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