−0.898−0.561−0.333−2.097−0.584−0.574Self-employed vs. enterprise unit——0.686−1.157−0.3840.558−2.540−1.114—Others vs. enterprise unit−0.844−0.1930.679−1.480−0.4750.616−2.160−0.7040.473Monthly income—−0.273——−0.221—−0.163−0.222—Travel purposeMandatory travel vs. leisure travel−0.477−0.284−0.425−0.341−0.388——−0.2300.138Intercity travel distance0.0040.001—0.002—−0.0020.003—−0.002Intercity travel cost0.0180.015—0.0270.0220.0010.0260.023—Intercity travel time−1.239−0.397—−1.265−0.4170.002−1.255−0.4820.036Safety0.5660.609—0.8180.685—−0.0980.621—Comfort—0.314−0.4330.1950.369−0.4630.6390.312−0.480Punctuality−0.3350.319−0.574−0.3770.317−0.525−0.4960.323−0.817Access time0.390—−0.2680.455—−0.2840.351−0.220—Departure time0.694——1.0260.264—0.796—−0.427Constant−7.703−5.8033.089−9.503−6.7982.328−5.985−5.5893.884Note: parameters that were significant at the 95% confidence level are shown in the table.Table 5
Parameter estimation in BMNL using imbalanced data.
VariableAirplaneHSRExpress busMeanSDCredit intervalMeanSDCredit intervalMeanSDCredit interval2.50%97.50%2.50%97.50%2.50%97.50%GenderMale vs. female0.5550.1430.2750.8330.1860.0570.0670.2950.3680.1670.0400.677Age0.2820.0890.1140.4540.3500.0910.1800.5380.2470.0840.0720.407OccupationPersonnel of institution vs. enterprise unit0.7100.1730.3771.0510.4080.0590.2950.5270.6510.1290.4030.913Student vs. enterprise unit0.1140.171−0.2170.435−0.3000.068−0.440−0.1671.3480.1811.0021.727Farmer vs. enterprise unit−0.4730.226−0.930−0.027−0.0780.063−0.2050.423−0.0310.158−0.3210.288Self-employed vs. enterprise unit−0.1470.187−0.5220.2280.0740.082−0.0830.2350.6860.1390.4090.967Others vs. enterprise unit−0.8440.161−1.173−0.526−0.1930.066−0.316−0.0590.6790.1440.3960.953Monthly income−0.0980.090−0.2700.089−0.2730.062−0.394−0.154−0.1210.070−0.2510.016Travel purposeMandatory travel vs. leisure travel−0.4770.196−0.871−0.096−0.2840.053−0.384−0.185−0.4250.130−0.699−0.192Intercity travel distance0.0040.0010.0030.0050.0010.0010.0010.002−0.0010.001−0.0020.001Intercity travel cost0.0180.0020.0140.0220.0150.0020.0110.1860.0010.002−0.0050.004Intercity travel time−1.2390.096−1.433−1.059−0.3970.044−0.485−0.311−0.0090.029−0.0640.048Safety0.5660.1490.2680.8470.6090.0860.4400.7820.0390.065−0.0790.173Comfort0.2450.124−0.0170.4740.3140.0530.2110.427−0.4330.099−0.634−0.254Punctuality−0.3350.13−0.586−0.0890.3190.0660.1890.440−0.5740.04−0.655−0.498Access time0.3900.1510.0740.677−0.080.056−0.1890.034−0.2680.106−0.472−0.066Departure time0.6940.1420.4280.9810.0290.060−0.0800.151−0.1610.132−0.4190.094Constant−7.7030.081−7.863−7.537−5.8030.098−5.997−5.623.0890.1242.8573.342Table 6
Parameter estimation in BMNL using oversampling of balanced data.
VariableAirplaneHSRExpress busMeanSDCredit intervalMeanSDCredit intervalMeanSDCredit interval2.50%97.50%2.50%97.50%2.50%97.50%GenderMale vs. female0.6830.1180.4740.9470.1970.0750.0520.3390.7130.0850.5560.872Age0.4160.1060.1900.6150.3570.0280.2980.4100.3460.0540.2410.452OccupationPersonnel of institution vs. enterprise unit0.3440.0760.2180.5100.1430.0540.0410.2560.3130.1070.0500.491Student vs. enterprise unit0.3160.0780.1260.436−0.3490.050−0.444−0.2561.9300.0601.8172.041Farmer vs. enterprise unit−0.8980.058−1.014−0.787−0.5610.077−0.712−0.417−0.3330.054−0.438−0.229Self-employed vs. enterprise unit−1.1570.120−1.398−0.928−0.3840.075−0.531−0.2320.5580.1420.2690.818Others vs. enterprise unit−1.4800.072−1.643−1.348−0.4750.116−0.695−0.2490.6160.1010.4230.794Monthly income−0.0440.061−0.1920.058−0.2210.047−0.315−0.1290.0150.052−0.0790.128Travel purposeMandatory travel vs. leisure travel−0.3410.033−0.396−0.264−0.3880.086−0.556−0.216−0.1270.064−0.2430.004Intercity travel distance0.0020.0010.0010.004−0.0010.001−0.0020.001−0.0020.001−0.003−0.001Intercity travel cost0.0270.0020.0230.0310.0220.0020.0180.0260.0010.002−0.0020.005Intercity travel time−1.2650.075−1.426−1.128−0.4170.022−0.459−0.3730.0020.024−0.0470.045Safety0.8180.0690.6710.9470.6850.0470.5940.7800.1550.104−0.0420.359Comfort0.1950.1200.0070.4900.3690.0330.3030.434−0.4630.094−0.644−0.284Punctuality−0.3770.116−0.602−0.1640.3170.0410.2420.399−0.5250.080−0.680−0.370Access time0.4550.0810.2550.587−0.1360.110−0.3570.066−0.2840.058−0.409−0.175Departure time1.0260.1710.7171.3560.2640.0330.2010.329−0.2020.111−0.4180.012Constant−9.5030.080−9.678−9.362−6.7980.092−6.976−6.6052.3280.0672.1642.433Table 7
Parameter estimation in BMNL using undersampling of balanced data.
VariableAirplaneHSRExpress busMeanSDCredit intervalMeanSDCredit intervalMeanSDCredit interval2.50%97.50%2.50%97.50%2.50%97.50%GenderMale vs. female1.2310.2660.7191.7640.3840.1140.1670.6200.7330.1650.4351.075Age0.3960.1020.2060.5950.2320.143−0.0800.5060.3800.0830.2200.541OccupationPersonnel of institution vs. enterprise unit−0.1620.130−0.4030.081−0.1760.106−0.3930.0350.1390.171−0.2350.444Student vs. enterprise unit0.0410.170−0.2740.366−0.1210.210−0.5290.2881.4540.1311.1981.718Farmer vs. enterprise unit−2.0970.191−2.450−1.722−0.5840.061−0.709−0.458−0.5740.223−1.017−0.128Self-employed vs. enterprise unit−2.5400.232−3.011−2.105−1.1140.081−1.280−0.9540.0210.231−0.4490.485Others vs. enterprise unit−2.1600.211−2.563−1.735−0.7040.085−0.906−0.5740.4730.1340.2170.740Monthly income−0.1630.067−0.305−0.031−0.2220.101−0.418−0.027−0.1280.075−0.2840.020Travel purposeMandatory travel vs. leisure travel−0.0380.215−0.4700.352−0.2300.113−0.471−0.0130.1380.205−0.2530.554Intercity travel distance0.0030.0010.0010.0050.0000.001−0.0020.002−0.0020.001−0.004−0.001Intercity travel cost0.0260.0040.0200.0350.0230.0030.0160.0310.0000.003−0.0060.006Intercity travel time−1.2550.062−1.378−1.146−0.4820.056−0.598−0.3880.0360.043−0.0490.126Safety−0.0980.133−0.3570.1510.6210.0990.4320.8240.0770.096−0.1130.274Comfort0.6390.0350.5740.7060.3120.1200.0560.526−0.4800.134−0.753−0.223Punctuality−0.4960.158−0.800−0.1900.3230.0180.2900.363−0.8170.118−1.065−0.582Access time0.3510.0730.2160.490−0.2200.030−0.278−0.1590.0420.070−0.0980.178Departure time0.7960.1090.5841.029−0.0500.063−0.1780.064−0.4270.115−0.641−0.200Constant−5.9850.135−6.242−5.731−5.5890.207−6.001−5.2003.8840.1733.5404.203Table8 shows the estimated coefficients of variables from the MNL model using the same variables. Parameter estimates of variables are shown in Tables 9–11. Similar to the BMNL model, the parameter estimates differ to some extent between imbalanced and balanced data, and the signs of significant variables are consistent. The symbols of significant variables in the MNL model were consistent with those in the BMNL model. However, the significant variables in MNL were not completely consistent with those in the BMNL model. For example, the travel purpose is significant in the BMNL model but not in the MNL model. Gender was significantly related to the choice of HSR in the BMNL model, but not in the MNL model.Table 8
Parameter estimation in MNL.
VariableImbalanced dataOversampling balanced dataUndersampling balanced dataAirplaneHSRExpress busAirplaneHSRExpress busAirplaneHSRExpress busCoefficientCoefficientCoefficientCoefficientCoefficientCoefficientCoefficientCoefficientCoefficientGenderMale vs. female—————0.681——0.723Age—0.349——0.3660.360———OccupationPersonnel of institutions vs. enterprise unit—————————Student vs. enterprise unit——1.298—−0.3521.856——1.642Farmer vs. enterprise unit—————————Self-employed vs. enterprise unit—————————Others vs. enterprise unit—————————Monthly income−0.128−0.289——−0.226————Travel purposeMandatory travel vs. leisure travel—————————Intercity travel distance0.0040.001—0.002—−0.0020.003——Intercity travel cost0.0170.014—0.0260.022—0.0310.027—Intercity travel time−1.211−0.380—−1.242−0.421—−1.395−0.638—Safety—0.585—0.8010.678————Comfort——−0.458——−0.461——−0.418Punctuality—0.299−0.575——−0.513——−0.617Access time—————————Departure time0.731——1.030—−0.185———Constant−7.673−5.8213.058−9.522−6.7982.303—−5.2973.420Note: parameters that were significant at the 95% confidence level are shown in the table.Table 9
Parameter estimation in MNL using imbalanced data.
VariableAirplaneHSRExpress busCoefficientP>zCredit intervalCoefficientP>zCredit intervalCoefficientP>zCredit interval2.50%97.50%2.50%97.50%2.50%97.50%GenderMale vs. female0.4740.321−0.4621.4100.1600.543−0.3550.6740.4090.121−0.1070.926Age0.3260.269−0.2520.9040.3490.0350.0240.6750.2530.128−0.0730.579OccupationPersonnel of institution vs. enterprise unit0.7250.290−0.6182.0690.4100.316−0.3911.2100.6420.191−0.3201.604Student vs. enterprise unit0.1160.885−1.4531.685−0.3620.390−1.1890.4641.2980.0020.4642.132Farmer vs. enterprise unit−0.4250.658−2.3071.458−0.0800.892−1.2341.074−0.0590.929−1.3591.241Self-employed vs. enterprise unit−0.2070.789−1.7201.3060.0810.849−0.7540.9160.6110.195−0.3141.537Others vs. enterprise unit−0.8240.366−2.6100.962−0.1730.732−1.1610.8160.7050.178−0.321.730Monthly income−0.1280.565−0.5630.307−0.2890.013−0.516−0.062−0.1060.329−0.3180.106Travel purposeMandatory travel vs. leisure travel−0.4430.340−1.3520.466−0.3020.256−0.8230.219−0.4120.112−0.9210.096Intercity travel distance0.0040.0010.0020.0050.0010.278−0.0010.002−0.0010.009−0.0030.001Intercity travel cost0.0170.0010.0130.0210.0140.0010.0100.0180.0010.828−0.0050.004Intercity travel time−1.2110.001−1.444−0.978−0.3800.001−0.483−0.276−0.0030.917−0.0610.055Safety0.4910.137−0.1561.1380.5850.0040.1880.9820.0590.760−0.3190.437Comfort0.2510.410−0.3450.8460.3580.056−0.010.725−0.4580.011−0.811−0.105Punctuality−0.2780.356−0.8660.3110.2990.104−0.0610.660−0.5750.002−0.936−0.213Access time0.4040.180−0.1870.994−0.0350.841−0.3740.304−0.2210.172−0.5390.096Departure time0.7310.0170.1311.3310.0470.791−0.3040.398−0.2100.269−0.5840.163Constant−7.6730.002−12.518−2.828−5.8210.001−8.592−3.0513.0580.0120.6675.450Table 10
Parameter estimation in MNL using oversampling of balanced data.
VariableAirplaneHSRExpress busCoefficientP>zCredit intervalCoefficientP>zCredit intervalCoefficientP>zCredit interval2.50%97.50%2.50%97.50%2.50%97.50%GenderMale vs. female0.6610.118−0.1671.4900.1960.443−0.3050.6970.6810.0010.2751.087Age0.3860.126−0.1080.8800.3660.0200.0580.6730.3600.0070.0970.624OccupationPersonnel of institution vs. enterprise unit0.3430.564−0.8241.5100.1380.723−0.6270.9030.3180.401−0.4241.061Student vs. enterprise unit0.2980.672−1.0821.679−0.3520.399−1.1710.4661.8560.0011.1932.519Farmer vs. enterprise unit−0.8980.309−2.6270.831−0.5460.376−1.7570.664−0.3380.488−1.2910.616Self-employed vs. enterprise unit−1.1070.126−2.5250.312−0.3870.376−1.2430.4690.5540.119−0.1421.250Others vs. enterprise unit−1.5180.055−3.0670.030−0.4790.305−1.3940.4370.5450.179−0.2501.340Monthly income−0.0400.836−0.4160.336−0.2260.043−0.445−0.007−0.0170.840−0.1820.148Travel purposeMandatory travel vs. leisure travel−0.3430.413−1.1660.479−0.3840.140−0.8950.126−0.1340.506−0.5290.261Intercity travel distance0.0020.0010.0010.004−0.0010.264−0.0020.001−0.0020.001−0.003−0.001Intercity travel cost0.0260.0010.0210.0310.0220.0010.0170.0260.0010.580−0.0030.005Intercity travel time−1.2420.001−1.432−1.053−0.4210.001−0.524−0.3180.0010.964−0.0500.052Safety0.8010.0060.2251.3780.6780.0010.2791.0770.1460.333−0.1490.440Comfort0.2360.404−0.3180.7910.3710.051−0.0010.743−0.4610.001−0.737−0.185Punctuality−0.3530.194−0.8860.1790.3210.082−0.0400.682−0.5130.001−0.808−0.219Access time0.4560.076−0.0480.959−0.1220.462−0.4470.203−0.2440.060−0.4990.010Departure time1.0300.0010.5061.5540.2710.130−0.0800.621−0.1850.232−0.4870.118Constant−9.5220.001−13.873−5.170−6.7980.001−9.530−4.0662.3030.0200.3564.250Table 11
Parameter estimation in MNL using undersampling of balanced data.
VariableAirplaneHSRExpress busCoefficientP>zCredit intervalCoefficientP>zCredit intervalCoefficientP>zCredit interval2.50%97.50%2.50%97.50%2.50%97.50%GenderMale vs. female0.8470.137−0.2681.9620.1750.637−0.5520.9010.7230.0100.1761.271Age0.4390.213−0.2521.1300.3050.183−0.1440.7540.2590.135−0.0800.598OccupationPersonnel of institution vs. enterprise unit0.2520.748−1.2841.787−0.0570.916−1.1130.9990.2200.657−0.7511.191Student vs. enterprise unit0.3170.742−1.5652.199−0.1280.831−1.3041.0481.6420.0010.7742.510Farmer vs. enterprise unit−1.6000.179−3.9310.732−0.7040.399−2.3390.931−0.5180.420−1.7770.741Self-employed vs. enterprise unit−1.9390.059−3.9530.076−0.8280.200−2.0960.4390.6460.176−0.2911.584Others vs. enterprise unit−1.8600.093−4.0280.307−0.7820.289−2.2290.6640.6320.256−0.4581.721Monthly income−0.1390.612−0.6760.398−0.2230.180−0.5500.103−0.0480.671−0.2710.175Travel purposeMandatory travel vs. leisure travel−0.3370.549−1.4390.764−0.3130.408−1.0550.428−0.2830.300−0.8190.252Intercity travel distance0.0030.0060.0010.0050.0010.960−0.0020.002−0.0020.008−0.0030.001Intercity travel cost0.0310.0010.0230.0400.0270.0010.0190.0360.0010.875−0.0060.005Intercity travel time−1.3950.001−1.686−1.105−0.6380.001−0.837−0.439−0.0130.763−0.0950.070Safety0.0840.838−0.7270.8960.5140.074−0.0501.0770.0140.945−0.3920.421Comfort0.3010.424−0.4371.0390.4660.074−0.0440.976−0.4180.023−0.780−0.057Punctuality−0.3890.256−1.0610.2830.1890.448−0.2980.675−0.6170.002−1.003−0.230Access time0.4220.237−0.2771.120−0.1940.430−0.6760.288−0.1350.434−0.4750.204Departure time0.6550.073−0.0611.371−0.0340.892−0.5300.461−0.2260.259−0.6170.166Constant−5.6960.050−11.3960.004−5.2970.006−9.039−1.5553.4200.0080.9125.928Figures3 and 4 show the relative importance of the factors obtained by RBF and MLP, respectively. There is a slight difference in the order of relative importance of factors. For example, using imbalanced data, intercity travel cost is most important in the RBF model, but second in importance in the MLP model, after intercity travel time. Slight differences exist in the relative importance of factors between imbalanced and balanced data in the same model. For example, in the MLP model, gender is the least important using imbalanced data, and travel purpose is the least important using balanced data. Overall, intercity travel cost, intercity travel time, intercity travel distance, comfort, safety, and punctuality are the most important factors in the intercity travel mode choice, followed by the monthly income, age, and occupation. Access and departure times, which reflect the accessibility of a transport hub, show moderate importance. Travel purpose and gender are the least important.Figure 3
Relative importance of each variable using RBF. (a) Imbalanced data. (b) Oversampling balanced data. (c) Undersampling balanced data.
(a)(b)(c)Figure 4
Relative importance of each variable using MLP. (a) Imbalanced data. (b) Oversampling balanced data. (c) Undersampling balanced data.
(a)(b)(c)


## 4.2. Model Comparison and Validation

### 4.2.1. Model Performance for Imbalanced Data

AUCs and confusion matrices were employed to compare the fitting and predictive performance of the MNL, BMNL, MLP, and RBF models. The confusion matrix of the four models using imbalanced data is shown in Table12. Through the analysis of the accuracy, it can be found that MLP has the best fitting performance (80.70%), and RBF is the worst (67.30%). BMNL (76.36%) and MNL (76.10%) have similar fitting performance. For the predictive set, the predictive performance of MLP (78.70%) is the best, followed by MNL (75.76%), BMNL (75.25%), and RBF (65.50%).Table 12
Confusion matrix and recall, precision, and accuracy of each model for imbalanced data.
ModelTraining setPredictive setPredictive classPredictive classModeAirplaneHSRTrainExpress busRecallAirplaneHSRTrainExpress busRecallMNLActual classAirplane109182084.50%3020093.80%HSR1624627683.40%35711377.00%Train3251812876.40%3544873.30%Express bus08545948.80%01121959.40%Precision85.16%82.83%68.56%63.44%76.10%83.33%87.69%65.67%63.33%75.76%BMNLActual classAirplane113142087.60%3020093.80%HSR1824328682.40%35513374.30%Train5241842677.00%3545775.00%Express bus37536149.20%00131959.40%Precision81.29%84.38%68.91%65.59%76.36%83.33%88.71%63.38%65.52%75.25%MLPActual classAirplane11892091.50%2930090.60%HSR1226813290.80%3646186.50%Train1301832377.20%0745776.30%Express bus05546251.20%02131753.10%Precision90.08%85.90%72.62%71.26%80.70%90.63%84.21%70.31%68.00%78.70%RBFActual classAirplane80416262.00%21110065.60%HSR17216451773.20%45312571.60%Train0391811776.40%19381164.40%Express bus018544940.50%01141753.10%Precision82.47%68.79%63.29%57.65%67.30%80.77%71.62%59.38%51.52%65.50%The bold values represent the accuracy of models.The ROC curves of the four models are shown in Figures5 and 6. For the training set, the AUC of the MLP for the airplane is 0.9857, which indicates that its fitting performance is better than that of BMNL (0.9732), MNL (0.9731), and RBF (0.9443). The MLP model is almost perfect, as its ROC curve rises rapidly toward the upper-left corner of the graph. Similarly, the AUCs of MLP for HSR and train are the largest, followed by BMNL, MNL, and RBF. These findings confirm that the MLP model outperforms BMNL and MNL, followed by RBF.Figure 5
ROC curves of models for imbalanced data training set. (a) Airplane. (b) HSR. (c) Train. (d) Express bus.
(a)(b)(c)(d)Figure 6
ROC curves of models for imbalanced data predictive set. (a) Airplane. (b) HSR. (c) Train. (d) Express bus.
(a)(b)(c)(d)For the predictive set, the AUC of MLP for airplane is 0.9905, which is better than RBF (0.9823), BMNL (0.9784), and MNL (0.9767). Similarly, MLP is almost perfect, as its ROC curve rises rapidly toward the upper-left corner of the graph. The AUC of MLP for HSR is also the largest, followed by BMNL, MNL, and RBF. The AUC of MLP for train is 0.9054, which indicates that its predictive performance is significantly better than that of MNL (0.8637), BMNL (0.8624), and RBF (0.8280). However, the AUC of BMNL for express bus is the largest, followed by MNL, MLP, and RBF.


### 4.2.2. Model Performance for Rebalanced Data

MNL, BMNL, MLP, and RBF were used to train and verify the balanced data with the same variables used for the imbalanced data. The confusion matrices of each model for undersampled and oversampled balanced data are shown in Tables13 and 14. The ROC curves for the undersampled training and predictive set are presented in Figures 7 and 8. The ROC curves for the oversampled training and predictive sets are presented in Figures 9 and 10.Table 13
Confusion matrix and recall, precision, and accuracy of each model for undersampling of balanced data.
ModelTraining setPredictive setPredictive classPredictive classModeAirplaneHSRTrainExpress busRecallAirplaneHSRTrainExpress busRecallMNLActual classAirplane11581192.00%2740087.10%HSR81027881.60%5211467.74%Train315792863.20%04151248.39%Express bus33259475.20%0182270.97%Precision89.15%79.69%70.54%71.76%78.00%84.38%70.00%62.50%57.89%68.55%BMNLActual classAirplane11671192.80%2830090.32%HSR1288141170.40%5183558.06%Train36813564.80%02171254.84%Express bus30289475.20%0182270.97%Precision86.57%87.13%65.32%66.67%75.80%84.85%75.00%60.71%56.41%68.55%MLPActual classAirplane12121196.80%2830090.30%HSR61077585.60%2251380.60%Train113921774.80%0419861.30%Express bus03308973.00%02101961.30%Precision94.53%85.60%70.77%79.46%81.80%93.33%73.53%63.33%63.33%73.40%RBFActual classAirplane105123584.00%2550180.60%HSR2079151163.20%3203564.50%Train112832767.50%0222771.00%Express bus19288468.90%0282167.70%Precision82.68%70.54%64.34%66.14%70.20%89.29%68.97%66.67%61.76%71.00%The bold values represent the accuracy of models.Table 14
Confusion matrix of each model for oversampling of balanced data.
ModelTraining setPredictive setPredictive classPredictive classModeAirplaneHSRTrainExpress busRecallAirplaneHSRTrainExpress busRecallMNLActual classAirplane275181193.22%7111195.95%HSR18235231979.66%9555574.32%Train6231907664.41%110402354.05%Express bus786321773.56%01274662.16%Precision89.87%82.75%68.59%69.33%77.71%87.65%82.09%54.79%61.33%71.62%BMNLActual classAirplane276171193.56%7111195.95%HSR18235222079.66%9546572.97%Train6231947265.76%110412255.41%Express bus757321071.19%00284662.16%Precision89.90%83.93%66.90%69.31%77.54%87.65%83.08%53.95%62.16%71.62%MLPActual classAirplane277161193.90%7201197.30%HSR13241212081.70%6555874.30%Train3212095871.80%113421856.80%Express bus0133124484.70%02155777.00%Precision94.54%82.82%79.77%75.54%83.10%91.14%78.57%66.67%67.86%76.40%RBFActual classAirplane2443361282.70%58103378.40%HSR51176373159.70%14438958.10%Train2371886464.60%215411655.40%Express bus2187219668.10%03185371.60%Precision81.61%66.67%62.05%64.69%68.14%78.38%60.56%58.57%65.43%65.90%The bold values represent the accuracy of models.Figure 7
ROC curves for undersampled balanced data training set. (a) Airplane. (b) HSR. (c) Train. (d) Express bus.
(a)(b)(c)(d)Figure 8
ROC curves for undersampled balanced data predictive set. (a) Airplane. (b) HSR. (c) Train. (d) Express bus.
(a)(b)(c)(d)Figure 9
ROC curves for oversampled balanced data training set. (a) Airplane. (b) HSR. (c) Train. (d) Express bus.
(a)(b)(c)(d)Figure 10
ROC curves for oversampled balanced data training set. (a) Airplane. (b) HSR. (c) Train. (d) Express bus.
(a)(b)(c)(d)The results show that MLP provides the best fitting for both oversampled and undersampled data, followed by BMNL and MNL, and RBF has the poorest fitting performance. The results are consistent with those of the four models using imbalanced data. Hence, whether the data are balanced will not affect the relative fitting performance of the models.For the predictive performance of the models, we found that MLP performs best regardless of oversampling or undersampling balanced data. More importantly, BMNL and MNL show the same predictive performance when using oversampling balanced data, and RBF models have the worst predictive performance. Similarly, BMNL and MNL have the same predictive performance using undersampled data, but their performance is lower than that of RBF.The fitting performance of models based on balanced data is a slight improvement over using imbalanced data. For example, the fitting performance of MLP model is 80.70% using imbalanced data, and 81.80% and 83.10%, respectively, with undersampled and oversampled data. However, except for the RBF model, the predictive performance of these models based on balanced data is slightly lower than that when using imbalanced data.The ROC curve was also used to intuitively judge the predictive performance of each model, and AUCs were used to quantitatively compare their predictive accuracy under different modeling techniques. We found that the results from AUCs are consistent with those from the confusion matrices for each model.


## 4.2.1. Model Performance for Imbalanced Data

AUCs and confusion matrices were employed to compare the fitting and predictive performance of the MNL, BMNL, MLP, and RBF models. The confusion matrix of the four models using imbalanced data is shown in Table12. Through the analysis of the accuracy, it can be found that MLP has the best fitting performance (80.70%), and RBF is the worst (67.30%). BMNL (76.36%) and MNL (76.10%) have similar fitting performance. For the predictive set, the predictive performance of MLP (78.70%) is the best, followed by MNL (75.76%), BMNL (75.25%), and RBF (65.50%).Table 12
Confusion matrix and recall, precision, and accuracy of each model for imbalanced data.
ModelTraining setPredictive setPredictive classPredictive classModeAirplaneHSRTrainExpress busRecallAirplaneHSRTrainExpress busRecallMNLActual classAirplane109182084.50%3020093.80%HSR1624627683.40%35711377.00%Train3251812876.40%3544873.30%Express bus08545948.80%01121959.40%Precision85.16%82.83%68.56%63.44%76.10%83.33%87.69%65.67%63.33%75.76%BMNLActual classAirplane113142087.60%3020093.80%HSR1824328682.40%35513374.30%Train5241842677.00%3545775.00%Express bus37536149.20%00131959.40%Precision81.29%84.38%68.91%65.59%76.36%83.33%88.71%63.38%65.52%75.25%MLPActual classAirplane11892091.50%2930090.60%HSR1226813290.80%3646186.50%Train1301832377.20%0745776.30%Express bus05546251.20%02131753.10%Precision90.08%85.90%72.62%71.26%80.70%90.63%84.21%70.31%68.00%78.70%RBFActual classAirplane80416262.00%21110065.60%HSR17216451773.20%45312571.60%Train0391811776.40%19381164.40%Express bus018544940.50%01141753.10%Precision82.47%68.79%63.29%57.65%67.30%80.77%71.62%59.38%51.52%65.50%The bold values represent the accuracy of models.The ROC curves of the four models are shown in Figures5 and 6. For the training set, the AUC of the MLP for the airplane is 0.9857, which indicates that its fitting performance is better than that of BMNL (0.9732), MNL (0.9731), and RBF (0.9443). The MLP model is almost perfect, as its ROC curve rises rapidly toward the upper-left corner of the graph. Similarly, the AUCs of MLP for HSR and train are the largest, followed by BMNL, MNL, and RBF. These findings confirm that the MLP model outperforms BMNL and MNL, followed by RBF.Figure 5
ROC curves of models for imbalanced data training set. (a) Airplane. (b) HSR. (c) Train. (d) Express bus.
(a)(b)(c)(d)Figure 6
ROC curves of models for imbalanced data predictive set. (a) Airplane. (b) HSR. (c) Train. (d) Express bus.
(a)(b)(c)(d)For the predictive set, the AUC of MLP for airplane is 0.9905, which is better than RBF (0.9823), BMNL (0.9784), and MNL (0.9767). Similarly, MLP is almost perfect, as its ROC curve rises rapidly toward the upper-left corner of the graph. The AUC of MLP for HSR is also the largest, followed by BMNL, MNL, and RBF. The AUC of MLP for train is 0.9054, which indicates that its predictive performance is significantly better than that of MNL (0.8637), BMNL (0.8624), and RBF (0.8280). However, the AUC of BMNL for express bus is the largest, followed by MNL, MLP, and RBF.


## 4.2.2. Model Performance for Rebalanced Data

MNL, BMNL, MLP, and RBF were used to train and verify the balanced data with the same variables used for the imbalanced data. The confusion matrices of each model for undersampled and oversampled balanced data are shown in Tables13 and 14. The ROC curves for the undersampled training and predictive set are presented in Figures 7 and 8. The ROC curves for the oversampled training and predictive sets are presented in Figures 9 and 10.Table 13
Confusion matrix and recall, precision, and accuracy of each model for undersampling of balanced data.
ModelTraining setPredictive setPredictive classPredictive classModeAirplaneHSRTrainExpress busRecallAirplaneHSRTrainExpress busRecallMNLActual classAirplane11581192.00%2740087.10%HSR81027881.60%5211467.74%Train315792863.20%04151248.39%Express bus33259475.20%0182270.97%Precision89.15%79.69%70.54%71.76%78.00%84.38%70.00%62.50%57.89%68.55%BMNLActual classAirplane11671192.80%2830090.32%HSR1288141170.40%5183558.06%Train36813564.80%02171254.84%Express bus30289475.20%0182270.97%Precision86.57%87.13%65.32%66.67%75.80%84.85%75.00%60.71%56.41%68.55%MLPActual classAirplane12121196.80%2830090.30%HSR61077585.60%2251380.60%Train113921774.80%0419861.30%Express bus03308973.00%02101961.30%Precision94.53%85.60%70.77%79.46%81.80%93.33%73.53%63.33%63.33%73.40%RBFActual classAirplane105123584.00%2550180.60%HSR2079151163.20%3203564.50%Train112832767.50%0222771.00%Express bus19288468.90%0282167.70%Precision82.68%70.54%64.34%66.14%70.20%89.29%68.97%66.67%61.76%71.00%The bold values represent the accuracy of models.Table 14
Confusion matrix of each model for oversampling of balanced data.
ModelTraining setPredictive setPredictive classPredictive classModeAirplaneHSRTrainExpress busRecallAirplaneHSRTrainExpress busRecallMNLActual classAirplane275181193.22%7111195.95%HSR18235231979.66%9555574.32%Train6231907664.41%110402354.05%Express bus786321773.56%01274662.16%Precision89.87%82.75%68.59%69.33%77.71%87.65%82.09%54.79%61.33%71.62%BMNLActual classAirplane276171193.56%7111195.95%HSR18235222079.66%9546572.97%Train6231947265.76%110412255.41%Express bus757321071.19%00284662.16%Precision89.90%83.93%66.90%69.31%77.54%87.65%83.08%53.95%62.16%71.62%MLPActual classAirplane277161193.90%7201197.30%HSR13241212081.70%6555874.30%Train3212095871.80%113421856.80%Express bus0133124484.70%02155777.00%Precision94.54%82.82%79.77%75.54%83.10%91.14%78.57%66.67%67.86%76.40%RBFActual classAirplane2443361282.70%58103378.40%HSR51176373159.70%14438958.10%Train2371886464.60%215411655.40%Express bus2187219668.10%03185371.60%Precision81.61%66.67%62.05%64.69%68.14%78.38%60.56%58.57%65.43%65.90%The bold values represent the accuracy of models.Figure 7
ROC curves for undersampled balanced data training set. (a) Airplane. (b) HSR. (c) Train. (d) Express bus.
(a)(b)(c)(d)Figure 8
ROC curves for undersampled balanced data predictive set. (a) Airplane. (b) HSR. (c) Train. (d) Express bus.
(a)(b)(c)(d)Figure 9
ROC curves for oversampled balanced data training set. (a) Airplane. (b) HSR. (c) Train. (d) Express bus.
(a)(b)(c)(d)Figure 10
ROC curves for oversampled balanced data training set. (a) Airplane. (b) HSR. (c) Train. (d) Express bus.
(a)(b)(c)(d)The results show that MLP provides the best fitting for both oversampled and undersampled data, followed by BMNL and MNL, and RBF has the poorest fitting performance. The results are consistent with those of the four models using imbalanced data. Hence, whether the data are balanced will not affect the relative fitting performance of the models.For the predictive performance of the models, we found that MLP performs best regardless of oversampling or undersampling balanced data. More importantly, BMNL and MNL show the same predictive performance when using oversampling balanced data, and RBF models have the worst predictive performance. Similarly, BMNL and MNL have the same predictive performance using undersampled data, but their performance is lower than that of RBF.The fitting performance of models based on balanced data is a slight improvement over using imbalanced data. For example, the fitting performance of MLP model is 80.70% using imbalanced data, and 81.80% and 83.10%, respectively, with undersampled and oversampled data. However, except for the RBF model, the predictive performance of these models based on balanced data is slightly lower than that when using imbalanced data.The ROC curve was also used to intuitively judge the predictive performance of each model, and AUCs were used to quantitatively compare their predictive accuracy under different modeling techniques. We found that the results from AUCs are consistent with those from the confusion matrices for each model.


## 4.3. Model Interpretation

We use the results of the BMNL with better statistical performance and MLP models with better predictive performance to explain the effects of factors on intercity travel mode choice.From Table4 and Figure 4, it is found that gender was positively correlated with the choice of HSR and express bus, indicating that men were prone to traveling by HSR or express bus, and women by train. This finding is consistent with a previous study [2], which revealed that women preferred using train more than men. The models show that personnel of government-sponsored institutions were more likely than enterprise personnel to choose an airplane. Farmers and the self-employed were less likely than enterprise personnel to travel by airplane. Similarly, students and farmers were not prone to choosing HSR, and farmers were prone to using an express bus [2, 8]. These results are supported by a previous study [1, 3] that found that passengers working in the state sector are likely to choose airplane over coach. Monthly income was found to be positively associated with airplane choice, and negatively with express bus choice. This result agrees with the result of a study [4, 7] that found that higher- and lower-income individuals favor air and bus travel, respectively.The variable of travel purpose had a significant positive effect on HSR choice and was ranked 11th in the relative importance of all variables. This finding is similar to that of a past study [1] and reveals that, compared to the train, leisure passengers prefer HSRs or airplanes more than passengers for mandatory travel. It is possible that leisure passengers can afford the higher travel cost and are more willing to travel in a comfortable mode. The modeling results also show the significant impact of travel distance on intercity travel mode choice, which is third most important. This result implies that, compared to the train, the longer travel distance favors airplane and HSR, and the shorter distance favors express bus, which is consistent with previous studies [3, 10]. Intercity travel cost is the most important variable and is a positive sign for the airplane or HSR choice, indicating that passengers incurring higher travel costs are more likely to travel by airplane or HSR. Intercity travel time is the second most important factor, showing a negative association with the choice of airplane and HSR, indicating that passengers spending less travel time are more likely to select airplane or HSR. This finding is intuitive because airplanes and HSRs are faster than trains.Safety ranked fourth, and this variable affects the choice of airplane and HSR, showing that passengers with a higher safety demand are more likely to travel by airplane or HSR. Comfort is the fifth most important factor; it positively influences the choice of airplane and HSR and is negatively associated with express bus. This result is expected, as airplanes and HSRs have better service facilities and environments than trains [1]. Punctuality ranked ninth and is positively related to HSR choice and negatively associated with airplane and express bus. This shows that a higher punctuality demand favors HSR and does not favor airplane and express bus. This result is expected, as external conditions such as bad weather can easily affect the operation of airplanes and express buses, but its impact on HSRs and trains is relatively small [1].Access time ranked seventh in relative importance and is found to have a positive effect on airplane choice and a negative effect on express bus compared to train, indicating that passengers spending longer access time prefer traveling by airplane and are less likely to travel by express bus. The finding is straightforward because the airport is generally farther than the railway station from the city center, and the highway passenger station is closer [10]. A similar result was found for the effect of departure time.


## 5. Discussion and Conclusions

We investigated modeling techniques BMNL, MNL, MLP, and RBF for passengers’ intercity travel mode choices. Data from a large individual-level survey in the city of Xi’an were used to develop the model. More comprehensive factors such as socioeconomics, travel demand, service quality, and accessibility of transport hub were incorporated in the models.The comparison results show that MLP has the best predictive performance, BMNL and MNL have approximately equal predictive accuracy, and RBF has the poorest performance using imbalanced data. It was found that the fitting performance of the four models with balanced data was slightly higher than those with imbalanced data. However, it was surprising that the predictive performance of these models with balanced data was slightly lower than those with imbalanced data. A potential reason could be that the degree of imbalance for the original data is very small. These findings suggest that the MLP and BMNL modeling approaches are recommended for the analysis of passengers’ intercity travel mode choice. Significant variables in the BMNL model include gender, age, occupation, travel purpose, intercity travel distance, intercity travel cost, intercity travel time, safety, punctuality, access time, and departure time, which is not completely consistent with those in the MNL model. However, the signs of significant variables in the BMNL model were in line with those in the MNL model. Regarding the MLP modeling results, the travel cost was found to be the most important factor in intercity mode choice, followed by travel time and travel distance. Comfort, safety, and punctuality were relatively important factors for passenger travel mode choices. The influence of individual characteristics on intercity travel mode choices was relatively low, and monthly income was the most important factor among individual characteristics.These findings can provide a reference for traffic management departments to formulate traffic demand management strategies and provide technical support for data analysts and high-tech enterprises to develop intelligent decision-making systems for the choice of passenger intercity travel modes. Through our research conclusion, we can find that intercity travel time, intercity travel cost, intercity travel distance, and the service quality of a transportation mode are important factors affecting intercity travel mode choices. Traffic transportation management departments can accordingly develop a green transportation development strategy by optimizing ticket prices, increasing vehicle speeds, and improving the quality of service, so as to push travelers from transportation with high energy consumption to that with low energy consumption. Our findings show that the predictive performance of models does not significantly improve when using balanced data instead of imbalanced data. This can provide a basis for data analysts to fully understand the impact of data structures on the predictive performance of models.There are some limitations to this study. The results may only apply to the selected dataset and therefore must be verified using datasets from more cities. The degree of data imbalance and proportion between the training set and the prediction set may also affect the fitting and predictive performance of the models, and it is necessary to explore the fitting and predictive performance of models using extremely unbalanced data and other proportions in the future. In addition, although no significant multicollinearity was found in the independent variables for the models, intercity travel time and intercity travel cost varied with travel distance. It is necessary to generate the fare rate and intercity travel time per kilomile by standardizing the intercity travel time and intercity travel cost and incorporate the transformed variables into the models to eliminate the potential impact of travel distance. Moreover, more variables that might be associated with intercity travel mode choices, such as the characteristics of the destination city, weather, and coronavirus disease, should be investigated. Advanced modeling techniques, such as the Bayesian random parameter model capturing more unobserved heterogeneity, the Probit model with endogenous variables, and the XGBoost model, should be applied in future studies.



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*Source: 9219176-2021-09-14.xml*