Transportation Research Record 890 11
forward as would testing the transferability of the cal Review, Vol. 78, 1971, pp. 71-80. coefficients of Stevens' Law among localities in 5. R.H. Erikson. The Effects of Perceived Place different geographic areas and with different char Attributes on the Cognition of Distance. Depart acteristics. Preliminary psychological research !il ment of Geography, Univ. of Iowa, Iowa City, suggests that it may be possible to develop a single Discussion Paper 23, 1975. equation that captures the relations between reality 6. R. Briggs. Urban Cognitive Distance. In Image and perception for all types of travel characteris and Environment: Cognitive Mapping andSpatial tics. Behavior (R.M. Downs and D. Shea, eds.), Aldine Another potentially fruitful area for further Publishing Co., Chicago, 1973. research would be an integration of the Stevens' Law 7. o. Bratfish. A Further Study of the Relation concept with the concept of cognitive dissonance. Between Subjective Distance and Emotional In The usefulness for transportation choice modeling of volvement. Acta Psychologica, Vol. 29, 1969, the theory of cognitive dissonance, with its impli pp. 244-255. cations regarding the interrelation of attitudes and 8. D. Cantor and S.K. Tagg. Distance Estimation in behavior, has been explored by Golob, Horowitz, and Cities. Environment and Behavior, Vol. 7, 1975, Wachs (14), Dumas and Dobson (15), and others. pp. 59-80. Further -application of the insights into human 9. R.A. Lowrey. Distance Concepts of Urban Resi behavior that are available in the literature on dents. Environment and Behavior, Vol. 2, 1970, psychology and marketing should prove beneficial in pp. 52-73. improving both knowledge of travel behavior and the 10. P. Burnett. Time Cognition and Urban Travel ability to forecast future behavior. Behavior. Presented at Geographical Perspec tives on the American City Conference, Phila ACKNOWLEDGMENT delphia, 1976. 11. E.J. Williams. Regression Analysis. Wiley, New The collection of the data on reported travel times York, 1959, pp. 129-137. and costs was supported by a grant to Northwestern 12. T.A. Domencich and D. McFadden. Urban Travel University from the U.S. Department of Transporta Demand. North-Holland, Amsterdam, Netherlands, tion. I would like to thank E. Hauer of the Univer 1975. sity of Toronto and several anonymous referees for 13. T.J. Adler and M. Ben-Akiva. Joint-Choice Model helpful comments. for Frequency, Destination, and Travel Mode for Shopping Trips. TRB, Transportation Research REFERENCES Record 569, 1976, pp. 136-150. 14. T.H. Golob, A.D. Horowitz, and M. Wachs. Atti 1. P.L. Watson. Problems Associated with Time and tude-Behaviour Relationships in Travel-Demand Cost Data Used in Travel Choice Modeling and Modelling. In Behavioural Travel Modelling Valuation of Time. HRB, Highway Research Record (D.A. Hensher~and P.R. Stopher, eds.), Croom 369, 1971, pp. 148-158. Helm, London, 1979. 2. A.H. Meyburg and Brog. Validity Problems in w. 15. J. Dumas and R. Dobson. Traveler Attitude: Empirical Analyses of Non-Home-Activity Pat Behavior Implications for the Operation and terns. TRB, Transportation Research Record 807, Promotion of Transport Systems. TRB, Transpor 1981, pp. 46-50. tation Research Record 723, 1979, pp. 64-71. 3. S.S. Stevens. On the Psychophysical Law. Psy chological Review, Vol. 64, 1957, pp. 153-181. 4. R. Teghtsoonian. On the Exponents in Stevens' Publication of this paper sponsored by Committee on Traveler Behavior and Law and the Constant in Ekman's Law. Psychologi- Values.
Design and Analysis of Simulated Choice or Allocation Experiments in Travel Choice Modeling
JORDAN J. LOUVIERE AND DAVID A. HENSHER
A new approach for modeling traveler trade-offs and choices is proposed, de gained a following in the analysis and forecasting scribed, and illustrated. Based on research in psychology, marketing, and eco of travel behavior. If real choice data satisfy the nomics, a method for developing discrete choice models from controlled labo· conditions assumed in the statistical choice models, ratory simulation experiments is developed and presented. The method bor· it is possible to derive aggregate-level trade-offs rows statistical theory from discrete choice theory in econometrics and from and to simultaneously forecast choice behavior. the design of statistical experiments to marry work in trade-off analysis with Hence, methods based on revealed choice have high choice analysis. The method is illustrated by means of several travel-choice related examples that involve choice of mode and destination. Recent evidence external validity and practical applicability to of validity in forecasting the actual behavior of real markets is reviewed in sup strategic policy problems. port of the approach. Other approaches have recently gained attention- notably, laboratory simulation methods such as vari ations of conjoint measurement or trade-off analysis Since the early 1970s, the study of revealed-choice (7-9) and functional measurement (10-15), which are behavior based on the random utility derivations of the-primary methods of approach for-developing quan discrete choice theory in econometrics <.!-~) has titative descriptions of multiattribute individual 12 Transportation Research Record 890 and group judgments, trade-offs, or utilities. of choice models that at best can be tested only These approaches are based on the responses of weakly with revealed-choice data. travelers to hypothetical travel alternatives and not on their observed behavior. The former type of THEORY data is here called "intended choice" and the latter type "revealed choice". It is assumed that the derivations of discrete The intended-choice approaches to trade-off choice theory based on random utility notions are analysis have limitations that hamper their applica approximately true--that is, that the random utility bility, including the following: version of the Luce (20,21) choice axiom as derived by McFadden (5) and Yellot (22) holds for aggregate 1. One is usually forced to make untestable choices or allOcations: ~ assumptions about the functional form of the trade offs in practical applications. (I) 2. One must make assumptions about the relation between choice and utility that are untestable and are contrary to most assumptions in practical random where utility choice models. 3. It is difficult to incorporate individual p(alA, VjeA) probability of selecting alterna constraints on choice effectively except in an ad tive a from choice set A, of which hoc or post hoc fashion. a is a member, defined over all j 4. External validity assessment is less obvious members of A, including ai than with revealed-choice methods. utilities or scale values of a and j, respectivelyi and The revealed-choice methods, on the other hand, e = base of the natural logarithms. have major limitations: One normally assumes that the scale values (utili 1. One must make assumptions about functional ties) may be expressed as a linear in the parameters form a priori and, in contrast to the intended and additive functioni e.g., for alternative a, behavior methods, one cannot ever guarantee that it will be possible to test these assumptions ade (2) quately with real data. 2. One must make assumptions about mean utility where parameters or at least segmented mean parameters that are known from evidence to be often false Ua scale value of the ath alternative, (10,12,13,15,16) and that are used for the sake of b's constants to be estimated from the data, and tractability "rither than empirical reality. x's attributes of the ath alternative. 3. Measurement errors and correlations among variables cannot be controlled to any satisfactory Equation 1 states that the probability of choos degree, or at least have not historically been well ing any particular alternative from a set containing controlled (18). at least one other is expressible strictly as a 4. The forecasting accuracy of the models has function of conditional probabilities. Equation 2 been disappointing, which suggests that external imposes a linear in the parameters and additive validity of observations of choice is insufficient structure on the conditional probabilities to de to guarantee internal validity or forecast accuracy. scribe each alternative. In general, the attributes are specific to a particular alternative (e.g., al Recently, the consequences of failure to satisfy ternative a), but it is possible in some contexts to a number of these assumptions have been examined by treat the attributes as generic--i.e., attributes Horowitz (18,19). Suffice it to say that the that are common to all or some subset of alterna intended-choice approach can guarantee satisfaction tives. Other problems require mixtures of generic of many of the assumptions by design while sacrific and alternative specific attributes. ing immediate external estimation validity, whereas If one assumes Equation 1 to be true, it is pos the revealed-choice approach cannot guarantee satis sible to develop straightforward methods for col faction of its assumptions with real choice data but lecting data and estimating the parameters of the does have immediate external estimation validity. choice models derived therefrom. The results of This paper attempts to partially bridge the gap such choice studies are similar to those of conjoint between the two approaches by developing a method analysis, trade-off analysis, functional measure for estimating intended-choice models that satisfies ment, or the like in that estimates of levels of to the extent possible the necesssary statistical utility can be derived, various algebraic forms of conditions for a variety of econometric choice utility (or decision) models can be tested, and models and can be used to make forecasts to test policy-relevant parameters such as elasticities can external validity. Evidence in support of external be obtained (1,7-10,12-17). More important, how validity is presented later in the paper. In this ever, the choic; -;-odel;-derived forecast choices regard, the approach represents an improvement in directly without the necessity of developing a simu the ability to analyze choice behavior with in lation routine combined with a number of assumptions tended-choice data because it actually involves ob (such as "highest" ranked equals first choice) that servations on choice or allocation behavior in con are required to predict choices from rankings or trolled situations. Because the models derived are ratings data (16). The approach to this problem is estimated from experimentally observed choices, they discussed in the next section of this paper. directly forecast choice behavior rather than judg ments, utilities, or rankings. Although it is not CONSIDERATIONS ON DESIGN OF CHOICE EXPERIMENTS explored in this paper, the approach also has the ability through the use of statistical principles in Equation 1 implies that any experimental design that experimental design to rigorously test various ensures the independent estimation of conditional assumptions inherent in, or deductions derived from, effects (scale values) should suffice as a choice discrete choice models in econometrics (18,19). design. Although we readily admit that in theory This permits one to rigorously test various -;;pects Transportation Research Record 890 13
random samples of choice sets will satisfy this cri mation of a separate, individual-specific choice terion, in practice it is impossible a priori to model. Unfortunately, the theory of maximum likeli know the statistical properties of such designs. hood estimation developed for multinomial logit Hence, we favor the use of controlled statistical choice models !!r~l only holds for large-sample experiments that can be designed a priori to have problems, and the properties of the estimates for certain statistical properties of interest. This individual-level choice models are currently un paper concentrates on two such design properties: known. However, because each individual makes a series of discrete choices from statistically de 1. The condition that the probability of a signed sets of choice sets, there is likely to be choice alternative being in a choice set and the more than enough choice data in the aggregate across probability of choosing the alternative given that a typical sample (say, 400 individuals) to satisfy it is in a choice set be independent and balanced the large sample requirements. By "aggregate" we across all sets of choice sets so that one can de mean both (a) the total of discrete choices avail termine whether alternative a has a higher proba able (the number of individuals times the number of bility of being chosen over b because it is pre choices in all choice sets) and (b) the aggregated ferred to b or because it is available to be chosen choice frequencies obtained by calculating the total more often than b, and number of choices made by individuals for all alter 2. The condition that the attributes of the natives in all choice sets. choice alternatives be as independent of one another We now illustrate the method of estimation for as possible (i.e., orthogonal) both within and be aggregated choice data; Louviere and Woodworth (~) tween alternatives. have demonstrated its asymptotic efficiency for large samples, as have others (!, l!!_, ~) • The esti In practice, it is possible to guarantee the sat mation method involves weighted least-squares re isfaction of these two conditions by the appropriate gression in which Equation 1 is put in linear form choice of an experimental design plan ( 9, 12, 17, 23- as follows. 27). In particular, it is always possible-tosat The relative frequency with which alternative j isfy these two conditions by treating each attribute (= 1,2, ... ,J) is chosen in choice set i (= 1,2, ••• , as a factor "nested" under the appropriate alterna I) is denoted as Rfij. This relative frequency is tive. By judicious choice of design plan, it is taken as an estimate of the unknown choice probabil also possible to test for violations of Equation 1 ity, and Equation 1 is rewritten as follows: by using some of the ideas contained in Horowitz's various tests for choice model adequacies (18,19). Rfij (al A, \ljeA) = e Uia/K;. (3) Most such tests require one to be able to estimate certain interactions in addition to main effects; where Ki is E eUji and all other terms are as previ- however, one can almost always design such condi VjeA tions a priori so that they will be satisfied by the ously defined. That is, for the ith choice set, the data (24-26). denominator is a constant for all j alternatives. In general, main-effects plans that treat each Taking logarithms to the base e of both sides yields attribute of each alternative as a factor will suf fice for model estimation if Equation 1 is approxi ln[Rfij(alA, \ljeA)] -ln(ki) (4) mately true. Louviere and Woodworth (25) have shown =u. these design plans to be near optimal for parameter estimation in terms of efficiency. The next section Equation 4 implies that the Ua can be estimated by of this paper outlines parameter estimation for ag creating dummy variables for each j and for each gregated choice data. We concentrate on aggregated i--in particular, a weighted multiple linear regres data for the sake of exposition of ideas; future sion analysis in which each choice response (rela papers will explore individual-level models, tive or absolute choice frequency) is associated repeated-measures designs, and covariance analyses. with a design matrix of (1,0) dummy coded indices so that, if the choice observation (Rfij) pertains to choice alternative a, the dummy index for alterna PARAMETER ESTIMATION FOR AGGREGATED CHOICE DATA tive a is coded one, otherwise zero. Similarly, if the choice observation appears in choice set i, the For many applications, such as sketch planning, dummy index for choice set i is coded one, otherwise aggregated choice data are sufficient to derive zero. In practice, of course, only (J - 1) and policy implications. If sample sizes permit, the (I - 1) dummy indices can be used in estimation un choice data may be disaggregated into various policy less one "centers" the regression about the origin. categories of interest (assumed to be mutually ex Another estimation method (29) permits one to dis clusive) and aggregates of choices may be developed pense with choice set constants by using the log for analysis. So there is some limited flexibility odds with respect to some base alternative as the for market segmentation with this approach. If dis dependent variable. It is easy to demonstrate that aggregated results are desired, the data must be treated as a series of discrete choices at the the denominators or choice set effects cancel out individual-respondent level and maximum likelihood for this case. As in disaggregate multinomial logit estimation used to derive parameter estimates. Such estimation, one choice alternative serves as a base methods are now well-known in travel analysis and alternative--the "origin" of the scale values. need not be pursued here (1-6). However, because Weighted least squares is used because the de the problem of repeated meas-;;r-;s on individuals has pendent variable is a proportion (the relative fre quency of choices in choice set i) , which does not yet to be treated, caution should be used in any conform to classical homoscedasticity assumptions in applications of traditional logit choice algorithms multiple 1 inear regression. Louviere and Woodworth to the types of data described in this paper. ( 25) and Grizzle, Starmer, and Koch (l!!_) discuss It is important to note that each individual is weighting for this condition. The method yields asked to make choices (or allocate choices, money, modified minimum chi-square estimates that are time, etc.) from a series of choice sets. The ex asymptotically efficient and consistent in large perimental designs briefly outlined in the previous samples. section generate the appropriate choice sets to be administered to each individual, and each individual makes a sufficient number of choices to permit esti- 14 Transportation Research Record 890
EXAMPLE APPLICATIONS Only the scale values are of interest in the ex amples; the choice set parameters are needed merely This section illustrates the application of the ap to ensure that the probabilities sum to one in each proach to three travel-choice-related examples and choice set and because they are algebraically neces also provides evidence from three validity tests sary in the model form to be estimated. One could that suggests the approach is predictive of the ac recover the original choice proportion data (the tual behavior of people in real markets. relative frequencies) by using the scale values es timated in the regression. Thus, the degrees of 8imple Destination Choice ¥roblem: choosing a freedom necessary to account for the choice data are Fast-Food Restaurant for Lunch always much less than indicated in the regression analyses. Nonetheless, it should be noted that Example A involved 99 upper-class undergraduates in Equation 1 implies a constant cross elasticity for marketing at the University of Iowa, who were shown all attributes of all alternatives and the choice 10 different choice sets consisting of various com set constants contain all cross-elasticity effects. binations of the five major hamburger chains in Iowa If one suspects that this hypothesis is not true, City: Wendy's, Burger King, Hardee' s, McDonald's, more detailed analysis of each choice alternative and Burger Palace. The choice sets were developed will be necessary. by treating each restaurant as a factor with two levels: available or unavailable. All possible Simple Modal-Choice Problem: Bus Versus Automobile sets of choice sets would be the 2 5 combinations Versus Other of availability of each restaurant. This is a fac torial design. We selected 8 choice sets from the A modal-choice task was developed by manipulating 32 possible according to an orthogonal main-effects three attributes of bus systems and three attributes plan (24). One of the 8 sets selected is the null of automobiles in an experimental design. The at set (all unavailable); hence, there is a target tributes of bus (and their levels) were fare (25¢ group of 7 sets for analysis. Subjects were shown 3 and 50¢), travel time (15 and 40 min), and. walking preliminary sets of no analytic interest to acquaint distance (1 and 5 blocks); the attributes of auto them with the task. mobile were gasoline cost per gallon ($1.35 and Subjects indicated which restaurant they would be $1.75), travel time (10 and 20 min), and parking most likely to choose for lunch given that only the costs per hour ( 20¢ and 50¢) • In other words, the ones listed in a particular set were available. experimental design was created by treating each Subjects were informed that some restaurants could attribute as a factor with two levels and selecting fail or others enter the market, and we wished to a fraction of the 2 6 complete factorial design. know what they would do if some now present were The orthogonal fraction selected from Hahn and closed. The discrete choice data were aggregated to Shapiro (~) has 16 treatment combinations, each of relative frequencies for analysis by weighted least which is a choice set. That is, a choice set con squares regression: sists of a description of the levels of the three bus attributes and the levels of the three automo Rf" = 130 +131 Wendy's" + 13 2 Burger King" + 13 3 Hardee's" + 134McDonald's" bile attributes; subjects were requested to indicate +13 5 Setl" +136 Set2. +13 7 Set3"+13aSet4" +139Set5" +l310Set6" (5) whether, given their present circumstances, they would choose to travel to the University of Iowa for where regular morning classes by the described automobile, bus, or other (left unspecified). Subjects were the observed relative frequency for same 99 undergraduates involved in example A. the Kth (K = 1,2, ... , K = The discrete choice data were aggregated to rela 40) choice possible in the task; tive frequencies for analysis by weighted least Wendy's, Burger (1,0) dummy variables to repre squares regression. The following model was es King, etc. sent (J - 1) alternatives (res timated: taurants) (each choice observa tion is coded one if it is the Rf" = 130 + 131 bus"+ l32auto" + 13 3 fare ($)if bus.+ 134time (min)if bus" alternative in question, zero + 13 5 walk (blocks) if bus"+ 136gasoline ($/gal) if auto" otherwise) ; + l37parking ($/h) if auto" + 13 8 time (min) if auto" Set 1, Set 2, (1,0) dummy variables to repre 15 etc. sent the (I - 1) different de +i~1 °'iCi (6) nominators or "choice set ef fects" (each choice observation where is coded one if it was observed in the ith set, zero other kth relative frequency of wise) ; and choice observation (k 1,2, empirical regression parameters ... ,K;KisixJ); to be estimated from the data. bus, auto = alternative specific con- stants, deriYed by treating The statistical results are as follows: each as a (1,0) dummy variable; fare, time, etc. alternative specific attri Estimated butes that have their numeri Restaurant Scale Value Standard Error cal values if the choice ob Burger Palace o.oo servation pertains to the mode Wendy's 2.56 0.11 in question or are zero other Burger King 1.82 0.11 wise; Hardee's 1. OB 0.11 Ci 15(I - 1) (1,0) dummy variables McDonald's 2.39 0.11 used to represent choice sets; and The F (14,26) 48.36, which has a probability of empirical constants to be esti occurring by chance of less than O. 0001. The R2 mated from the data. value is 0.98. The model appears to give a good account of the aggregated choice data. Transportation Research Record 890 15
The results of the analysis are as follows Rf" = llo + (3 1 air" + (J2 bus. + (J 3 otherk + (J4 air cost" + (J 5 bus cost" (choice set results suppressed): + (3 6 bus food" + (37 bus drink" + (3 8 bus food x drink" Parameter Standard + (J 9 choice set I"+ (J 10choice set 2" + ... + (J23choice set 15" (7) Variable Estimate Error where all terms are as previously defined or self Bus l.26 0.55 evident. Auto -l.30 l.07 This model implies that there are different ef Other -2.31 0.57 fects for dollar costs depending on whether the mode Bus time -0.07 0.01 is bus or air and that food and drink have (poten Bus fare -2.58 0.85 tially) nonadditive effects within bus. The results Bus walk -0.17 0.05 are as follows: Auto gas ($) -0.10 0.48 Auto parking ($) -0.57 0.64 Parameter Standard Auto -0.01 0.02 time Variable Estimate Error Air 0.344 0.403 The F (24,24) was 36.971 the probability of an Bus l. 208 0.254 F-value that large occurring by chance is less than Other -l.464 0.169 0.0001. The R2 is 0.95, so this model also gives Air cost -0.019 0.004 a reasonably adequate account of the logs of the Bus cost -0.127 0.010 relative frequencies of choice data. Results indi Food 0.140 0.057 cate that, whereas University of Iowa students in Drink 0.043 0.056 marketing prefer buses to other modes, they are par Food x drink 0.135 0.057 ticularly sensitive to bus attributes in comparison with automobile attributes. It is notable that the These results indicate that bus is preferred to travel-time coefficient for bus is almost nine times air, which is probably the result of the preponder larger than that for automobile, which clearly indi ance of the sample of bus travelers and students and cates that time is not the same via either mode. the larger number of different bus choices. In this With the bus equation, the implied value of travel respect, it is important to note that the sample is time is about $1. 65/h 1 however, these are student six times more sensitive to bus cost than to air subjects. cost and is much more influenced by the provision of a food service than a drink service. The (food x Intraurban Modal-Choice Example: Bus Versus Air drink) interaction implies that having both is bet ter than having either separately but having neither An intraurban modal-choice task was developed by is considerably less preferred. If the sample were asking Iowa City individuals to make choices between representative, it would imply that considerable the regular air service operating from Cedar Rapids, leverage on patronage could be gained by the food Iowa, to Chicago, Illinois (which requires Iowa City drink option and by offering air or bus travel cost residents to drive approximately 26 miles to the specials. Cedar Rapids Airport) and several different bus ser vices proposed to operate directly from Iowa City to SELECTED EVIDENCE OF EXTERNAL VALIDITY Chicago. At the time this paper was written, regu lar air service was offered by Ozark, Midstate Air, This section briefly outlines the results of three and Mississippi Valley Airlines. All operate non recent tests of intended-choice-based models derived stop services with flying times that range from 54 from controlled experimental manipulations of choice min to an hour and 45 min. All airlines had bever alternatives as described in previous sections of age but no in-flight food service. this paper. Other evidence of validity is reviewed Individuals were asked to choose among six alter by Levin, Louviere, Norman, and Schepanski (13) and natives: (a) regular air service at a particular elsewhere (8,ll,12,14,15,25,30) and is therefore price, (b) a bus service with drink and food service omitted in theinterests Of brevity. Suffice it to at a particular price, (c) a bus service with drink say that since 1975 intended-choice-based methods service but no food at a particular pr'ice, (d) a bus have compiled a consistent record of empirical suc service with food service but no drink at a particu cesses in validity trials in the United States, Aus lar price, (e) the current bus service with no food tralia, and The Netherlands. The results reported or ·drink service at a particular price, and (fl some here are representative of these other findings. other method of travel, such as private vehicle. The first choice study to use the methods de Respondents were asked to make choices in 16 differ scribed above was conducted on behalf of a major pet ent choice sets, which were developed by considering food manufacturer. Because the results are propri the air and four bus modes as factors with four etary, we provide only sufficient description to levels of pricei other was not given a price because assess the outcome. it would vary from respondent to respondent. Random samples of pet food users were selected Respondents consisted of a sample of 99 individ from several major markets in the United States in uals chosen for convenience and willingness to par such a way as to be representative of the market. ticipate and were drawn from three groups: (a) 33 Subjects interviewed were shown 16 different choice Iowa City air travelers interviewed in the departure sets consisting of combinations of 13 target pet areas of the Cedar Rapids Airporti (b) 33 bus food products based on a main-effects plan
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