Work Travel and Decision Probling in the Network Marketing World

Transcription

1 TRB Paper No WORK TRAVEL MODE CHOICE MODELING USING DATA MINING: DECISION TREES AND NEURAL NETWORKS Chi Xie Research Assistant Departent of Civil and Environental Engineering University of Massachusetts, Aherst 141 Marston Hall Aherst, MA Phone: (413) E-ail: Jinyang Lu Research Assistant Departent of Civil and Environental Engineering University of Massachusetts, Aherst 141 Marston Hall Aherst, MA Phone: (413) E-ail: Eily Parkany Assistant Professor Departent of Civil and Environental Engineering Villanova University 800 Lancaster Avenue Villanova, PA Phone: (610) Fax: (610) E-ail: Text: 5,600 words Tables and Figures: 8 Total Length: 7,600 words Subitted for presentation at the 82nd Transportation Research Board Annual Meeting, January 12-16, 2003, Washington, D.C. and publication in the Transportation Research Record

2 1 Work Travel Mode Choice Modeling Using Data Mining: Decision Trees and Neural Networks Chi Xie, Jinyang Lu and Eily Parkany ABSTRACT Travel ode choice odeling has received the ost attention aong discrete choice probles in travel behavior literature. Most traditional ode choice odels are based on the principle of rando utility axiization derived fro econoetric theory. Alternatively, ode choice odeling can be regarded as a pattern recognition proble in which ultiple huan behavior patterns reflected fro explanatory variables deterine the choices between alternatives or classes. This paper investigates the capability and perforance on work travel ode choice odeling of two eerging pattern-recognition data ining ethods: decision trees (DT) and neural networks (NN). Models based on these two techniques are specified, estiated, and coparatively evaluated with a traditional ultinoial logit (MNL) odel. For coparison, the paper presents a unique three-layer forulation of the MNL odel, and identifies the siilarities and differences of the odels echaniss and structures, coparing the in the odel specifications and estiations. Two perforance easures, individual prediction rate and aggregate prediction rate, respectively representing the prediction accuracies on individual and ode aggregate levels, are applied for evaluating and coparing the perforance of the odels. Diary datasets fro the San Francisco Bay Area Travel Survey (BATS) 2000 are used for odel estiation and evaluation. The prediction results show that the two data ining odels offer coparable but slightly better perforance than the MNL odel in ters of the odeling results, while the DT odel deonstrates highest estiation efficiency and ost explicit interpretability and the NN odel gives a superior prediction perforance in ost cases. Keywords: travel behavior, ode choice odeling, data ining, decision trees, neural networks, ultinoial logit odel

3 2 INTRODUCTION Discrete choice odeling of travel behavior can help estiate the proportion of copetitive, utually exclusive alternatives and hence the resulting travel deand and teporal distribution across different travel and activity patterns. The disaggregate choices, e.g., destination, ode, departure tie, or route choice, constitute iportant coponents in the fraework of activitybased travel deand and duration odeling. The choice preference and echaniss for the foundation of travel and activity patterns in the context of activity generation and scheduling. Travel ode choice has received the ost attention aong discrete choice probles in travel behavior literature. Mode choice odeling and prediction relate closely to transportation syste policies and travel deand control and congestion itigation strategies. Most ode choice odels are based on the principle of rando utility axiization derived fro econoetric theory. Since the ultinoial logit (MNL) odel (1) was developed in the 1970s, the paraetric odel faily including different logit odels with different structures and coponents has becoe the ost widely used tool for ode choice analysis. However, any of these odels suffer fro the property of independence of irrelevant alternatives (IIA), which iplies that the effects of attributes of an alternative are copensatory and result in biased estiates and incorrect predictions in cases that violate the IIA property (2), although significant iproveents on eliinating the IIA property have been ade. Their pre-deterined structures ay often isestiate or ignore partial relationships between explanatory variables and alternative choices for specific subgroups in a population. The linear property and synergy effects of the utility functions ay not adequately odel the coprehensive and coplex correlations aong explanatory variables and between the and dependent variables. Recently, coputational process odels have triggered the interests of travel behavior researchers for discrete choice odeling (see (3)). These algoriths odel choice behavior without aking paraetric functional for assuptions or with seiparaetric assuptions. Bayesian techniques are applied to discrete choice analysis because they provide a principal approach for incorporating non-saple prior inforation and they avoid asyptotic approxiations. Different fro classic logit odels, Bayesian discrete choice odels treat paraeters as rando variables; thus Bayesian inference conditions depend on the observed data. Consequently, Bayesian ethods have been incorporated into conditional and nested logit odels (4, 5) and a ultinoial probit odel (3). Fro another perspective, discrete choice odeling acts as a pattern recognition proble in which ultiple coplex patterns fored by the cobination and interaction of explanatory variables deterine the choice decisions aong alternatives or classes. Many pattern recognition algoriths in the data ining field have been developed to discover the coplicated relationships between input variables and output targets, which are difficult to identify by atheatical or statistical ethods. Data ining odels have ore flexible structures to represent the relationship between the attributes of alternatives and choices than traditional logitbased odels. As supervised learning systes, they can learn and identify pattern characteristics extracted fro saple data and for adaptive structures through the coputational process. Thus, they potentially offer insights into the relationships that rando utility odels cannot recognize. Several recent studies of applying data ining techniques, e.g., decision trees (6-8) and neural networks (9-11), to discrete choice behavior analysis deonstrate the considerable benefits on prediction perforance of discrete choice behavior odeling.

4 3 This paper investigates the capability and perforance on work travel ode choice odeling of two widely used data ining ethods: decision trees (DT) and neural networks (NN). Models based on these two ethods will be specified, estiated and coparatively evaluated with a MNL odel. No published work has copared the three odels. For coparison, the MNL odel is forulated as a unique three-layer structure. The data for estiating and evaluating the odels are the diary datasets fro the San Francisco Bay Area Travel Survey (BATS) DATA MINING Data ining, the exploration and analysis of large quantities of data in order to discover and establish eaningful patterns and rules (12), includes any ethods or algoriths to reveal and represent the conditions and echaniss underlying various interrelated decisions leading to observed and unobserved coplex huan behavior patterns. Two very coon data ining techniques for classification, i.e., tree induction and neural induction, or the so-called decision trees and neural networks, are introduced below before their applications, along with their potential benefits for discrete choice odeling. Both techniques are based on supervised learning, the process of autoatically creating a classification odel fro a set of observations or cases. The induced odels consist of visible or hidden patterns, essentially generalizations over cases, which are useful for distinguishing the classes. Once a odel is induced, it can help predict the class of other unclassified cases. Supervised induction techniques offer several advantages over traditional statistics-based odels (e.g., the faily of logit odels) in discrete choice odeling: 1) no specific odel structure need be specified in advance and no IIA property is assued, thus reducing the incopatibility between odel structure and explanatory data; 2) they have the capability of odeling non-linear systes (12), which represent ore coplex relationships involved in huan behavior; and 3) the induced patterns can be extracted fro a subgroup of observations with hoogeneity while statistics-based odels check only for conditions that hold across an entire population of observations in the training dataset. Decision Trees Decision trees are a type of rule-based tools. The attractiveness of decision tree-based odels rests on the fact that decision trees represent intuitive rules. Decision trees are drawn with the root at the top and the leaves at the botto. An observation enters the tree at the root node, where a test driven by a trained algorith deterines which branch node the observation will encounter next. This process repeats until the observation arrives at a leaf node. Different leaves ay ake the sae choice, but each leaf akes that choice for a particular reason. The tests are chosen to best discriinate aong target choices. Each path fro the root to a leaf represents a decision rule. The ost coonly used decision tree algoriths include 2 χ autoatic interaction detection (CHAID) (13), classification and regression trees (CART) (14), and C4.5 algorith (15). C4.5 algorith is gaining ore popularity. Copared to the first two decision tree algoriths, C4.5 can produce trees with varying nubers of branches at each node (over CART algorith) and deal with both continuous and discrete variables (over CHAID algorith). This study uses C4.5 for constructing the decision tree (DT) odel.

5 4 Neural Networks Artificial neural networks are inforation processing structures consisting of basic units designed to odel the behavior of huan neurons. Like the physical architecture of the brain, they are coposed of a nuber of parallel, distributed and interconnected neurons or processing eleents (PEs) to produce linear or nonlinear apping between input and output variables (16, 17). Neural networks have been widely applied to transportation probles including driver behavior odeling, autoated driving, vehicle detection, paveent aintenance, traffic pattern recognition, and vehicle scheduling and routing (18-20). For discrete choice odeling, neural networks use pattern association and error correction as the underlying echaniss to represent a proble or relationship, as copared to the rando utility axiization rule used in the logit odels. Neural networks operate as a siple process. A unit or neuron cobines its inputs into a single output value, a process called the unit s activation function. An activation function has two parts: cobination function, which erges all the inputs into a single value; and transfer function, which transfers the value of the cobination function to the output of the unit. A network can contain units with different transfer functions serving different operations. A coon neural network structure used for classification is the topology, or architecture, called ulti-layer feedforward neural networks (MLF). The priary advantage of this type of neural network is its ability to solve non-linear ulti-diensional pattern recognition and classification probles (17). We apply an MLF-type neural network (NN) odel to the work-trip ode choice proble in this study. DATA The Database The data used for ipleenting the data ining odels coe fro the San Francisco Bay Area Travel Survey (BATS) 2000, conducted by MORPACE International, Inc. coissioned by the Bay Area Metropolitan Transportation Coission and Bay Area Rapid Transit (BART). Fro nine counties in the Bay Area, a total of 15,064 residences containing 34,680 respondents were randoly sapled. Each respondent provided a two-day travel diary in the database, and detailed individual and household socio-deographic data. The whole database consists of four interrelated datasets respectively reflecting household, person, trip, and vehicle characteristics. The first three datasets were erged to for the database used in this study. This study ephasizes the work trip or trip-to-work ode choice, i.e., the priary trip in a hoe-to-work activity chain prior to a work activity, in which we assue the longest travel trip in the chain is the work trip. Other activities, such as the ode access trip (e.g., walking to a bus stop or a train station), or ode change activity, (e.g., switching between transit odes), does not belong to the defined work trip and hence is excluded in this study. The alternatives for work travel ode choice used in this study include SOV (car, van, otorcycle and oped), carpool (carpooling and vanpooling), transit (bus, train and ferry), bicycle, and walk. These five odes were identified as the five ain coute odes in the Bay Area (see RIDES (21)). The travel deand odeling for each ode has a considerable or potentially considerable influence on transportation infrastructure investent decision and travel deand control and anageent policyaking in this area. Although transit and bicycle capture relatively less arket share (approxiately 1% each) of the work trips, neither should be ignored.

6 5 Furtherore, the total database was split randoly into two datasets with the sae nuber of observations: one for the odel estiation and another for the subsequent validation test. The actual ode split proportions in the total database as well as the training and test datasets are shown in Table 1. Explanatory Variables Two sets of explanatory variables, as seen in Table 2, were identified for work travel ode choice odeling: 1) individual/household socio-deographic attributes, which include hhsize, hhbicyc, hhcycle, tenure, dwelltyp, gender, relation, age, licdrive, epstatus, eptype, hhincoe and hhveh; and 2) trip level-of-service attributes, which include saptype, traveltie, peak, and opcost. For the variables dwelltyp, relation, epstatus and eptype, a certain value of a variable ay be associated with few observations, which are thus ignored. The variable hhincoe was coded using the nubers fro 1 to 15, indicating low to high incoe level. The variable startie was initially recorded as inutes elapsed fro the starting oent of 3:00 a. Considering trips in the peak and off-peak periods have different ipacts on ode choice behavior, for convenience and siplicity, startie was transfored to be a duy variable called peak that equals 1 if the observation is a peak hour trip, and 0 if an off-peak hour trip. The peak hours included: 7:00-9:00 a and 4:00-6:00 p, according to the Metropolitan Transportation Coission (22), while trips starting in other periods are considered off-peak. The variable traveltie was readily calculated as endtie inus startie. Finally, the variable opcost expresses the su of all visible out-of-pocket costs, including transit fare and vehicle parking fee. DATA MINING IMPLEMENTATION This section focuses on the specification and estiation of the decision tree (DT) odel and neural network (NN) odel. The perforance easures and balance weight are explained prior to the odel developent. Perforance Measures Mode choice odeling predicts travelers ode choice decisions and hence induced travel deand for each ode or deand distribution across odes. Two types of prediction rates or atch rates are defined and used to evaluate and copare the ode choice odeling perforance of the data ining odels. They respectively reflect the odeling perforance on individual and aggregate levels. Individual atch rate ( r i ), or hit ratio, is the ratio of the nuber of correctly predicted individual observations for one ode ( N pi ) over the total nuber of the actual observations choosing this ode ( N ), expressed as, a a N pi r i = (1) N Aggregate atch rate ( a r ) reflects the prediction accuracy on the ode aggregate level, defined as the ratio of the nuber of predicted observations (including correctly and incorrectly

7 6 predicted observations) for one ode ( N pa ) over the nuber of the actual observations choosing the ode ( N ). Its siilar functional for is, a a N pa r a = (2) N In ode choice odeling, we generally are ore concerned about the prediction of aggregate choice distribution for each ode, than that of individual choice. The forer reflects the odeling perforance on the acroscopic level while the latter the icroscopic level. The iproveent on the aggregate atch rate in travel deand applications ay be ore eaningful than that of the individual atch rate (6), although the latter reflects the actual prediction accuracy. In this study, the individual and aggregate atch rates are both used as the perforance easures. The individual atch rate is always less than 1 while the aggregate atch rate ay be greater than 1 or less than 1, with the individual atch rate always no ore than the aggregate atch rate. Although the expected best values of both are 1, their iplications for prediction accuracy ay not be the sae when they are equal to 1. Balance Weight In all discrete choice odeling there exists a non-negligible proble in training or calibration caused by the data induction property in a single odel structure: the odel tends to readily recognize classes with ore observations in the training dataset but neglect other classes with less (e.g., in Table 1, the percentage of the observations of the SOV ode approaches 80% while that of the transit ode is approxiately 1%). The huge discrepancy in the nuber of observations of the different classes akes the odel structure and paraeters overwhelingly adaptive to distinguish the patterns induced by the SOV observations, and therefore the odel ay fail in the prediction for the transit odes, because the only estiation objective of the data ining odels is to axiize the individual atch rate (approaching 1). This is reflected by the expected results that the odel ay have the best prediction perforance on the SOV ode but perfors worse on the other classes (i.e., erroneously classifies the other odes as the SOV ode). In a recent study using the C4 and CHAID algoriths to predict ode choice the results indicated that the two data ining odels underfitted non-sov odes (see (6)). In order to balance classification perforance aong odes (and also balance the optiization of the individual and aggregate atch rates), a variable tered balance weight is introduced in the estiation of the odels. Applying balance weight iproves the aggregate atch rate of the odels. It has the functional for, N w ax = N = N { N } ax α = 1,...,5 0 α 1 (3) w is the balance weight, applied on ode by repeating its observations w ties in where the training, and N and N ax represent the nuber of observations of the ode and of the

8 7 ode with the axiu observations in the training dataset, respectively. The coefficient α deterines the scale of the weight. When α = 0, then w = 1, and thus the proportion of observations of ode alternatives stays original. On the other end, when α = 1, w = N ax N, and w is the frequency weight. By applying frequency weights, each ode has exactly the sae proportion of observations in the training data. By iposing a frequency weight uch greater than 1 on infrequently chosen odes, their attributes would be recognized by the odel ultiple ties (i.e., w ties) in the training. Consequently, the odel ay overfit these odes. Therefore, the critical α value should fall between 0 and 1, calibrated to best atch the actual ode split or achieve an optial balance of proportions aong the ode alternatives. The balance weight can be deterined when the estiation objective of the aggregate atch rate is epirically realized as, in 5 = 1 N a N N a p = 1,...,5 (4) where N a and N p denote the nuber of actual and predicted observations of ode, respectively. Such a balance weight is applied to the estiation of the DT, NN, and MNL odels copared here. The deterination of balance weight is based on the assuption that each observation under different odes has the sae iportance or the involved cost of an observation under different odes is equal. However, this ay be not true in the real world. The resulting average social and operational cost, apparently, differs for any individual choosing different travel odes for the sae trip (i.e., the trip with the sae route, destination and departure tie). For exaple, the cost for one to choose a SOV ode should be uch higher than that for a transit ode because the forer causes uch ore infrastructure investent and aintenance activities, vehicle cost, consued fuel, eitted pollution, congestion, participation degree of the traveler and others. Consequently, the cost of one traveler switching fro one ode to another also differs. When we consider using balance weight to adjust the proportions of the observations in the training data, it is reasonable and necessary to incorporate a cost coefficient for each ode prior to the estiation of the balance weight so as to reasonably odel the variations fro the actual ode splits. It is a great challenge to estiate the average individual social and operational cost on a reasonable and acceptable level for each ode and incorporate it into the ode choice odeling. Decision Tree Model The DT odel applied for ode choice odeling in this study is based on the C4.5 algorith (15). As a supervised learning algorith, C4.5 uses recursive partitioning to for a tree structure with if-then rules (each of which is applied with an explanatory variable) as splitting criteria. Each branch on different levels of the tree represents a subgroup of observations with hoogeneity of different degrees. Hoogeneity increases fro top to botto where the botto leaves contain the cases with the sae ode choice while the top branches offer the roughest split. Each branch fro the top node to a botto leaf node can be described as an if-then rule sequence or ruleset.

9 8 The C4.5 algorith generates a DT odel in two phases: construction and pruning. The construction of a DT odel follows these principles. Fro top to botto of a decision tree, a training data group is divided at each stage of subdivision (i.e., node) according to an explanatory variable selected based on the splitting criterion. The division continues until all observations in a subgroup have the sae ode choice at the botto. The splitting criterion used in C4.5 is the so-called inforation gain ratio based on inforation theory. The detailed procedure to generate the gain ratio can be referred to in (15) and (6-8). The generated C4.5 decision tree often becoes too coplex, overfitting the training data when another hypothesis that perfors less well on the training data actually perfors better on the test data (6). A pruning strategy helps avoid overfitting based on the expected error rate. C4.5 prunes the decision tree using a pessiistic pruning ethod: the error rate at each leaf is exained based on the assuption that the true error rate will be substantially worse. For a given confidence level, C4.5 gives the confidence interval, which is the range of expected error rates. C4.5 assues that the observed error rate on the training data arks the low end of this range and substitutes the high end to get a leaf s predicted error rate on the test data. Out towards the few observation leaves, substituting this pessiistic error rate for the observed one often causes the error rate of a whole subtree to be higher than that of one of the nodes above it, in which case it gets pruned. In the pruning process, a question arises: how to deterine a confidence level (or confidence interval) for the pessiistic pruning, or, what is an acceptable tree size of the trained DT odel with sufficient prediction accuracy after pruning? We exaine the relationship of prediction error rate and decision tree size through epirical analysis. We obtain little iproveent on prediction accuracy when the tree size increases to a certain value (50 leaves in this study), aking this threshold an appropriate place to prune. It represents a critical point for the balance between siple and readable tree structure and high prediction accuracy. According to the epirically deterined optial tree size, we estiate the DT odel for ode choice. The best DT odel has 50 leaves and the total classification error rate (i.e., total individual erroneous atch rate) is 21.0%. The detailed tree structure appears in Figure 1. Each leaf with its paraeters represents one if-then decision rule. On each leaf the nuber of observations ( n ) apped by the odel and the nuber of observations erroneously classified ( ) are presented as n. The priary leaves with relatively high individual atch rate ( ( n ) n ) for each ode alternative are underlined and followed by their atch rate. Clearly, a nuber of decision rules are generated for the choice of the SOV ode and they involve a variety of attributes; oreover, these rules provide quite high prediction rates ranging fro 80% to 100%. Two priary if-then rules for the carpool ode are identified, which iply these conditions: 1) a traveler with a bicycle and no license or ability to drive, with 3 vehicles or less in the household, would take a zero-out-of-pocket-cost trip in peak hours with travel tie of ore than 7 inutes (as an exaple, this branch is highlighted with bold-italic text in Figure 1); and 2) a traveler without a license but with one or ore bicycles, older than 32 years, with 3 vehicles or fewer in the household, also with a zero-out-of-pocket-cost trip with travel tie of ore than 7 inutes. There is only one decision rule for taking the transit ode: one would take a bus or train if the charged out-of-pocket oney is no ore than $4. This rule akes sense to us in that only transit users and parkers report non-zero-out-of-pocket costs. Since ost parking fees exceed $4, this is a good threshold for identifying transit users. For the bicycle ode, no successful rule with an acceptable atch rate appears in the generated decision tree. The DT

10 9 odel cannot identify underlying patterns for the bicycle ode, possibly due to the very liited observations of the bicycle ode in the training dataset. Finally, four priary leaves or rules with significant atch rate for the walk ode also appear. The involved explanatory variables identified for the walk ode include the nuber of vehicles and bicycles in household, household incoe, age, possession of a driver s license, travel tie and out-of-pocket cost. Please refer to the tree structure in Figure 1 for details. In the DT odel tree structure, variables lying on different hierarchies indicate different effective scopes of ipact on ode choice, and hence different ipacted nubers of ode choice decisions. For exaple, the variable out-of-pocket cost occupies the tree top, thus ipacting all ode choices. A variable existing only on the botto, such as gender, has relatively liited influence on travel ode decisions. Soe explanatory variables, such as dwelling type, residential tenure type, household size, eployent type and sapling type (i.e., urban or suburban sapling), are winnowed in the tree structure because the odel recognizes their weak ipacts on travelers ode choice decisions. As a result, the ost iportant variables identified by the DT odel for the work travel ode choice include trip out-of-pocket cost, household vehicle nubers, household incoe, possession of a driver s license, traveler s age, and travel tie. Neural Network Model Neural network odeling does not require an algorith to copute a specific output for a preset functional for (18). Nonlinear transfer functions and the autonoous identification of inforation contained in input patterns of a neural network enable ode choice estiation. The NN odel with a MLF (ulti-layer feedforward) topology or architecture used in this study consists of PEs (processing eleents) arranged in three layers: the input layer, the hidden layer, and the output layer, as shown in Figure 2. Interconnected PEs in adjacent layers have connection weights w i, j and v j,. When an input vector (or an observation) is presented to the network, each input eleent (or an explanatory variable) is ultiplied by an appropriate weight and connected to all the PEs on the hidden layer. This procedure is realized through a transfer function f ( x) and produces an output value h j on the hidden layer, expressed atheatically as, h n = f wi i= 1 o + b h j, j i j j = 1,..., p (5) where o i represents the ith explanatory variable, the bias value of the j th PE in the hidden layer, b, adjusts the agnitude of the output, and ( x) h j f is a sigoid (or logistic) function that is failiar to transportation researchers fro trip deand analysis and other travel behavior studies (23). The sigoid function, f ( x) x 1 = 1 + e (6)

11 10 is repeated between the hidden layer and output layer, which can be expressed in siilar functional for as, p p = f v j= 1 + o j, h j b = 1,...,5 (7) where p and o b indicate the k th output eleent and bias value on the output layer. The input vector o i coprises 17 explanatory variables ( n ) (23 if duy variables are included) as input eleents. Each input vector represents an observation. The nuber of PEs ( p ) were decided on the hidden layer, in ters of the best classification result fro a series of experients with p on this layer ranging fro 6 to 45; the output layer gives nuerical ode choice results where the output eleent that produces the axiu value is transfored to 1 and others to 0. Each output vector fits into one of the five ode choices, where the output vector [ ] T corresponds to the SOV ode, and [ ] T, [ ] T, [ ] T and [ ] T 0 denote the other four odes, respectively. The NN odel ay be trained through presenting a set of input-target pairs to the network and updating the network paraeters in ters of the coonly used backpropagation algorith (16, 17), which seeks to ipleent a gradient descent of an error function of the network s output (see (24) for the detailed procedure). For each input vector, the output produced by the network is copared with the target vector, to adjust the weights (i.e., w i, j and v j, ) and biases (i.e., h b j and o b ) in the gradient descent direction of the output error surface until the agnitude of output error becoes acceptable. During the training, an adaptive learning rate and a oentu rate (0.7 in this study) are eployed for faster training while keeping learning stable. The initial learning rate was set as A total of 640 training sessions (for 40 different nubers of PEs, i.e., 6-45 PEs, on the hidden layer and 4 different transfer functions on the hidden and output layers) used the sae training dataset to seek the optial configuration of the NN odel structure and paraeters. The training dataset was grouped into two parts: 80% for paraeter adjustent and 20% for cross validation. The training session lasted for a axiu of 5,000 epochs, with each epoch equivalent to one presentation of all of the input vectors in rando order. At the end of each epoch, the trained network is tested on the validation dataset to deterine whether the updated paraeters are saved or discarded. The training results indicate that, as aforeentioned, 33 PEs are identified on the hidden layer and the sigoid transfer function is applied on both the hidden and output layer. The prediction results fro applying the estiated NN odel on the sae dataset show that the NN odel can provide 78.3% individual atch rate (i.e., 1,587 out of 2,373 are correct hits) for the total of five ode choices. High individual atch rate occurs not only for the SOV ode, but also for the odes of transit (100.0% atch rate), bicycle (97.5%) and walk (92.6%). For the carpool ode, however, a relatively low individual atch rate (59.9%) is realized. The NN odel provides aggregate atch rates of 90.9%, 102.7%, 234.8%, 277.5%, and 151.6% for the SOV, carpool, transit, bicycle, and walk odes respectively, which shows a coparable ode choice odeling capability to the DT odel on the aggregate level. Overall, it can be suggested

12 11 that the NN odel has a ore robust perforance on travel ode choice prediction copared to the DT odel in the odel estiation stage. Sensitivity analysis enables neural networks to explain which inputs are ore iportant than others. This analysis can be perfored inside the network, using the errors generated fro backpropagation, or externally, by poking the network with specific inputs (12). In this study, the latter ethod exaines the iportance of the explanatory variables using the predeterined subgroups of observations, one of which contains only observations with the single value of one variable (here, the continuous variables are discretized into the ordered categorical variables) and one type of travel ode. The exaination results prove that the ost significant variables across the odes include household size, household vehicle nuber, gender, possession of a driver s license, travel tie, tie-of-day, and out-of-pocket cost. EVALUATION The sae test dataset derived fro our database is applied to exaine the perforance of the two developed data ining odels and copare the with a traditionally used ultinoial logit (MNL) odel. Result Analysis Confusion (or isclassification) atrices easure the effectiveness of the discrete ode choice odels. Tables 3a and 3b present confusion atrices induced by the DT and NN odels for both the training and test datasets. In a confusion atrix, each row represents the actual observations of each ode while each colun denotes the predicted observations. The su on each row or colun represents the actual or predicted nuber of observations for each ode. The row head shares the sae order of ode alternatives with the colun head. Thus, the diagonal cells give the atch nuber between reality and prediction and non-diagonals provide the erroneous classification. The atch rate for each ode appears in the table as the index of prediction perforance. Overall, the NN odel outperfors the DT odel on both the training and test datasets when coparing of the individual prediction rates (i.e., the DT odel has 79.0% and 76.8% atch rates in the training and test while the NN odel has 83.6% and 78.2% respectively). The isclassification results reflect that the two odels present the sae prediction characteristics. For exaple, they both offer high prediction accuracy for the SOV ode in either the training or the test. Neither easily distinguishes the SOV and carpool odes in that any observations under these two odes are utually isclassified. This phenoenon indicates that the SOV and carpool odes, which share physical, technical, and socio-econoical attributes, exhibit ore hoogeneity within the explanatory variables than the other odes, which inevitably leads to the classification difficulty between the. Both odels yield a high individual atch rate for the transit ode under a large nuber of conditions (i.e., 3 out of 4) where ost of the observations choosing the transit ode are not isclassified as the other odes. In the confusion atrices of the DT odel, the nuber of observations of the transit ode choice is estiated very well but the bicycle ode is underestiated heavily, although they both have fewer observations in the whole database. A large part of the isclassified observations of the bicycle ode go to the carpool ode, which ay iply soe unobserved siilar preferences between carpooling passengers and bicycle users. Fro the sae perspective, the transit ode is unique sharing few attributes or travelers preferences with other odes.

13 12 Copared to the DT odel, the NN odel shows worse transferability in that the atch rates for both the total or single ode decrease considerably with varying degrees fro the training to the test, especially to the transit, bicycle, and walk odes. The NN odel ight overfit the training data on these odes, or ight not identify coplete data patterns. Underestiation ay be caused by insufficient observations under these odes. We conclude that both data ining odels ade acceptable predictions of the ode choice distribution on the aggregate level. Both odels show siilar aggregate prediction patterns, providing a relatively accurate aggregate prediction rate for the SOV and carpool odes, but both overestiate the aggregate nubers of observations of the transit, bicycle and walk ode. Coparison with a Multinoial Logit (MNL) Model An MNL odel developed as a benchark to evaluate the perforance of the two developed data ining odels can be expressed using a siilar structure to the MLF-type NN odel, as illustrated in Figure 3. The diagra and forulation below are unique to this paper. The MNL odel has three layers: the input layer, the utility layer and the output layer. The input layer s input eleents are the explanatory variables (including the duy variables). The utility layer (coparable to the hidden layer of the MLF-type NN odel) contains 5 nodes corresponding to the utilities of the 5 travel odes. The transfer function on the utility layer has the following functional for, h n = f wi, oi + b (8) = 1 where o i represents the ith explanatory variable, i variable in the utility function of the ode (coparable to the connection weight h the ode specific constant (coparable to the bias value b j ), and ( x) x (different fro the sigoid function) to the ode utility x, ( ) function on the output nodes has the atheatical expression, w, the coefficient of the ith explanatory w i, j ), b f an exponential operation f x = e. Then, the likelihood p = 5 h = 1 h (9) as distinct fro the sigoid transfer function on the output odes in the NN odel. The connection weights and biases between the utility layer and the output layer are 1 and 0, respectively. The output layer gives the probabilities of each ode choice where the node with the axiu probability is assigned as 1 (selected) and others nodes are assigned as 0 (discarded), sae as the NN odel. Furtherore, two priary discrepancies exist between the NN and MNL odels: 1) estiation ethod; and 2) interpretability. The NN odel is estiated using the standard backpropagation algorith while the MNL odel takes the axiu likelihood ethod for estiation. In the MNL odel, the agnitude and sign of the coefficients indicate the iportance and ipact of the corresponding variables on ode choices and the values of the Z-

14 13 statistic or t-statistic tests indicate their confidence level. Coparatively, the NN odel shows weak interpretability, although the iportance of explanatory variables can be identified through sensitivity analysis. We used the sae training dataset to estiate the MNL odel, expanding each observation to accoodate the duy variables for the incorporation of all values of the categorical variables. The SOV ode is arbitrarily used as the base alternative. The base utilities of the other odes relative to this base ode are represented by alternative specific constants. Fro the estiation results, the ost significant variables to influence a traveler s ode choice decision identified by the MNL odel include: household size, household incoe, household vehicle nuber, license possession, travel tie, trip tie-of-day and out-of-pocket cost. These variables approxiately atch the iportant variables induced by the DT or NN odels. An overall perforance coparison was conducted based on the prediction results of the three odels tested on the validation dataset. Figure 4 shows the correctly predicted individual and aggregate observations of the three odels by each travel ode, in which the actual nubers of observations for each ode are also labeled. The three odels show coparable prediction perforances. None of the can give a best prediction rate for each ode on individual level or aggregate level. On the individual prediction level (see Figure 4a), the NN odel (88.0%) shows a best overall perforance over the other two odels (86.0% and 86.7% for the DT and MNL odel) in the prediction of the SOV ode. The MNL odel perfors worst in the prediction for the carpool ode, underestiating ost of the carpool observations. Hence, the MNL odel (72.9%) is worse than the DT and NN odels (76.8% and 78.2%) on the overall individual prediction perforance. The two data ining odels show the very close prediction results for each ode (the difference is less than 3%). On the aggregate prediction level (see Figure 4b), the three odels all deonstrated satisfactory accuracy and powerful practicability. The MNL odel shows the best prediction capability on the SOV ode (101.4%), but perfors worst on the aggregate prediction for the carpool ode. The NN odel outperfors on the prediction for carpool, bicycle and walk odes and shows close perforances to the best prediction results for the SOV and transit odes. In ost cases, the NN odel proves to be the best or nearly best odel on the aggregate ode choice prediction level. CONCLUSIONS The perforance of ode choice odeling rests on two aspects: data preparation and odel developent and estiation. Data preparation includes data collection and sapling, dependent and explanatory variable identification, data extraction and deduction, and data discretization and transforation. This paper focuses on the second aspect: investigating the feasibility of applying the eerging data ining techniques to travel ode choice behavior odeling. Two representative data ining odels, the decision tree (DT) odel and neural network (NN) odel, were developed and coparatively evaluated with a widely used ultinoial logit (MNL) odel. Both data ining odels show high flexibility and adaptability of the odel structure or paraeters to the training data due to their data induction property. No IIA property needs to be assued so the copatibility between the odel structure and the observations is enhanced in the odel estiation and hence the prediction perforance can be iproved copared to the

15 14 MNL odel. Both odels, however, have difficulty estiating odes with insufficient observations in the database, for the odels are induced by the data to recognize the ode with the ost observations. Balance weight is introduced in the odel estiation to epirically aintain a balance of individual and aggregate prediction accuracies aong the odes. Two perforance easures, individual prediction rate and aggregate prediction rate, respectively representing the prediction accuracies on individual and ode aggregate levels, are used for the odel evaluation. Coparative evaluation shows that the two data ining odels have coparable but slightly better prediction capability than the MNL odel on work travel ode choice odeling. The prediction results based on the separate test dataset show, on both individual and aggregate levels, that the NN odel outperfors the other two odels. The ost significant explanatory variables identified by all the three odels include two sociodeographic attributes: household vehicle nuber and license possession, and two level-ofservice attributes: travel tie and out-of-pocket cost. The DT odel perfors with its structure flexibility to adapt to the training data, and has the capability to produce explainable if-then rules and identify the significance of explanatory variables for each ode. The DT odel induces an if-then ruleset using a sequence of explanatory attributes; however, it cannot capture the correlations aong attributes or aong rulesets. Decision trees have probles with processing continuous data; data have to first be grouped into ranges anually or autoatically by a software tool. The selection of the ranges ay unwittingly hide useful patterns. The DT odel ay suffer fro its estiation algorith: during the estiation, once the odel akes a decision about a variable on which to split the node, the decision cannot be revised or iproved, due to the absence of a backtracking technique, for which the NN odel akes provision (25). Another data ining odel, the NN odel with a MLF topology, has a siilar three-layer structure copared to the MNL odel with its new structure interpretation. The discrepancies on the nuber of iddle layer nodes, layer connection weights and biases, and transfer functions yield different perforance and interpretability. The NN odel ay be saddled with an interpretation proble. However, considering its superior prediction perforance, we believe that it has practice value rather than explainability. In soe applications, the NN odel perfors well with its expected high prediction rate when the travel deand aount of each ode is the only concern. In other applications, the DT odel is preferred when the ability of a odel to interpret the reason for a choice and to identify iportant variables for policyaking is crucial. The priary features and capabilities of the DT, NN and MNL odels in this study are suarized in coparative for in Table 4. ACKNOWLEDGEMENTS The authors would like to acknowledge Dr. Kenneth Vaughn and Mr. Chuck Purvis at the San Francisco-area Metropolitan Transportation Coission (MTC) for providing the BATS 2000 datasets and constructive suggestions for building the work-trip database. Dr. Ross Quinlan at University of New South Wales, Australia, helped clarify the See5/C5.0 progra. The authors also benefited fro the discussion on selection and construction of the neural network odel in e-ail exchanges with Mr. Fang Yuan at University of Tennessee. However, the contents of this paper reflect only the views of the authors, who are solely responsible for the facts and the accuracy of the data presented herein.

16 15 REFERENCES 1. McFadden, D. Conditional Logit Analysis of Qualitative Choice Behavior. Frontiers in Econoetrics, P. Zarebka, ed., Acadeic Press, New York, NY, Koppelan, F.S. and Wen, C.-H. Alternative Nested Logit Models: Structure, Properties and Estiation. Transportation Research Part B, Vol. 32, No. 5, 1998, pp Brownstone, D. Discrete Choice Modeling for Transportation. Travel Behavior Research: the Leading Edge, D.A. Hensher, ed., Pergaon, Asterda, the Netherlands, 2001, pp Koop, G. and Poirier, D.J. Bayesian Analysis of Logit Models Using Natural Conjugate Priors. Journal of Econoetrics, Vol. 56, No. 3, 1993, pp Poirier, D.J. A Bayesian Analysis of Nested Logit Models. Journal of Econoetrics, Vol. 75, No. 2, 1996, pp Wets, G., Vanhoof, K., Arentze, T. and Tierans, H. Identifying Decision Structures Underlying Activity Patterns: An Exploration of Data Mining Algoriths. In Transportation Research Record 1718, TRB, National Research Council, 2000, pp Thill, J.-C. and Wheeler, A. Tree Induction of Spatial Choice Behavior. In Transportation Research Record 1719, TRB, National Research Council, 2000, pp Yaaoto, T., Kitaura, R. and Fujii, J. Driver s Route Choice Behavior: Analysis by Data Mining Algoriths. In Transportation Research Record 1807, TRB, National Research Council, 2002, pp Yang, H., Kitaura, R., Jovanis, P.P., Vaugh, K.M. and Abdel-Aty, M.A. Exploration of Route Choice Behavior with Advanced Traveler Inforation Using Neural Network Concepts. Transportation, Vol. 20, No. 2, 1993, pp Hensher, D.A. and Ton, T.T. A Coparison of the Predictive Potential of Artificial Neural Networks and Nested Logit Models for Couter Mode Choice. Transportation Research Part E, Vol. 36, No. 3, 2000, pp Mohaadian, A. and Miller, E.J. Nested Logit Models and Artificial Neural Networks for Predicting Household Autoobile Choices: Coparison of Perforance. In Transportation Research Record 1807, TRB, National Research Council, 2002, pp Berry, M.J.A. and Linoff, G. Data Mining Techniques: For Marketing, Sales, and Custoer. John Wiley & Sons, Inc., New York, NY, Hartigan, J.A. Clustering Algoriths. John Wiley and Sons, Inc., New York, NY, Brieen, L., Friedan, J.H., Olshen, R.A. and Stone, C.J. Classification and Regression Trees. Wadsworth, Belont, CA, Quinlan, J.R. C4.5: Progras for Machine Learning. Morgan Kaufann Publishers, San Mateo, CA, Wasseran, P.D. Neural Coputing Theory and Practice. Van Nostrand Reinhold, New York, NY, Zurada, J.M. Introduction to Artificial Neural Systes. PWS Publishing, St. Paul, MN, 1992.

17 Faghri, A. and Hua, J. Evaluation of Artificial Neural Network Applications in Transportation Engineering. In Transportation Research Record 1358, TRB, National Research Council, 1991, pp Dougherty, M. A Review of Neural Networks Applied to Transport. Transportation Research Part C, Vol. 3, No. 4, 1995, Hagan, M.T., Deuth, H.B. and Beale, M. Neural Network Design. PWS Publishing, Boston, MA, RIDES. Coute Profile 2001: A Survey of San Francisco Bay Area Coute Patterns. RIDES for Bay Area Couters, Inc., Septeber Metropolitan Transportation Coission. Travel Forecasting Assuptions '98 Suary: 1998 Update of Regional Transportation Plan. assue98.ht. Accessed April Stephanedes, Y.J. and Liu, X. Artificial Neural Networks for Freeway Incident Detection. In Transportation Research Record 1494, TRB, National Research Council, 1994, pp Ruelhart, D.E., Hinton, G.E. and Willias, R.J. Learning Internal Representations by Error Propagation. Parallel and Distributed Processing, D.E. Ruelhart, J.L. McClelland and the PDP Research Group, eds., Vol. 1, MIT Press, Boston, 1986, pp Cabena, P., Hadjinian, P., Stadler, R., Verhees, J. and Zanasi, A. Discovering Data Mining: fro Concept to Ipleentation. Prentice-Hall, Inc., Upper Saddle River, NJ, 1998.

18 17 LIST OF TABLES TABLE 1 Suary of the Mode Splits in the Datasets TABLE 2 Explanatory Variables TABLE 3 Confusion Matrices Generated by the DT and NN Models TABLE 4 Suary of the Features and Capabilities of the DT, NN and MNL Models

19 18 TABLE 1 Suary of the Mode Splits in the Datasets Total Database Training Dataset Test Dataset Mode Nuber Per (%) Nuber Per (%) Nuber Per (%) SOV 3, , , Carpool Transit Bicycle Walk Su 4, , ,

20 19 TABLE 2 Explanatory Variables Variable/Label 1 Definition Values Socio-deographic attributes 1 DWELLTYP Dwelling type A single-faily detached house; Duplex or duet; Apartent; Condoiniu or townhouse 2 TENURE Residential tenure type Rent; Own 3 HHSIZE Household size Continuous 4 HHINCOME Household incoe 1: Below $10,000; 2: $10,000-15,000; 3: $15,000-20,000; 4: $20,000-25,000; 5: $25,000-30,000; 6: $30,000-35,000; 7: $35,000-40,000; 8: $40,000-45,000; 9: $45,000-50,000; 10: $50,000-60,000; 11: $60,000-75,000; 12: $75, ,000; 13: $100, ,000; 14: $125, ,000; 15: Above $150,000 5 HHVEH No. of vehicles in household Continuous 6 HHMCYCLE No. of otorcycles in household Continuous 7 HHBICYC No. of bicycles in household Continuous 8 AGE Age of traveler in years Continuous 9 GENDER Gender of traveler Male; Feale 10 RELATION Relation in household Husband/wife/partner; Unrelated adult/partner; Son/daughter; Father/other/fatherin-law/other-in-law 11 EMPSTATUS Work status Full-tie; Part-tie 12 EMPTYPE Type of eployent Private, for-profit copany; Private, not-for-profit copany; Governental agency; Self-eployed 13 LICDRIVE Licensed or capable of driving 1: Yes; 0: No Level-of-service attributes 14 SAMPTYPE Sapling type Urban; Suburban 15 TRAVELTIME Travel tie in inutes Continuous 16 PEAK Activity travel tie 1: Peak hour; 0: Off-peak hour 2 17 OPCOST 3 Out-of-pocket travel cost in $ Continuous 1 Explanatory variables with ultiple options such as DWELLTYP or RELATION are converted to duy variables for the MNL odel used in the odel coparison. 2 Peak hours are between 7:00 and 9:00 a and between 4:00 and 6:00 p. Please refer to Metropolitan Transportation Coission (22). 3 OPCOST (i.e., out-of-pocket cost) includes TRFARE (i.e., fare of public transportation for a trip) and PARKCOST (i.e., parking cost for a trip).