STRUCTURE OF PASSENGER TRAVEL DEMAND MODELS by MOSHE EMANUAL BEN-AKIVA B.Sc., Technion - Israel Institute of Technology (968) S.M., Massachusetts Institute of Technology (1971) Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the ‘Massachusetts Institute of Technology June, 1973 Signature of Author . . . Departuent of Civil Engineering, May 4: Certified by se. epee eee ee Thesis Supervisor Accepted bys. ss + tees eee Chairman, Departmental Comittee on Graduate Students of the Department of Civil Engineering . ( UN 29 1973ABSTRACT STRUCTURE OF PASSENGER TRAVEL DEMAND MODELS by MOSHE EMANUEL BEN-AKIVA Submitted to the Department of Civil Engineering on May 11, 1973 in partial fulfillment of the requirements for the degree of Doctor of Philosophy. This study 1s concerned with the structure of travel demand models. ‘Two alternative structures are defined: simultaneous and recursive, each based on # different hypothesis about the underlying travel decision making process. che wimultaneous structure is very general and does not Fequire any specific assumptions, The recursive-structire-represents a specific conditional decision structure, i.e., the traveller is assumed to decompose his trip decision into eeveral stages. Thus, it is argued that the simultaneous and the recursive structures represent, respectively, simultaneous and sequential decieion making proces: Theoretical reasoning indicates that the simultaneous structure is more sensible. Moreover, if a sequence assumption is accepted, there are several conceivable sequences, and generally there are no a priori reasons to justify a selection azong them. A simultaneous model, however, 1s very complex due to the large number of alternatives that a traveller is facing in making his trip decision. An empirical study is conducted to investigate the feasibility of @ simultaneous model and to appraise the sensitivity of predictions made by a travel demand model to the structure of the model. ‘The data set for the empirical study was dravn from a conventional urban trani portation study dat. Two choices included in a trip decision are considered: destina- tion choice and mode choice. With the same data set, three disaggregate Probabilistic models are estimated for the shopping trip purpose: one model with a simultaneous etructure, and two recursive models with the two possible sequences ‘The simultaneous model proved to be feasible in terms of the computational costs and the estimation results. The resulte of the recursive models showed that estimated model coefficients vary considerably with the different model structures Thus, it is recommended that the simultaneous model structure should be used. Thesis Supervisor: Marvin L. Manheim Title: Professor of Civil EngineeringACKNOWLEDGEMENTS During the course of this research I have benefitted from the assistance and contributions of many individuals. Profescor Marvin Manheim, my thesis supervisor, has contributed the most to the development of this study. His constant encouragement and keen insights were invaluable. Professors Richard de Neufville and Wayne Pecknold, the other members of my doctoral committee, provided many valuable ideas and suggestions. The assistance and advice I received from Robert McGillivray, from the Urban Institute, also contributed greatly to the development and the presentation of the ideas in this research. I would also like to thank my colleagues and friends at M.I.T., in particular, Earl Ruiter, Frank Koppelman, and Len Sherman, for their constant help along the way. Dan Brand, Gerald Kraft and Thomas Domencich,with whom I have discussed this research, aleo contributed many ideas through their previous work in the subject area of this research. Carcl Walb and Marianne Koppelman contributed greatly in preparing the final document. Metropolitan Washington Council of Governments ~ Department of Trani portation Planning, and R.H. Pratt Associates are acknowledged for supply- ing the data for the empirical analysis. Charles Manski was most helpful in providing the logit estimation program that was used in this study. This research was supported in part by a grant to M.I.T. from the Ministry of Transport of the State of Israel for transportation planningresearch, Early stagea of the research were supported in part by a Sloan Research Traineeship from M.I.T. Finally, I would like to express my gratitude to my wife, Hagit and our son, Ori, whose contributions, of a different nature, were at least as important.TABLE OF CONTENTS Page TITLE PACE Se ee ee ee ee ee ee ed ACKNOWLEDGEMENTS 2. ee ee ee ee ee TABLE OF CONTENTS 20... eee eee ee ee ee eS CHAPTER I: Introduction and Summary... 1. eee eee eB Purpose of the Study 8 Models for Policy Analysis 10 Disaggregate Models 13 Choice Theory 14 ‘The Multinomial Logit Model 16 The Travel Choices 16 The Alternative Structures cv) Alternative Models 20 ‘The Empirical Study 21 Conclusions 27 Outline of the Report 29 CHAPTER II: Nature of Travel Demand and Prediction Models. . . .31 for Transportation Planning Introduction 3L The Complexity of Travel Demand 32 ‘The Demand for Travel as a Derived Demand 36 Interaction Between Location and Transport 38 ‘The Importance of the Work Trip a1 Short Run vs. Long Run, Static ve. Dynamic 42 The Overall Structure of Prediction in 43 Transportation Planning Alternative Structures 47 The Structure of the Urban Transportation 52 Model System Modelling Considerations 56 Disaggregate Models 6h A Disaggregate Modelling Framework 67 ‘A Hierarchy of Choices 69 ‘The Travel Demand Function 7 The Behavioral Unit 79 The Alternatives 80 Supply Effects with Disaggregate Demand Models 85Page CHAPTER III: Consumer and Chéice Theorles........... 87 Overview 87 Consumer Theory 87 Probebilistic Choice Theory 7 Constant Utility Models 201 The Set of Alternatives 105 Random Utility Models 108 Summary 15 GHAPTER IV: _Multi-Dimensional Choice Models: Alternative . , .117 Structures of Travel Demand Models Introduction 17 Dependencies Among Choices 118 The Overall Set of Alternatives 121 Alternative Structure: 122 Separability of Choices 125 The Identification Problem and Estimation of 127 Simultaneous Probability Structures Modelling the Travel Choices 131 Alternative Structures of Travel Demand Models 133 ‘The Aggregate Equivalent of Disaggregate Models 143 Direct and Indirect Travel Demand Models 149 The Empirical Problem 155 CHAPTER V: Review of the Structures of Current Approaches . .158 ‘to Travel Demand Modelling Introduction 158 A Typology of Travel Demand Models 158 Aggregate Recursive Models 160 Aggregate Simultaneous Models 165 Disaggregate Recursive Modele 166 Diaaggregate Simultaneous Models 168 Summary 169 GHAPTER VI: The Logit Model and Functional Specification of. .170 ‘Alternative Mode: Introduction 170 ‘The Multinomial Logit Model 170 The Specification of the Variables 173 Derivations. of the Logit Model 17 ‘The Choice Axiom and the Independence from 178 Irrelevant Alternatives Property Elasticities of the Logit Model 183 Aggregate Elasticity 185CHAPTER VII: Page Estimation Technique 187 Application of the Logit Model to a Simultan- 191 eous Travel Choice Model Application of the Logit Model to a Recursive 204 Travel Choice Model Previous Applications of a Disaggregate Logit 215 Model to Travel Demand Summary 25 Estimation of Alternative Modele ..- +. +. + -217 Introduction 217 The Data Set 219 ‘The Subsample Used for Estimation 221 Variables Used in the Models 226 Specification of the Variables 228 The Simultaneous Model 231 Alternative Recursive Models 232 Sequence d+ m: The Conditional Probability 233 Sequence d +m: The Marginal Probability 234 Sequence m +d: The Conditional Probability 238 Sequence m+ d: The Marginal Probability 239 Sequential Estimation of the Simultaneous Model 242 Comparison of Alternative Modele 244 Summary 251 Conclusions and Recommendations + +++ +++ + +252 Summary 252 General Conclusions 253, Theoretical Framework 253 Modelling a Simultaneous Structure 254 Choice Models 255 The Choice Set 255, The Aggregation Problem 256 Non-Home-Based Trips 256 Case Studies 256 Data : 257 tensions of this Research 257 BIBLIOGRAPHY. oe ee ee ee ee ee ee 0260 BIOGRAPHICAL SUMMARY. 2 6 eee ee ee ee eee 0267 ‘APPEND! List of Figuress se ee ee ee 1268CHAPTER I Introduction and Summary. Purpose of the Study Decision making in transportation planning, as in any other planning activity, requires the prediction of impacts from proposed policies. One of the inputs to the prediction process is the demand function which describes consumers’ expected usage of transport services. The most widely used approach to the prediction of passenger travel demand is the aggregate Urban Transportation Model System (UTMS).* It is characterized by a recursive, or sequential, atructure** which represents 2 conditional decision making process, i.e., the traveller ie viewed as decom- posing his trip decision into several stages. A trip decision consists of several travel choices, e.g., choice of mode, choice of destination, etc. In a recursive structure the travel choices are determined one at a time, in sequence. ‘Two recent developments in modelling travel demand have stimulated the present study. The first wi the recognition that the representation of the trip decieion as a sequential process is not completely realistic. It has been argued that the trip decision should be modelled simultaneously *The UTMS is described in a large number of references. See,for example, FHWA (1970), Martin et al (1961), and Manheim (1972). *kA model can be expressed mathematically in many different ways. The term “gtructure" refers to the format of writing a model that has a behavioral interpretation. A model can be used for forecasting in a format which hes no behavioral interpretation. The distinction between direct and indirect travel demand model (Manheim, 1972) is made with respect to the format used for forecasting and does not necessarily imply a different behavioral interpretation,without resorting to an artificial decomposition into sequential stages (Kraft and Wohl, 1967). Attempts to develop simultaneous models were made using the conventional approach of aggregate demand analysis, where the quantity demanded is taken as a continuous variable (e.g., Kraft, 19635 Quandt and Baumol, 1966; Domencich et al, 1968; Plourde, 1968). The second development was the introduction of disaggregate probabilistic demand models that relied on a more realistic theory of choice among qualitative trip alternatives. However, all the disaggregate models that were developed could be used either for a single stage of the UTMS (e.g., Reichman and Stopher, 1971), or, more recently, for all the stages, but again assuming a recursive structure (CRA, 1972). ‘The common denominator of these two developments is clearly a dis- aggregate probabilistic simultaneous travel choice model. However, due to the large number of alternative trips that @ traveller is facing, and the large number of attributes that describe an alternative trip, a simultaneous model can become very complex. This raises some important issues concerned with the feasibility of a simul- taneous model, and the sensitivity of travel predictions to the simpli- fying assumption of a recursive structure. ‘The purpose of this research is to investigate these issues and to recommend a strategy for structuring travel demand models. Specifically, this atudy first explores the alternative travel demand model structures and their inherent behavioral assumptions. Secondly, an empirical study is conducted to estimate the alternative models and furnish some10 evidence with respect to the feasibility and desirability of disaggre- gate simultaneous trave2 choice models. Models for Policy Analysis We first explain what models are, what their purpose is, and why their behavioral assumptions are important. In general, models are simplified representations of some objects or phenomena, In this study, we deal with econometric models, i.e., mathematical relationships describing economic phenomena of observed variables and unkaown but statistically estimable parameters, We use models to better understand real world phenomena 0 as to be able to make decieions based on this understanding. Travel demand models are used to aid in the evaluation of alter- native policies. The purpose of the models is to predict the conse- quences of alternative policies or plans. A model that determines travel consequences independently of the characteristics of various Policy options can obviously not be used to evaluate those options (unless policies are, in fact, irrelevant to consequences). The specification of a travel demand model necessarily embodies some assumptions about the relationships among the variables underlying travel behavior. Predictions made by the model are conditional on the correctness of the behavioral assumptions and, therefore, are no more valid than the behavioral assumptions on which the model is based. A model can duplicate the data perfectly, but may serve no useful Purpose for prediction if it represents erroneous behaviorala For example, consider a policy that will drastically change present conditions. In this case the future may not resemble the present, and simple extrapolation from present data can result in significant errors. However, if the behavioral assumptions of the model are well captured, the model ie then valid under radically different conditions. It should be noted that this discussion is very general. "Behavioral assumptions" are a matter of degree since there could be many levele of detail in which behavior could be described. (For example, sensi- tivity to policies could be regarded as a gross level of behavioral assumptions.) : ‘The requirement that models should be policy sensitive is necessary but not sufficient for planning purposes. The additional requirement is that the models should be based on valid behavioral assumptions. A model could be policy seneitive but be useless for policy analysis, even if it fite the data perfectly, if it is not based on valid umptions. In general, it is impossible to determine the correct specification of a model from data analysis. It should be determined from theory or a priori knowledge which are based.on experience with, and understanding of, the phenomenon to be modelled. The problem is that frequently we do not have a comprehensive theory that will prescribe a specific model. Moreover, important variables are often missing due to lack of data or to measurement problems. There are other potential problems which involve the different kinds of data that could be used to esti- mate the model (e.g., time series vs. crose-section, attitudinal vs.12 engineering, etc.),:and the need to use a mathematical form which is amenable to a feasible statistical estimation technique. The result is that we may have several alternative models to evaluate, Unfortunately, "in statistical inference proper, the model is never questioned... The methods of mathematical statistics do not provide us with a means of specifying the model" (Malinvaud, 1966). In other words, given several alternative models and a data set, statistical inference will not be conclusive as to which model repre- sents the "true" process, This does not say, hovever, that the data does not play a role in the selection among models. At various stages of an empirical analysis we may revise some aspects of our assumptions that do not agree sufficiently with the findings. More generally, the accumulated pat evidence from empirical studies influences the formu- lation of the umptions’ of new efforts. Suppose that we are faced with a choice among some alternative models that were not discarded in the course of analysis of the data. If these alternative models were based on different sets of assumptions, we should decide which set makes the most sense according to our a priori knowledge about behavior, taken together with “goodness of fit" measures and statistical significance tests. In modelling passenger travel demand, we are concerned with the trip-making behavior of individuals or households. Hence, a prerequisite to travel demand modelling is a set of assumptions that describe the Process of trip-making decisions of these individuals or households.13 The basis for comparing different travel demand models should be the reasonableness (or, the correspondence with a priori knowledge) of the behavioral assumptions of each model. In this study we consider two alternative structures of travel demand models: simultaneous and recursive, each representing a dif- ferent travel behavior assumption. We assume a priori that a eimul- taneous structure is appropriate. However, we also consider modele with recursive structures, in order to evaluate their significant differences from a simultaneous model. Disaggregate Models The behavioral assumptions of a demand model alway take the point of view of an individual consumer as he weighs the alternatives and makes a choice. An aggregate model could be constructed based on aggregates of consumers by location or socio-economic category. However, aggregation during the model construction phase of the analysis will only cloud the actual relationships and can cause a significant loss of information (Fleet and Robertson, 1968; McCarthy, 1969). An aggregate model that is constructed based on averages of observations of socio-economic types and geographic location, would not necessarily represent an individual consumer's behavior, and there is no reason to expect that the seme relationships would hold in another instance or another location. For plenning purpo ve are concerned with the prediction of the behavior of aggregates of people. However, in princi- ple, ation to any desired level that is required for forecasting14 could always be performed after estimation, In Urban Transportation Planning (UTP) studies the data are collected on the disaggregate level,and aggregated to a zonal level for use in the conventional UTMS (Martin et al, 1961). Using this disaggre- gate data directly in disaggregate travel demand models can bring about large savings in data collection and processing costs. Since the data are used in the original disaggregate form, and are not aggregated to the zonal level, a comprehensive home interview survey is not essential as it 1s for the conventional aggregate models. The experience from previ- ous work with disaggregate travel demand models (e.g., Reichman and Stopher, 1971; CRA, 1972) indicates that it is a feasible modelling approach. Thus, disaggregate travel demand models have several practical advantages over aggregate models: the possidle reductions in data collection costs, the transferability of the models from one area to another, and the possibility of using the same set of models for various levels of planning. The problem of aggregating a disaggregate model for forecasting requires more research. However, some simplified methods, such as the use of homogenous market segments (Manheim, 1972; Aldana, 1971) are available and could be used. Choice Theory In general, modele that describe consumer behavior are based on the principle of utility maximization subject to resource constraints. Conventional consumer theory, however, is not suitable to derive models that describe a probabilistic choice from a qualitative, or discrete,13 set of alternatives, Therefore, the travel demand models developed in this study rely on probabilistic choice theories.* The consumer is visualized as selecting the alternative that maximizes his utility, The probabilistic behavior mechanism is a result of the assumption that the utilities of the alternatives are not certain, but rather random variables determined by a specific distribution. Denote the utility of alternative 4 to consumer t as U,,. ‘The choice probability of alternative i 1s therefore: P(AtA,) = ProblU,, 2 V, Iyer ¥ 3eA,) where A, ie the set of alternative choices available to consumer t. The utilities are essentially indirect utility functions which are defined in theory as the maximum level of utility for given prices and income. In other words, the utility U,, ie « function of the variables that characterize alternative 1, denoted as X,, and of the socio- economic variables describing consumer t, denoted as S,. Thus, we can write Uy, * Uy Cy, 5.) The set of alternatives A, io mutually exclusive and exhaustive such that one and only one alternative is chosen. The deterministic equi- valent of this theory ie simply a comparison of all alternative: available and the selection of the alternative with the highest utility. ‘*Choice theories are reviewed in Chapter III. See also Luce and Suppes (2965), CRA (1972), and Brand (1972),16 ‘The mathematical form of the choice model is determined from the assumption about the distribution of the utility values. The coefficients of the utility functions are estimated with a cross section of consumers using observations of actual choices. Therefore, the observed dependent variable has a value of zero or one, The forecast of the model is a set of probabilities for the set of alternatives The Multinomial Logit Model There are a number of probabilistic choice models that are available: two of the most popular and most useful are the Probit and Logit models. The multinomial Logit model, as described below, appears to be superior to Probit due to the practical considerations of computational time require- ments. We write the Logit model as follows.* nae) PLA.) = Tae roe jea, gregate cross-sectional data, the logit model ie estimated using the maximum likelihood method (McFadden, 1968). The Travel Choices A trip decision for a given trip purpose consists of several choices: choice of trip frequency (e.g., how often to go shopping), choice of destination (e.g., whre ‘to shop), choice of time of day ‘Whe derivation of the model from a distribution assumption is presented in Chapter III. The Logit model and its properties are described in detail in Chapter VI.7 (e.g., wnen to go), choice of mode of travel, and choice of route. In a probabilistic choice approach we are interested in predicting the following joint probability: P (£,d,h,m,: HMR, ) which is defined ae the probability that individual or household t will make a trip with frequency f, to destination d, during time of day, h, using mode m, and via route r, ‘The set of alternatives FDIMR, consists of all possible combinations of frequencies, destinations, times of day, modes, and routes, available to individual t. Consider for the purpose of presentation only two travel choices: destination and mode, Denote the set of all alternative coubinations of destinations and modes as DM. ‘(For simplicity we drop the subscript t.) We can partition this set according to destination to get the sets of alternative modes to a given destination M,. If modes and destina— tions had no common attributes and the two choices were independent then Mj is independent of d and could be written as M. However, this ie an unrealistic assumption since there are many attributes, euch ai travel time, that are in fact characterized by all the travel choices, Therefore, it is We are interested here in pre- dicting the joint probability: P(d,m:DM), The Alternative Structures If we assume that the two choices are independent, we write the18 following independent structure:* P(4:D) = Probl, 2 Uy, Hated) P(miM) = Prob[U, > U,,, m'eM) and P(djm:DM) = P(d:D) + P(m:M) where: D = the set of alternative destinations M = the set of alternative modes Ug = the utility from destination d = the utility from mode m Consider a conditional decision making process in which, for example, destination is chosen first, and then conditional on the choice of destination a mode 1s chosen, For this jumption we write the following recursive structu: P(diD) = ProblUg 2 Uys, ¥ ate] - ‘ (uM, ProblUg|q 2 Yar ge ¥ meg] and P(d,m:DM) = P(d:D) * P(mM4) where: My = the set of alternative modes to destination d "hla = the utility from mode m given that destination d is chosen, “This 1s an unrealistic structure for travel demand, but it 18 presented for the purpose of comparison with other atructures.19 If we assume that the choice of mode is dependent on the choice of destination and vice versa, we write the following structur P(GD,) = ProblUy)g 2 Uyr| »¥aten J Mo) = " Pam, Probity)g > Uys ge ¥ateH,] where: D, = the set of alternative destinations by mode m In the independent and recursive structures we predict the joint probability by multiplying the structural probabilities. However, in @ simultaneous structure the two conditional probabilities are insufficient information to predict the joint probability. Therefore, we need to estimate either a marginal probability, yy P(4:D), or estimate directly the joint probability, The problem with the first approach is that we need to define a utility Ug where we originally specified Palme The second approach requires a specification of the joint utility Va» where we consider the combination dm as a single alternative. This approach is more logical since it corresponds with the notion of a simultaneous choice. Hence, in the simultaneous structure, we need to tdmate the following choice probability: ¥ a'm' ep] P(d,m:DM) = ProblUs, 2 Ugig! Given the joint probability we can derive any desired marginal or con- ditional probability, For example,20 Alternative Models For simplicity, we write the probabilities in this section without. the notation for the set of alternatives. tn other words, we will write P(d,m:DM,) Py (dim), and PQamM,,) ae P (ala). In predicting the following joint probability: P, (£.d.m,h,r) the set of alternatives consists of all possible trips, or all possible » times of day and combinations of frequencies, destinations, mod routes, available to individual t. In a simultaneous structure using the logit model, this will be the definition of the set of alternatives, and the choice probability will be for an alternative £,d,m,h,r combi~ nation, ‘The joint probability can be written as a product of marginal and conditional probabilities as follows: P(E) + PLCal£) + PL (mle,a) + Pehl f,d,m) + P, (zl £,d,m,h) We can write thie product in many different ways, e.g., Fee) + PL tale) + Py (mléyh) + PL(4|£,h,m) + P. (el£,hym,d)2 In a recursive structure we will use a logit model for each proba bility separately, and arrange the set of alternatives for each choice according to the sequence implied by the way we write the above product. For example, the probability P, (aff) is the probability of choosing mode m, when the set of alternatives consists of the modes available to individual t, to destination d, with trip frequency £. Estimating a sequential model requires further assumptions beyond the definitions of the relevant sets of alternatives for each choice, Consider, for example, the choice model for the probability P, (al fn). The problem is how to include in the model all the variables which for a given mode vary across destinations, e.g., travel time, travel cost, etc. Clearly, we cannot use all these variables as separate variables with their own coefficients. Therefore, we need to construct composite. variables, There are many possible composition achemes. In addition there is the possibility of constructing the composite variables from several original variables together such that the tradeoff among them is kept constant in all choices. For example, for an alternative destination we define a generalized price by each mode which is a function of travel time and travel cost, then we aggregate across destinations to create a composite generalized price which is specific only to mode. ‘The Empirical Study ‘The data for this study was taken from a data eet prepared by R.H. Pratt Associates (RHP) for the Metropolitan Washington Council of Governments (WCOG). The data set was combined from a home interview22 survey conducted in 1968 by WCOG and a network (i.e., level of service) data set assembled by WCOG and RHP. Due to the scale and the objectives of this empirical study, it was decided to use only a small subsample of the original data set for a single trip purpose: shopping. The data were kept in the dicaggre- gate form where the observation unit is a household. This follows the assumption that the behavioral unit for a shopping trip is also a household. Hence, the disaggregate data were exclusively dravn from conven- tional urban transportation study data. Specifically, trip and socio— economic data from a home interview survey, and level of service data from coded networks and other user cost data customarily collected by transportation planning agencies, were used. Since our purpose is to evaluate the sensitivity of the predic- tions to the structure of the model we consider in the empirical work only the joint probability of destination and mode (given.that a trip is taken) — P, (md). We model this joint probability with three alter— native structures; namely, a simultaneous logit model that estimates this probability directly*, and two possible recursive model sequences: ‘The justification of thik choice from other choices 1s as follows: The choice of time-of-day is assumed to be insignificant since the sample included only off- peak shopping trips. Route choice is not reported in the available data, The actual frequency is also not reported. Trips are reported for a 24 hour period. Therefore, the observed daily frequency is either 0 or 1 (and in a few cases 2). If we use an aggregate of households, this is sufficient information to compute an average (cont'd on next page)23 PL) + P, (ala) and Ppa) * PLCalm), where a logit model is appliéd to each probability separately. We also investigate alternative wa} of constructing composite variables for the marginal probability. The sample that was used for estimation consists of 123 household home-shop-home round trips that were selected randomly from the original home interview sample in the northern corridor of Metropolitan Washington. Each household has a choice between two modes - the family car and bus ~ and several shopping destinations, ranging from one to eight according to the location of the household residence. It is important to note that we need to consider only alternatives that have Positive choice probabilities, Therefore, a shopping location that ie 00 far" or a mode that ie "unsafe" and consequently not feasible, or assumed to have negligible choice probability, need not be included in the set of alternatives. The data consist of level of service variables by mode and desti- nation, shopping opportunities by destination, and socio-economic * (cont'd) frequency. For a disaggregate model the actual frequency 1s not avail- able. We are forced to assume that the choices of mode and destination are independent of the actual frequency and, therefore, can be modelled Separately, Note that.with 0, 1 daily frequencies: P, (f@1|d,m) = 1 and P, (f=0|d,m) = 0,24 characteristics of the household. Each observation included the value of the variables for all the relevant alternatives for this household and the observed choice. The simultaneous model that included observations with up to 16 alternatives and 7 variables gave reasonable coefficient estimates. The computer cost was only slightly higher (=20%) than the cost of a binary mode choice model with 5 variables, This indicates that a simultaneous model is feasible for the two choices of destination and mode, It also indicates that expanding the set of choices and therefore increasing the number of alternatives and variables may not be an unrealistic objective. Comparison of the coefficient estimates of the simultaneous model with those of the various recursive models that were estimated suggest that the predictions are sensitive to the structure of the model. In order to demonstrate this sensitivity here, it 1s not necessary to present in detail all the models that were estimated in thie etudy.* It will be sufficient to show some examples of the important tradeoffs and elasticities The following table shows the values of time implied by the different models: *The estimation results are described in detail in Chapter VII.25 Estimated from a model for: P(m,d) Pala) P(d|m) Value of Out-of-Vehicle 3.02 $/hr 1.36 $/hr 4.67 $/hr Travel Time (1.44) (.98) (4.36) Value of In-Vehicle +78 $/hr «28 $/hr 2.21 $/hr Travel Time (68) (66) (2.01) The figures are for a household with annual income between $10,000 and $12,000. The aumbers in parentheses are standard errors. Although the standard errors are relatively large, this is not typi- cal for estimates of value of time (e.g., Talvitie, 1972). (The estimated model coefficients that were used to compute the values of time were signif- icantly different from zero.) Estimated values of time from the simultaneous model are greater than those estimated from a mode choice model (given destination), and smaller than those estimated from a destination choice model (given mode). The following table shows some direct elasticities of the mode choice probability: Mode Bus Auto Estimated From a Model for: P(m,d) P(m|d) P(m,d) — P(m|d) Out-of-Vehicle Travel Time 1.01 82 13 10 In-Vehicle Travel Time = .3L | =.26 -.05 =.03 Out-of-Pocket Cost = 40 -.91 -.13 12326 The figures are computed for the following c ~ a household with annual income between $10,000 and $12,000. the probabilities of choosing bus and auto are .2 and .8, respectively, out-of-vehicle travel times are 20 minut by bus, and 10 minutes by auto, - in-vehicle travel times are 30 minutes by bus and 15 minutes by auto, out of pocket costs are 50 cents by bus and 50 cents by auto. The most striking variation in this table is in the cost elasti- city. The mode choice model derived from an estimated joint probability gives cost elasticities which are about half the elasticities computed from a recursive mode choice model. The differences among the models could be attributed to specifi- cation errors which affect differently a mode choice model and a desti- nation choice model, The effects could be in the opposite directions and therefore the joint probability model gave estimates that are in some way between the estimates of the two other models. The marginal probabilities of the recursive models which were formulated with composite variabl. also demonstrated significant dif- ferences from the corresponding probabilities derived from the simul- taneous mode: All the alternative models that were estimated resulted in essen- tially equal goodness of fit.27 Thus, the chosen structure can make a big difference in terms of the values of the estimated coefficient: Since there are a priori reasons to assume a simultaneous structure, rather than recursive, we should estimate directly the joint: probabilities. -Then, if necessary, we can derive any conditional probability. Conclusions Models based on disaggregate data and cho1ce theory were estimated in the past either for a single travel choice, primarily mode choice, or for several choices but in a recursive structure. The empirical study that was conducted in this research demonstrated the estimation of a disaggregate simultaneous model, The results from the estimation of a simultaneous destination and mode choice model indicate that thie approach is feasible within reasonable computation cost. Moreover, the estimation results of models with recursive structures for the same two choices show that important coefficient timates vary considerably with the different model structures. This empirical study was limited in scale, and it is recommended that the evidence should be extended to include: alternative data sets, different trip purpose categories, a complete t of travel choices, and a more extensive set of explanatory variables (in particular, attraction description). The empirical evidence taken together with the theoretically appealing assumptions of a simultaneous structure and the advantages of disaggregate modele suggest that future efforte in travel demand28 modelling should be in the direction of simultaneous disaggregate probabil- fetic models. Given the joint probability (from the similtaneous model), one can derive conditional probabilities and use the model for forecasting 4n sequential stages, corresponding with the UTMS procedure. One of the important problems in using disaggregate modele for fore- casting is the aggregation problem. Future research efforts should invee- tigate this problem. However, for the short run, simplified aggregation procedures, such as market segmentation, are available and can be used. The use of disaggregate modele suggests new emphasis in data collec~ tion efforte for transportation planning. It ie not clear yet how much data is needed for disaggregate models, but it is clear that a change dn the general methodology of travel data collection ie appropriate. ‘The comprehensive home interview survey covering an entire planning region might be replaced by several more descriptive small samples, in selected areas of the region. Thus, the emphasis should be to attempt to represent the full range of socio-economic characteristics affecting travel behavior, rather than on sampling all parts of the region at a uniform rate. Smaller scale surveys will make possible the collection of the detailed information (not conventionally collected) that are importent for disaggregate demand models. Yor example, car pool information, information on how often a trip 16 made (instead of reporting only the tripe made during the last 24 hours), information on institutional constrainte such as preferred arrival time, and so forth, would be29 obtained. In addition to the travel data requirements, better information ie aleo needed with respect to the attributes of alterna- tive trips. In particular, the attraction data that is available from conventional data sources used in Urban Transportation Planning are not very descriptive. More detailed attraction data is needed in order to achieve better predictions of destination choic In depth studies of travel behavior based on detailed interviews and attitudinal data could be fruitful. However, it appears that the most beneficial directions for research toward improvements of trans— portation planning capabilities are: the aggregation problem, the behavioral modelling of round trips with non-home-based links, and the experimental application of ‘simultaneous disaggregate modele to case atudies of important transportation 4¢ at different levels of planning. In conclusion, this research has indicated the desirability and the feasibility of a simultancous disaggregate travel choice model. Qutline of the Report In Chapter II, the nature of the demand for travel is discussed in terms of ite inherent characteristics and its relation to other economic goods. The system of models used for transportation planning is out- lined and the implications for disaggregate modelling of mobility and travel choices are discussed. Chapter III presents a review of some concepts from consumer and choice theories. It indicates that choice theory, rather than demand anslysis, is the appropriate approach for the30 modelling of mobility and travel choices. Chapter IV establishes alternative model atructures, each representing different jumpt ions with regard to dependencies among choices. Chapter V reviews the structures of current approach: to travel demand modelling, In Chapter VI the multinomial logit model and ite application to the alternative travel demand models is described. Chapter VII reports the results of an empirical study in which the alternative models were estimated on a comparable basis. Finally, Chapter VIII presents a discussion of the implications from the theoretical considerations and the empirical evidence toward the modelling of travel demand. It also points the desirable directions for research.31 CHAPTER II Nature of Travel Demand and Nature of Travel Demand and Prediction Models for Trans; portation Plann: ARSE CEEOn Models for Transportation Planning Introduction This chapter examines the nature of the travel demand process and the overall structure in which it is embodied. An attempt is made to survey the theoretical considerations on which travel demand models are based, ‘The overall structure of the system of models used for prediction in transportation planning hi implications for the specification, data collection and estimation, and usage of the various planning models, Therefore, we consider the travel demand process and ite relations to. other proce 4.e+, socio-economic activities and transport supply. We establish first an overall structure of the system of models and then focus on the travel demand model, ‘The models used for planning take a market point of view. However, it 18 argued that the models that describe consumer behavior should be developed and estimated for the unit that makes the decisions; the individual consumer. Thus, the chapter also establishes the modelling framework to be used in demand modelling from the point of view of an individual consumer.32 The Complexity of Travel Demand ‘The complexity of travel demand is apparent from the way we char~ acterize a trip--origin, destination, time of day, modes of travel, route, and purpose. Trips are spatially disaggregated; we speak of a trip as made from an origin to a destination. For a work trip the origin and the destina~ tion are fixed by the choices of residential location of the household and the tripmaker's job eite. However, for most leisure trips one has a choice among several destinations. For example, shopping trips can be made to a nearby grocery store or to a distant shopping center. Peaking effects bring out the importance of the time-of day in which a trip 1s taken (perhaps also the day of the week if it is not an every day trip). For the majority of workers, working hours are not totally in their control; however, they can still decide to arrive early at their jobs in order to avoid the inconvenience of the peak hour, Staggering working hours in downtown areas is often suggested as a means of relieving congestion during the peak hours. Some leisure activities are less constrained and the consumer has a range of hours in which he can make a trip to those activities. In most urban areas the traveller has a choice between public trans- portation modes and private autozobile. Even when there is no public transportation available, a traveller can sometimes choose between driving his own car, being driven, or participating in a car pool. In some cases, taxi, walking, and two wheeled vehicles