Division of Research Graduate School of Business The University of Michigan Admini stration July 1973 CONJOINT MEASUREMENT: A MARKETING LITERATURE REVIEW WITH AN ANNOTATED BIBLIOGRAPHY Working Paper No. 81 by Gerald Linda Research Fellow FOR DISCUSSION PURPOSES ONLY None of this material is to be quoted or reproduced without the express permission of the Division of Research,

CONTENTS Introduction Conjoint Measurement What is it? How does it work? What are its advantages and limitations? What are some implications? Conclusion Placing Conjoint Measurement in the Taylor-Kinnear Multivariate Method Class System 1 I 1 5 11 14 15 17

I TABLES 1. Rank Order by Weight 2. A Conjoint Measurement Solution 6 7

FIdURES 1, A Classification of Multivariate Methods 18

I

Introduction Conjoint measurement is a fundamentally different, relatively new means of measurement developed by Tukey and Luce in 1964, In the nine or so years since their break-through only a limited literature has evolved, mainly in mathi ematical psychology and psychometrics. The marketing literature dealing with conjoint measurement is even-more scanty, consisting of only two Journal of Marketing Research articles and a handful of working papers and presentations of limited circulation, (However, Green and Rao do have a book forthcoming. ) This limitation is not as severe as might be supposed, however, because Young has shown that the nonmetric, multidimensional scaling models represent 1/ a special case of the more general conjoint measurement model - The literature is replete with discussions of these models even though their history goes back onlyAtwo years to Shepard in 1962. Conjoint Mea surenment What is it? The literature which does exist provides these explanations for conjoint mea surement: The word, "conjoint" has to do with the fact that we can measure relative values of things considered jointly which might not,be measurable: taken one at a time. 2/ I/ Forest W. Young, "A Model for Polynomial Conjoint Analysis Algorithms, in Multidimensional Saling, Vol..I, ed. by Roger N,. Shepard, A. Kimball Romney, and Sara Beth Nerlove (New York: Seminar Press, 1972), p. 70. 2/ Richard M. Johnson, Trade-off Analysis: A Method for Quantifying Con s.-umer Values (Chicago: Market Facts, Inc., September, 1972), p, 2,

.Z An outco me or an event is conjoint if it represents a combination of two or more elements~ Response to relatfonships involving pairs of objects is conjoint as is also the case of a response to a pair of items involving a person and an object. If we can establish an order relation on such pair. s we may be able to upgrade the data to some stronger form of scale [Italics-in the original]o 3... This appr'oa'ch holds some promise for describing aspects of personal choice among complex alternatives where no alternative '"dominatess" the others (io e, is at least as good as any other on all attributes of interest andis strictly better than any other on at least one)o 4/ Conjoint measurement is concerned with the joint effect of two or more independent variables on the order'n of a dependent variable [Italics in the original]o5 / In the conjoint measurement series we are concerned with deriving a set of values from a specified polynomial of lowest degree, such that the values map into a set of ranksoo o new measurement models by which one's preferences over a set of multi-attribute alternatives can be structured in terms of the part-worth contribution that each attribute state makes to one's overall evaluation of a multi-attribute alternative, This approach [is] called conjoint measuremento 7/ 3/ Paul E. Green and Frank J. Carmone, Multidimensional Scaling and Related Techniques in Marketing Anal sis (Boston: Allyn and Bacon, 1970), po 10. 4/ Paul E, Green, "M'lti-.Attribute Decisions in Marketing Behavior, The Wharton Quarterl Volo VII (Fall 1972)., p 47 5/ Paul E. Green and Vithala Rao, "Conjoint Measurement for Quantifying Judgemental Data, " Journal of Marketing Research, Volo VIII (August 1971), p, 3550 6/ James C. Lingoes, "A General Survey of the Guttman.-Lingoes Nonmetric Program Serie s, " in Multimexsio Scaling Vol. I, ed, by Roger Shepard, A. Kimball Romney, and Sara Beth Neerlove (New York: Seminar Press, 1972), p. 63, 7/ Green, "Multi-Attribute Decisions, "

"3" Green notes further that conj.oint measurement represents a new type of measurement because behavioral scientists cannot usually obtain data more strongly scaled than rank order, yet the results of conjoint measuemrent are 8/ intervally scaled.- And Johnson has used conjoint measurement to produce ratio- s caled value s Young has outlined the general nature of conjoint measurement as follows: it is often-the case that while one of the goals of scientific investigation is the decomposition of complex phenomena into basic factors, the factors cannot be measured independently and that only *the- ord;er:; heir joint effects is known, This is the conjoint measurement pro'Oble.m and the combination.r.ule is known. a's the conjoint measurement mode l. 9 To further help conceptualize the ature of conjoint measurement, note that Taylor (in a-conve rsationwith the author) suggested that:the method can be thought of as the analysis of variance for ranked data, This is, in fact, how Young described. Tukey and Luce s original work: "it is 'ba-s:ically an additive model and,, an analog of two way analysis of variance. 10/ 3Res 8earch i'nto the chara cter of conjoint measurement has proceeded:in two directions: one ha s- been a continued:vestigation into-tits -theoretical bases, and the other has been the development of computer "algorithms for!1/ constructing the actual scales themselves. -/ While Green's work has ~II — -~-, —......... 8/ Ibid,, p. 48. 9/ Young, "A Model, p, 69. 10/ Green, "Multi-Attribute Decisions," p, 48. 11/ Young, "'A Mdelt p. 77,

focussed on an additive version of the model, Young and others have shown that a great many other model formulations are possible (multiplicative, lexicographic, interactive, etc. ). Several versions of the additive and multiplicative models are well known and available. Further, though additive models are more frequently encountered in practice, according to Johnson the difference between them and' a multiplicative model is important only in a 12 / computational sense.,- For example, by the use of logs a multiplicative model could be converted to an additive one, Researchers at Market Facts, Incorporated, a private market research firm, have tied conjoint measurement to classical economic utility theory, Fiedler, for example, has suggested that, "'It is possible that the consumer is unawa re of the numeri'cal values of his utilities, but: that they may be revealed 13/ through his choices among product concepts, -- Moreover, Johnson has added, "The basic idea is that by providing consumers with stimuli from among which to chose, we can make inferences about their value systems ba-sed upon behavior 14 / rather than self-reports.O 1 Johnson has also argued that conjoint measurement provides data superior to that obtained from asking consumers for judgements regarding the 12/ Johnson, Trade.off Analysis, po 4. 13/ John A. Fiedler, Condominium Design and Pricing: A Case Study in Consumer Trade-off Analy.sis (Chicago: Market Facts, Inc., at the Association for Consumer Research, November 3, 1972), pp 1. 14/ Johnson., Trade-off'Analysis, p. 2Z

importance of variou attributes, because these judgments are not necessarily 15/ meaningful unless obtained in a specific context.'/ Thus the importance of the attribute, safety, might vary as it refers to childrengs pajamas or to automobiles Further, a conjoint measurement procedure is seen as superior to the task of having the consumer identify ideal levels of attributes because ii many cases this ideal will vary from consumer to consumer, and in other cases all consumers will want as high or as low a level for an attribute as is possible, i9 e, safety 16/ or priceIn conclusion, "conjoint measurement is considered a pra;ctical application of the economists' utility theory of buyer behavior in that, o, choice behavior is governed by a trade-off between. o values such that though the utilities may not be able to be articulated, they will be revealed by choice 17., / behavior. '" 1 How does it work? Operationally, the essence of conjoint measurement can be simply described. The first step is to obtain rank-order data on all critical combinar tions of attributes. In theory there can be any number of attributes, 'and each attribute can be multir'leveled, i e., several prices or colors, etc. This e.. e. sever ices or 15/ Ibid, p.,'- - 1. 16/ Ibid. 17/ Ibid., p 2.

arrangement can be conceived as a matrix, with each cell containing a number which indicates the rank (relative desirability) of that combination of attribute S (The existing algorithms can handle ties and missing datao ) The next step requires the 'use of one of the computer algorithms to generate a model whose coefficients are such that when they are combined (added, multiplied, etc. ) they will produce a matrix whose numerical values in each cell rank in the sarme:order as the original datao TABLE 1 Rank Order by Weight Size _ Platinum Gold Silver Steel -Alumiwnu m Largest 1 2 5 8 15 Large 3 4 9 11. 20 Medium 6 7 13 14 22 Small 10 12 17 19 24 Smallest 16 18 21 23 25 b........ Source: Richard M, Johnson, Multiplicatve Conjoint Measurement: A Physical Example (Chicago, Ill.: Market Facts, Inco, October, 1972), p. 1o Table 1 corresponds to the first step: A respondent ranked twentyfive metal balls in terms of their weight,,

-7 -TABLE 2Z A Conjoint Measurement Solution. F s.. Column Factors Row Factors499.10.4.2 - - Z999; 1499. 0.9 - z - 090.4717.1943 (1 1415(2) 077. (3) (4) (9) 20(8).03 ).2376.o979 3).0712,0356().0259(11). 069(2.1716 0707(6).055(7) 0 (3) 7(14) 0050(22),~(0858.0354(1).0257(12) 09(17) 4(91 o (24) ~ 0332 1 3 7 1 3 ) 010 0 003 6 o0009.0332.0137(6.0,oos21.0 362.. 009(25) Source: Richard M. Johnson, Multiplica.ti've Conjoint Measurement: A Physical. Example (Chicago, I1i.: Market Facts, Inc., October, 1972), p. 2. Table 2 corre-sponds to the second step: A m.rodel-.was '. created so. that when its coefficients (the row factors and column factors) were multiplied. together the numbers yielded were ranked in the same order as in the original matrix.. Johnson pointed out;that the row and column factors in Table 2 can be modified in two ways without destroying their ordering propertyo For example, each set of row factors or column factors could be multiplied by a constant or 18/ raised to the same power, and the ranking order would be preserved.-8/ Thus, by rescaling these row and column factors, we can approximate not only the original rank orders of the metal balls but also their actual weights when these were unknown t'o begin with! 18/ Richard M. Johnson, Multiplicative Conjoint Measuremen Physical Example (Chicago: Market Facts, Inc9, October, 1972), pp. 2-3.

The conjoint measurement programs are iterative in natur'e and usually 19/ cease calculating when one of three conditions is met:1o when a goodness or badness of fit criterion is at an i. a c ceptabte Ileve'; 20 when there is no significant improvement in fit after a specified number of iterations; 30 or when a specified number of iterations has been reached. There are several criteria used to establish goodness (or ba'dne'ss) of fito The most common-ly 'used is Kendall' s Tau, but another has been developed and called Theta by Market Facts, Still another developed by 20/ Market Facts has been termed Phi,- Tau is based on a count of errors between actual ranks and computed ranks without regard for their size; Theta is obtained by cumulating squared differences (and seems similar to 21/ Kruskal's Stress); and- Phi is based on ratioso — Johnson reported that, although the three meas'ures are theoretically different and have separate mathematical properties and weaknesses, i.eo, degeneracy, in practice 22/ all three have worked equally wello. Young-, in his paper on conjoint 19/ Jo Do Davidson, Forecasting Demand for a New Mode of -Trans, portation (Chicago: Air Canada, Association for Consumer Research, November 3, 1972), p. 40 20/ Johnson, Trade-off Analysis, pp. 1'011o 21/ Ibido 22/ Ibid,

-9" measurement, discusses his versions of these fit criteria in somewhat 23/ different terras.- So far there have been two ways to collect data usable for conjoint mfeasurement. One method has been that chosen by Green and Rao, and the other has been developed by Market F lcts, Inc. The Green-Rao method can be considered more realistic conceptually, but operationally it is more difficult to use. Their approach consists of providing respondents witfh product concept descriptions with each concept having a defined levet-el of each attribute. The respondent's task is to provide rank orders of preference among a set of such concepts, 4/ Because each concept is elaborately defined, realism is presumed to adhere, but "for many product categories it appears that upwards of a dozen product attributes may have to be studied simultaneously, ' and "it is hard to see how this many attributes can be handled if all concepts are to be given a specified 25/. level of each attribute.. "'/The point here is — that very quickly we can see that a respondent could be called on to make an awesome number of comparisons, many of which would be of an extremely difficult;:nature, This procedure is clearly unfeasible as is the design of such a questionnaire. Therefore, Green, Wind, and Jain, 23/ Young, "A Model," pp. 8084, 24/ Johnson, Tradeoff Analysis, p, 130 25/ Ibid, po 250

-10 - in one experiment, used only thirty out of a possible sixty combinations in a 26_/ menu-ranking tasko- And Green used a Latin Square design with what he perceived as the chief combinations of attributes in a hypothetical example 27/ involving the design of a floor- wax package. — The Market FPacts data -collection procedure "has respondents rank order several subsets, with the concepts in each subset varying in only' two attributes ~-/ Here again there can be only so many ranking tasks before respondents fatigue, but at least each ranking task is feasible. The procedure Market Facts has used most often cod'sist's of a personal interview in which the respondent is given a booklet, each page of which contains a trade-off matrix "with. rows representing var iou's levels of one attribute and columns representing levels of a second attribute',t- / The respondent is asked to rank the cells in this matrix, considering all other attributes to be held at a constant; It is at this point that the Market Facts procedure differs critically from Green and Rao's, The "'other things being equal"' instruction makes the whole procedure less realistic. 26/ Paul Eo Green, Yoram Wind, and Arun K. Jain, "Preference Measurement of Item Collections, Journal of Mareting search Vol IX (November 1972), p. 373. 27/ Green, "Multi4Attribute Decisions," pp. 48-9. 28/ Johnson, Trade-off Analysis, po 13o 29/ Ibid, p. 12. ---. — _.

-...1 - Market Facts has derived from its experience several rule s;- of thumb which are worth noting: 1. Three appears to be the optimal number of levels for an attribute, In no case should a trade-off matrix have more than sixteen cells and nine is greatly to be preferred. This is a psychological limitation as respondents are overwhelmed by large matrices. 2. Each attribute should be compared to at least two and preferably three other attributes. 3. A respondent should have no more than about twenty rankingI tasks 4, Each pair of attributes which are not compared directly should be connected by a chain of comparisons no longer than about three links. 50 About sixteen attributes is the largest number that can be handled without compromising the above conditions, A smaller number is preferable. 0/ Additionally, Johnson noted that the role of the interviewer is important, for he must ensure that the respondent does not begin to reply mechanistically 31/ to the ranking task.What are its advantages:and limitations? There are two very obvious and practical advantages to conjoint measurement. First, from the relatively weak data input of ranks, results 30/ Ibid. 31/ Ibid....._.-:_-. _

scaled at the interval or ratio level are possible. Since mnuch behavioral science data are really only rank ordered, despite working assumptions to the contrary, this procedure is quite, desirable. Second, conjoint measurement has a very wide area of applicability. A third and more theoretical advantage inherent in conjoint measurement is that a large n'umber of different models in diverpe areas of' behavioral science already conform to the notions of polynomial conjoint rmea sur ement. Sa vage:s -e.peted utility mode in e conomi c s, the HIullian and Spencian performance models in psychology and the scaling models in psychometrics are but a few example s:./ _ Young,goes even further in speculating about the usefulness of conjoint mea surement: If in fact the analytic method proposed here is an useful as it appear-s to be, and if specific polynomial conjoint measurement:'models are found to describe data from many areas of research in the behavioral sciences, then the structure- of polynomial conjoint measurmes nt theory becomes more than simply a t/heory of measurement. It becomes a general unifying theory of behavior 33/ This statement may sound extreme, but nonetheless it is interesting to contemplate such a possibility. There are also, of course, several limitations to the use of conjoint measurement, One set of weaknesses stems from the assumptions of the 32/ Young, "A Model,;" pp... 101-02. 33/ Ibido

*. '.. ' ' - 1 3!, model. The model assumes that the attributes studied are independent, Johnson explained that this assumption of independence has two ramifications, "The first is that the attributes must be non redundant or more accurately equally redundant. t-/ Here the problem is to prevent overlap or attribute substitutions when we present a list of attributes to a respondent. However, "lacking a good way to measure the. extent of redundancy among the attributes in a list, " it seems the best that can be done is "to attempt to formulate attribute lists which are as non-redundant as possible.The second ramification of the independent assumption is that interaction among the variables must be at or near zero, For example, the degree to which a respondent prefers a dessert is independent of what he has had for a main course. Clearly this assum ption bf no interaction will be false in some cases, but "itb appears to be nearly enough true to be workable under 36/ ordinary circumstances, "36-..Green a nd- Rao-: sugge sted additional limitations, One is the previously discussed problenm of getting around ranking tasks of too formidable a nature, T hey co mmented:hat pre setl yles et lyeee i s known about which (and how many) 34/ Johnson, Trade-off Analysis, p 13. 35/ Ibid,, p, 14. 36/ Ibid:

-14.- 37/ comparisons are the best ones to omit. - Finally, in the interests of elegance, they speculated that it may be possible tq obtain equally comparable results by asking respondents to provide numerical data directly rather than first obtaining ranks and using conjoint measurement procedures to generate 38/ numerical values for the utility analysis.- No tests of this hypothesis have been made to date. What are some applications? Although the number of articles in the literature is few, nonetheless many applications of conjoint measurement in marketing have been tried or suggested. Market Facts has used its multiplicative model of conjoint measurement in pricing condominium apartment units in a building, and it feels the 39/ model can be of use in planning future building configurations,-" In addition, Market Facts has eduse- its version to study inter-city air travel for Air Canada, "the market for sophisticated office equipment, the operation of urban 40/ mass transit systems.. [and] financial services and government regulation, "-/ 37/ Green and Rao, "Conjoint Measurement'," pp, 359-360. 38/ Ibid. 39/ Fiedler, Condominium Design and Pricing, p. 18. 40/ Ibid...... _

-1.5I. Green and Rao, as well as Green, Wind, and Jain, have also suggested several applications for conjoint measurement, Some of these applications have been selecting medical journals for ethical drug advertising; evaluating discount cards to be offered to housewives; evaluating the seriousness of various kinds of. drug abuse;. evaluating vendors; determining price-value combinations; appraising new ventures; measuring attitudes; measuring the joint aspects of a 41/ 42 / promotional campaign; --- and determining the utility of item colle ctionsOther sugge sted applications include evaluating package -de sign components; determinxing market segments on the basis of produ'ct benefits; deciding what type of label information to use; measuring the conttribution of testimonial advertising to commercial effectiveness, recall, believability, etc.; estimating management tility functions; and examining differences among 43/ interest groups regarding public-service activities, — -..... -Conclusion. In summation:... conjdint measurement models hold much! promise for both the marketing practitioner and the theorist, The practitioner can utilize the models to make better marketing decisions in situations where critical _.' l n..... -... 41/ Green and Rao, "Conjoint Measurement, " pp. 356-3630 42 / Green, Wind, and Jain, "Preference Measurement."t 43/ Green, "Multi-Attribute Decisions, p, 51.

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-1 7 -Placing Conjoint Measurement in the Taylor-Kinnear: m:.: ultivariate Method Class S sm..... Taylor and Kinnear have recently published a working paper in which 44 / they updated their clas"sificatory scheme for multivariate method's. / (See Journal of Marketing Vol. 35, No. 4 [October, 1971ljfor their original scheme ) One of the modifications they included was the addition of conjoint measurement to the group of nonmetric interdependence methods9 If, however, as Young argues, conjoint measurement is the general model for nonmetric multidimensional scaling, then the Taylor-Kinnear chart could be slightly modified as shown in Figure 1, 44/ James R. Taylor and Thomas C, Kinnear, "Multivariate Methods in Marketing Research," Working Paper No. 72 (Ann Arbor: Graduate School of Business Administration, The University of Michigan. 1973).

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-19 - Annotated Bibiog ra2hy Davidson, J.D. Forecasting Demand for a New Mode of Transportation. Chicagor Air Canada, Association for Consumer Research, November 3, 1972o This paper can be divided into two partso The first part utilizes the Market Facts conjoint measurement model to estimate the importance of various attributes involved in inter-city travel between Montreal and Ottawao The second half of the paper then uses the data so generated to build a forecasting model for air usage of STOL aircraft- Fiedler, John A, Condominium Design and Pricing: A Case Stady in Consumer Trade-off Analysis. Chicago: Market Facts, Inc., Association for Consumer Research, November 3, 1972. In this presentation is a very clear discussion of the background and solution to the problems faced by a building developer in New Jersey, A multiplicative conjoint measureP ment model was used to aid in the pricing of condominium apartments, some of which viewed the Manhattan skyline and others of which did note Green, Paul Eo Mimeographed rough notes handed out at the American Marketing Association Doctoral Consortium at Austin- Texas, 1972. Green, Paul E, "MMulti-Attribute Decisions in Marketing Behavior- 0: The Wharton Quarterly, Vol0 VII (Fall, 1972), pp. 47-51. This very brief article is really a recapitu.lation of what Green has written elsewhere concerning conjoint measuremento In it, however, he does present some addi-tional:' potential applications. Green, Paul E.:; and Carmone, Frank J. Multidimensional Scaling. and Related Techniques in Marketinag Ana lysiso Boston: Allyn' and Bacon, 1970, One" of the Marketing Science Institute Series, thisbook, though relatively short, introduces the basic methods and problems of multidimensional scalingo It includes a twentypage appendix on available computer programs and a thirty-six page bibliography

-20 - Green, Paul E.S., and Rao, Vithala. "Conjoint Measurement for Quantifying. Judgemental Datao o _JnurnaofMetn Res arch 01. VIII (August, 1971), pp. 355-63. This was the first article on conjoint measuremenf to appear in the marketing literature, Necessarily brief because of the journalts format, Green and'Rao skipped the background and explanation of conjoint measurement to focus on how it might be applied, They favor an additive model, Green, Paul E'; Wind, Yoram; and Jain, Arun K, "Preference Measures of Item Collections, Journal of Marketing Research, Vol. IX (Novembe-r 1972), pp. 371-77, - Here Green et al, extend the work of his first JMR article to the consideration of a collection of items so that taken together they could be viewed as a single attribute. Addittonal applications are also suggested0 Johnson, Richard- M Multiplicative Conjoint Measurement: A Ph sical Examptle. Chicago: Market Facts, Inc., October, 1972o In ten pages, by means of an ingenious physical example from physics, Johnson explains the basics of conjoint- measure ment,... -- Johnson, Richard M- Trade -off Analysis: A Method for Quantifyifg Consumer,. Values, Chicago: Market Facts, Inc-, September, 1972. —.... Written for the nonmathematician, this working paper, in superlative fashion, introduces the technique of conjoint measurement, It is highly recommended, Lingoes, James C. "A General Survey of the Guttman..Lingoes Nonmetric Program Seriesi Multidimensina Scaling VoL I Edited by Roger N. Shepard, A. Ki;iball Romney, and Sara Beth Nerlove New York: Seminar Press, 1972, ppo 49-68. As' you would expect from the title, in this selection Lingoes discusses in general terms the features of the several nonmetric multidimensional scaling algorithms which he and Guttman have written, Three conjoint measurement algorithms are mentioned,

-21-. Taylor, James R., and Kinnear, Thomas C, '"Multivariate Methods in Marketing Research," Working Paper Noo 72, Gradulate School of Bus ines s Administration, The University 'f Michigan, 1973 ' ' In this short presentation, the reader is intr-oduced to several of the very new multivariate research tools (MNA, THAID, and conjoint nmeasurement) There is also a highly useful'1 updating of their classification scheme for mu:ltivariate mnethod-s Young, Forest, W. "-A Model for Polynomial Conjoint Analysis Algorithms, MEultdim.nsal Scaln Vol. I. Edited by Roger N.:; Shepard, A, Kimball Romney, and Sara Beth Nerl:ove New York: Seminar Press, 1972, pp. 69..104, For the -psychometrician, Young, s se le ction seeks to consolidalte many of the existing conjoint measurement models -and nonmetric multidimensional- scaling models into one general theory0 He discusses at some length the mathematical and statistical underpinnings of the theory of conjoint measurement and its tests of goodness of fit.