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

*is study conducts a comprehensive comparative analysis of regression-based multinomial models and artificial neural network models in intercity travel mode choices. *e 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. *e standard multinomial logit (MNL) regression and Bayesian multinomial logit (BMNL) regression were compared with the radial basis function (RBF) and multilayer perceptron (MLP). *e results show that MLP performs best in terms of predictive accuracy, followed by BMNL andMNL, and RBF is the least accurate.*e 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. *is 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.


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][3][4], age [4][5][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]. e 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][16][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][20][21][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][25][26][27][28][29][30][31][32][33][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 (Ada-Boost), 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][36][37]. Hence, they have potential use in the study of travel mode choice. e 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. is 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.
is 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. e travel modes of airplane, HSR, train, and express bus were investigated. e 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. e remainder of this paper is organized as follows. Section 2 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.

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] T is the corresponding coefficient vector, and Z j � i is the choice of travel mode i for the j th observation. e likelihood function can be expressed as where N is the number of samples, I is the number of outcomes, and ε ij equals 1 when the discrete outcome of sample j is i and is 0 otherwise. e Bayesian approach using Markov chain Monte Carlo (MCMC) was utilized for model estimation. Based on Bayesian inference, the posterior joint distribution of parameters β conditional on dataset Z can be estimated as [19] where f(Z, β) is the joint probability distribution of Z and β, f(Z | β) is the likelihood of the conditional function based on β, and π(β) is the prior distribution of β. Due to lack of information on the random parameters, we used the noninformative prior distributions [1]: where 0 k is a vector of zeros and M k is the k × k identity matrix. e posterior joint distribution can be derived as [42] f

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 Figure 1, where k is the number of input variables, H is the number of hidden neurons, I is the number of output neurons (travel modes), . , y I ] T is the output, and w hi is the connection weight of the h th hidden layer neuron to the i th output layer neuron. A Gaussian function is generally used as the hidden layer excitation function. e output of the h th hidden layer neuron is and the linear mapping relationship between G h (x) and the i th output layer neuron is where c h and σ h are, respectively, the center vector of the Gaussian function and the base width of the h th 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][45][46], which measures the relative importance of each independent variable in predicting dependent variables.

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 Figure 2) [47]. e hyperbolic tangent function is selected as the activation function of MLP hidden neurons. e output from a hidden neuron is and the connection weight is the output of the net function, where k is the number of inputs, x p is the input, w p is the weight of the corresponding input (w p ; 1 ≤ p ≤ k), b is the bias weight, and the Levenberg-Marquardt training algorithm is selected [28].

Model Comparison and Validation.
e multiclassification confusion matrix (see Table 1) is used to calculate the accuracy of each model [48], where s im is the number of samples in which mode i is predicted as mode m.
e recall and precision of mode i are and the accuracy of the model can be calculated as [1] accuracy � I i�1 S ii N . (11) e 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].

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. e 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][39][40][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. rough 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. Tables 2 and 3 describe the categories and continuous variables for imbalanced and rebalanced data, respectively.

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. Table 4 presents the estimated means of variables from the BMNL model, and Tables 5-7 show their parameter estimates. e frequently used train was considered as the reference in the model. e 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. e 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. e signs of variables were found to be consistent between balanced and imbalanced data. Table 8 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. e 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. Figures 3 and 4 show the relative importance of the factors obtained by RBF and MLP, respectively. ere 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.

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. e confusion matrix of the four models using imbalanced data is shown in Table 12. rough 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%).
e ROC curves of the four models are shown in Figures 5 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). e 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. ese findings confirm that the MLP model outperforms BMNL and MNL, followed by RBF.
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. e AUC of MLP for HSR is also the largest, followed by BMNL, MNL, and RBF. e 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. e 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.

Model Performance for Rebalanced
e 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.

Journal of Advanced Transportation
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. e 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.
e 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.

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 Table 4 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. is finding is consistent with a previous study [2], which revealed that women preferred using train more than men. e 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]. ese 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. is result agrees with the result of a study [4,7] that found that higher-and lower-income individuals favor air and bus travel, respectively. e variable of travel purpose had a significant positive effect on HSR choice and was ranked 11th in the relative importance of all variables. is 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. e modeling results also show the significant impact of travel distance on    intercity travel mode choice, which is third most important.
is 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. is 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. is 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.
is shows that a higher punctuality demand favors HSR and does not favor airplane and express bus. is 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. e 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.

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.
e 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. ese 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. e influence of individual characteristics on intercity travel mode choices was relatively low, and monthly income was the most important factor among individual characteristics. ese 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. rough 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. is can provide a basis for data analysts to fully understand the impact of data structures on the predictive performance of models.
ere are some limitations to this study. e results may only apply to the selected dataset and therefore must be verified using datasets from more cities. e 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.

Data Availability
e data used to support the findings of this study are available from the corresponding author upon request.

Conflicts of Interest
e authors declare that they have no conflicts of interest.