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Applied Psychological Measurement

DOI: 10.1177/014662168300700404 1983; 7; 427 Applied Psychological Measurement

Lee G. Cooper A Review of Multidimensional Scaling in Marketing Research

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A Review of Multidimensional Scaling

in Marketing ResearchLee G. CooperUniversity of California, Los Angeles

The domain of this review includes the develop-ment and application of multidimensional scaling(MDS) in product planning; in decisions concerningpricing and branding; in the study of channels of dis-tribution, personal selling, and the effects of advertis-ing ; and in research related to the fact finding andanalysis mission of marketing research. In research onproduct planning, specific attention is given to marketstructure analysis, to the development of a master con-figuration of product perceptions, to the role of indi-vidual differences, to representing consumer prefer-ences, to issues in market segmentation, and to theuse of asymmetric MDS to study market structure.Regarding fact finding and analysis, this review dealswith issues in data collection such as the responserate, time, and accuracy of judgments; the validity, re-liability, and stability of judgments; and the robustnessof data collection techniques and MDS algorithms. Aseparate section on new-product models deals with thedetermination of relevant product markets, the identifi-cation of determinant attributes, the creation of prod-uct perceptual spaces, and the modeling of individualor market-segment decision making. Three trends arediscussed briefly; (1) a trend toward finer grained in-spection of individual and group perceptions, (2) atrend toward merging consumer level measurementand market level measurements, and (3) a trend to-ward the study of the creation of new markets, ratherthan new products in existing markets.

Understanding the choices people make in themarketplace is the main goal of marketing research.

How people perceive the alternatives from whichthey choose is a fundamental question for this do-main. Multidimensional scaling, cluster analysis,factor analysis, multiple discriminant analysis, andconjoint measurement, as methods for representingperceptions, have all received major attention inthe marketing research literature.

The professional marketing research communityhas not lagged behind the academic community.In a survey of American Marketing Associationmembers who were company marketing research-ers or suppliers of marketing research to compa-nies, Bateson and Greyser (1982) reported extern-sive relevant applications of 13 techniques. Almost70% of the company researchers surveyed had usedmultidimensional scaling (1~~~), with two-thirdof these users finding the techniques relevant totheir problems. Almost 809k had used cluster anal-ysis, 86% had used factor analysis, and 56% hadused conjoint measurement. More than three-quar-, ters of the users of these techniques found themrelevant to the problems the researchers con-

fronted. Research suppliers surveyed had slightlyhigher usage and satisfaction rates.

Such technological diffusion is more likely tooccur when there is a symbiosis between the needsof the marketing manager and the curiosity of themarketing researcher. To understand the symbiosisand to help structure a review of the contributionsof 1~~~ to marketing research, it is useful to pre-sent a classic conceptualization of the role of themarketing manager.



428

In the late 1940s a marketing manager was termeda &dquo;mixer of ingredients&dquo; by Borden (1964), whodesigned a list of important elements or ingredientsthat make up a marketing program and a list offorces that bear on the marketing operation of afirm. The marketing mix includes product planning(e.g., what product lines are to be offered, whatmarkets to enter, and new product p®licy), pricingpolicy, branding, channels of distribution (e.g., thepaths products take from the manufacturer to theconsumer), personal selling, advertising, promo-tions, packaging, displays, servicing, physical han-dling, and fact finding and analysis. The marketforces that bear on the marketing mix include con-sumers’ buyer behavior (e.g., motivation in pur-chasing, buying habits, and situational influences),the trades’ behavior (e.g., the structure, practicesand attitudes of wholesalers and retailers), com-petitors’ position and behavior (e.g., industrystructure and direct competition as well as indirectcompetition), and governmental behavior (e.g.,theregulatory environment).On the role of a marketing r~~r~~~~r9 Borden

(1964) stated:The skillful marketer is one who is a percep-tive and practical psychologist and sociolo-gist, who has keen insight into individual andgroup behavior, who can foresee changes inbehavior that develop in a dynamic world, 9... His skill in forecasting response to hismarketing moves should well be supple-mented by a further skill in devising and usingtests and measurements to check consumer ortrade response to his program or parts thereof,for no marketer has so much prescience thathe can proceed without empirical check, (pp.4-5)

That such a complex and comprehensive man-date for marketing management has fostered theevolution of a specialization in marketing researchshould come as no surprise. Also contributing tothe Zeitgeist were the twin notions that marketingresearch should not be merely reactive, helping tofind a consumer market for the products whichspring forth as did Athena, fully grown from thehead of Zeus, but rather that marketing researchshould be proactive in aiding the design of products

that better match the needs and desires of con-

sumers.

It was in March of 1964 that Kruskal publishedhis work on nonmetric ~lC3S. By the summer of1964 data were being collected in six cities to useKruskal &dquo;s ~1~~4.~, 1964b) algorithm to help designthe ’perfect cup of coffee&dquo; (cf. Brown.. Cardozo, 9Cunningham, Salmon, & Sultan, 1968). The prob-lem was to array brand-to-brand similarities in amultidimensional space along with the verbal de-scriptions of product features, then to assess wherenew products (e.g., new blends of coffee) werejudged to fall. When the new coffee blend wasfound that matched the desired feature descriptionsin the judgments of consumers, the share of corn-petitive choices for this new coffee, as well as thesource of those choices, could be used to help es-timate the market potential of a new brand. Thelinking of brand perceptions with linguistic de-scriptions was the key contribution of sociologistand linguist Stefflre (cf. Brown, et al., 1968; Silk,1969; Stefflre, 1968). With a linguistic descriptionto help anchor the perceptions of the new productone could go about trying to design packaging andadvertising that conveyed the same or similar im-age as the new product itself. These are importantsteps in the design of an entire marketing programto convey a desired image.

Stefflre ’ similarity judgments came from a sim-plification of the conditional rank order task. In theconditional rank order task each stimulus serves in

turn as the key, and the other stimuli are rankedfrom the most similar to the key to the least similarto the key. In Stefflre’s simplified version eachbrand served in turn as the key, and the respondentsmerely checked the other brands in the list that theyconsidered &dquo;most similar to&dquo; the key. Aggregatedover individuals, these data correlated rather wellwith expensive brand-switching data from con-sumer purchase panels. Linguistic descriptions (e.g., 9&dquo;~ very dark rich coffee&dquo;) were imbedded into thespace in a seemingly ad hoe manner, individualdifferences were aggregated away, no account wastaken of the substantive asymmetries of the switch-ing data, and preferences were not formally con-nected to the spatial representation, but the ideasfit together in a compelling fashion. The work dealt



429

simultaneously with product planning, advertising,and packaging; and with the market forces of theconsumer’s buyer behavior and the competitors’position and behavior.

The early reviews and overviews (Frank & Green,1968; Green, 1970; Green & Carmone, 1969; Green,~~r~®~~, ~ Robinson, 1968; Net dell, 1969) mademarketing researchers aware of the broad spectrumof problems to which MDS could be applied. Theearly books and chapters (Green & Carmone, 1970,1972, 1973; Green & Greenberg, 1974; Green &Rao, 1972b; Green & Wind, 1973; Greenberg &Green, 1974; Stefflre, 1972) filled in the technicalpicture, and along with Green (1975a), delineatedlingering issues such as interpretation of ~b~5 con-figurations, stability and reliability, the relation ofperceptual analyses to choices, and issues of in-dividual differences.

This review will deal with the problems and pro-posed solutions as they developed principally inthe journal literature. The marketing mix elementswill serve as an organizing theme.

Product Planning

Product planning involves many different stagesand problems. In this section the studies have beenorganized into interrelated subtopics concerning ( 1 )market structure, (2) the evolution of a master con-

figuration for perceptions, (3) individual differ-

ences, (4) preferences, (5) market segmentation,and (6) market structure models using asymmetricdata. Models for new product planning, and stra-tegic models linking product planning to other ele-ments of the marketing mix, will be reviewed afterresearch on other elements is reported.

Market Structure Analysis

Market structure analysis deals with issues in

product planning as well as issues in the under-standing of the forces of competition. Two pointsare illustrated by ~l~.hr~s (1970) study of majorbrands in the cigarette market. Klahr showed thatwhen the dominant distinguishing feature of brandsis a binary characteristic (e.g., filter tipped versusnonfilter), nonmetric MDS algorithms can produce

degenerate results, progressively reducing the within-category distance and increasing the between-cat-egory distance until two points in space representthe two categories of brands.The first point is that marketing researchers re-

ceived very early warning of this kind of degen-eracy, This degeneracy made individual level anal-ysis tenuous, but 5 of the 10 judges in l~l~hr’s

study had significant correlations between their

preference scales and the distance of each brandfrom their most preferred brand in the individualspaces. The most preferred brand was used as asurrogate for an ideal brand.The second point is that it is practically impos-

sible to discuss the structure underlying similarityjudgments without dealing with the relations ofperceptions to preferences. Klahfs (1969) study ofhow college admission officers judged applicantsserved to underscore that not just brands, but theperceived interrelations among many sets of choicealternatives, could be represented with nonmetric~1~~. Nonmetric MDS was thus useful in under-

standing how people make choices.

The Evolution ®1° ~ Master forPerceptions

In this subsection are reported a series of studiesby Green and his colleagues which have providedleadership in this field and have brought richermeaning to market structure analysis. The Greenand Carmone (1968) study of the structure of thecomputer market over time introduced product lifecycle analysis using nonmetric MDS. They com-pared obverse factor analysis (i.e., factor analysisthat explores the structure underlying brands ratherthan the structure underlying descriptive variables)with TORSCA (Young & Torgerson, 1967) andparametric mapping, i.e., a nonmetric 1~~~ rou-tine that emphasizes maintaining local monoton-icity but relaxes monotonicity for very dissimilarobjects (Shepard & Carroll, 1966; cf. Coxon, 1982,p. 159 ff.). Rather than just looking at the trendsin aggregate sales over time to reflect where a prod-uct was in the cycle of introduction, growth, ma-turity, and decline, comparisons based on productcharacteristics in an innovative market, such as



430

computers, could reveal this cyclical structure. Pro-file distances from 75 normalized characteristicswere calculated over the 12 computers, and the 12x 12 distance matrix was analyzed by all threemethods. Obverse factor analysis and TORSCAfound clusters of three generations of computers. aParametric mapping did not. Emphasis was placedon multimethod comparisons when little was knowabout the match of the functional relations under-

lying objects to the assumptions implicit in an anal-ysis. o

Green and P/Iaheshwari (1969) investigated theperceptions of common stocks as investment ve-hicles. They used multiple regression to imbed

property vectors into the two-dimensional space.The ratings of each object on each property werethe dependent measures, and scale values of theobjects on each dimension were the independentvariables. The multiple regression weights wereused as the coordinates of the property vectors. Aswas also found by Krampf and Williams (1974), 9the oblique vectors of perceived growth and per-ceived risk correlated highly with the two dimen-sions of the configuration. For each of the twogroups in this study, preferences were imbeddedinto the space using Carroll and Changes (1967)external analysis of preferences. For one group, avector model indicating the direction of preferencegave an adequate representation. For the other group, 9ideal coordinates were appropriate. On one dimen-sion the closer stocks were to an ideal location, themore preferred they were; whereas on the otherdimension the closer stocks were to an anti-ideal

location, the less preferred they were.Green, Maheshwari, and Rao (1969b) used non-

metric MDS to investigate the notion that con-sumers purchase products that have images similarto their own self-image. By scaling average simi-larities, imbedding property vectors for interpre-tation and using self-image ratings as a surrogatefor preference, they found that some consumers doand some do not desire automobiles with imagessimilar to self-images. This equivocal conclusionhelped foster an understanding of the need to rep-resent the systematic nature of individual differ-ences in perception and preference.

Again working with automobiles, Green, Ma-heshwari, and Rao (1969a) collected similarities,preferences, and semantic differential ratings fromtwo groups of respondents. Each group rated 11 1cars from a 17-car list, with 5 cars in commonacross groups. They demonstrated stability for theproduct spaces derived from the similarity mea-sures compared to the spaces derived from profiledistances over 20 semantic scales. The set of 5 cars

remained stable over changes in surrounding stim-uli. Comparison of TORSCA versus parametricmapping showed at least one stable dimension acrossthe two methods.

Green and Carmone (1971) used a three-wayINDSCAL analysis to demonstrate that task-spe-cific ratings tap only a subset of the dimensions inthe conceptual space of the individuals. Hustad,I~ey~r9 and Whipple (1975) integrated eight usageoccasions and context-specific ideal points into ananalysis of market structure. Mauser (1980) scaledpolitical candidates along with campaign themesto discover themes that were highly popular andthat appealed to a candidate’ current supporters.

Green, ~ir~d9 and Jain (1972) demonstrated thatheterogeneous collections of stimuli can be mean-ingfully scaled in a common space. Respondentsjudged the relevance of common personality traitsto ’ &dquo;other persons’

&dquo; choices of automobile brands,occupations, and magazines. For each of five carsa respondent was shown a list of 14 personaltytraits and asked to rank the traits according to thelikelihood that a person who owned that car would

possess that trait. This was repeated for five oc-cupations and then for five magazines. Then eachrespondent was shown, sequentially, two sets of25 cards each: all combinations of five magazinesand five cars formed the first set and five occu-

pations together with five cars formed the secondset. These were sorted into four ordered categoriesto reflect the probability that a person with a par-ticular occupation would own a particular car orthat a person who read a particular magazine wouldown a particular car.Even though the data were ranked and ordered

categories, all variables were converted to standardscores and the Howard-Harris (1966) clustering



431

routine was used to find four homogeneous groupsof individuals, Within each group the original 14trait rankings were averaged over individuals forthe 15 cars, occupations, and magazines. ProfileEuclidean distances were computed on these av-erage ranks. Acceptable three-dimensional stressesfor the TORSCA-8 solutions were found for each

group. The occupation-car and magazine-car or-dered category scales were averaged within groups.The complex matrix of associations would havenine sections for the Cartesian product of the setof occupations with the set of magazines and theset of cars. With only the occupation-car and mag-azine-car sections being of interest, the sublist

splitting feature ®f I~-I7-~CA~ V (Kruskal, 1968)was used so that the nonmetric constraints weremaintained only over the two sections. Good fitswere again obtained in three dimensions for eachgroup.The two configurations for each of four homo-

geneous groups of individuals were used as eightpsuedo-subjects of an INDSCAL (Carroll & Chang,1970) analysis by computing interobject distancesin each configuration. The three-dimensionalINDSCAL solution was comparatively easy to in-terpret in terms of (1) a prestige dimension, (2) asportiness-versus-conservatism dimension, and (3)something akin to a masculinity-femininity dimen-sion. The respondents’ perceptions of object con-gruences (occupation-car pairs and magazine-carpairs) &dquo;were highly associated with the relativenearness of these objects in an independently ob-tained (reduced) trait space&dquo; (p. 208).

If the Perreault and Young (1980) illustration ofALSOS had been available earlier, the rank-orderdata would not have forced the methodologicalchoices made here. Averaging rank-order data isnot a very desirable methodological alternative.

Further, profile distances can produce compara-tively low stress solutions while doing a relativelypoor job of recovering structure (Dr~s~~~v ~ Jones,1979). Despite the information loss inherent in theprocedures, it does appear that quite heterogeneousitem collections can be meaningfully displayed ina common space.

Green and Rao (1972a) used a similar series of

methods to develop a master configuration for 15bakery items that might be eaten at breakfast. Di-rectly judged similarities for men and women inthe respondent pool were averaged separately andscaled in three dimensions using TORSCA. Ratingof the bakery items on 7-point bipolar scales wereaveraged for men and women; Mahalanobis dis-tances were computed over 10 scales and the resultsalso scaled in three dimensions by TORSCA. Fi-nally, preference ranking of the items on each ofsix different usage occasions were averaged formen and women and parametrically mapped ontoa stimulus configuration in three dimensions.The Euclidean interobject distances from these

16 scaling solutions became the input to an IND-SCAL analysis. The resulting dimensions (1) sep-arated the meal type items from the snacks, (2)separated the sweet from the nonsweet items, and(3) separated the cake-like items from the bread-like items. The dimensions were correlated. The

pseudo-subject dimensional saliences were easilyinterpretable and gave a clear representation of howdifferent usage occasions corresponded to differentdimensional saliences. It is difficult to assess what

impact the averaging of ordinal ranks had on theseresults. Arabie, Carroll, 9 1~~~~rb® and Wind (1981)reanalyzed these data and found five overlappingclusters of pastries, 9 f®®d spread with butter, toastedfoods, sweet foods, and relatively simple breadfoods.

The last two studies involve the imbedding offeatures into a product space. Green (1974) col-lected subjective ratings from respondents regard-ing { 1 ) the degree of belief that if a particular fea-ture is present, then feature j would also be presentin a typical brand, (2) the degree of belief that aparticular brand possesses a particular feature, and(3) the desirability of a particular feature in eachof a series of usage occasions. For m features, nbrands, and p usage occasions this results in an(m + n + p) X m data matrix for each respon-dent. Green based his analysis on the average ofthe subjects’ matrices. The two-dimensional con-figuration from M-D-SCAL V was interpreted asan approximate radex. The circumplex notion didseem to fit to a certain extent. Associated items



432

frequently showed up as neighbors in an MDS con-figuration. Neighbors connect to other neighbors,forming something like a circumplex regardless ofwhether or not a simple interpretation exists for thedimensions. In any case, Green’s method of imbed-

ding features into a product space is much less adhoc than Stefflre’ methods (cf. Brown et al., 1968,p. 464).

Finally, Green, Wind, and Claycamp (1975) de-veloped a master configuration from the same basicdata as described above, but with different anal-

yses. Ross and Cliff’s (1964) generalization of theinterpoint distance model was used to develop threefeature configurations, one from each section ofthe (m + n + p) data matrix for the average in-dividual. Interfeature distances in these three con-

figurations became psuedo-individuals in an IND-SCAL analysis. A five-dimensional solution re-

suited, with two common dimensions (i.e. natural-artificial and rich-light), and three solution-specificdimensions. The two common dimensions became

the target for fitting brands into the space withPREFMAP (vector model) and then for fitting de-sirability ratings for features of the favorite brandinto the space using the ideal point version ofPREFMAP. From this master configuration can bejudged the aggregated association of features withbrands as well as the features desired in a particularfavorite brand. Arabie et al. (1981) suggested thatoverlapping clustering in this master configurationwould be particularly interesting.

Probably the least desired result of an MDS studyis a product or brand map that seems uninterpret-able. The series of studies just described in thissubsection offer ways of enriching the interpreta-bility of a perceptual space by positioning featuresof products, associated life style items, and pref-erences into the map alongside the brands.

~~dl~l~a~~l Differences

Although studies of the systematic differencesamong individuals appear throughout this review,three studies are reported here to introduce the topic.In the first, Kinnear and Taylor (1973) used a re-sponse measure, an ecological concern scale, tosegment the sample. In the second, Rao (1972),

induced individual differences by an experimentaldesign involving the information each respondentreceived. In the third study Ritchie (1974) formedgroups of individuals by clustering their dimen-sional weights from an INDSCAL analysis.

Kinnear and Taylor (1973) studied the effects ofecological concerns on the perceptions of con-sumers of laundry detergents. At the height of con-cem about water pollution from phosphates andenzymes in detergent, they sampled 500 membersof a consumer panel. A behavioral and attitudinalscale of ecological concern was used to segmentthe sample into five subgroups expressing increas-ing ecological concern. Similarities judgments forfive phosphate detergents, two nonphosphate prod-ucts and an explicit rating of an ideal detergentwere collected before the attitudinal measures wheretaken. The three-dimensional INDSCAL solutionfit quite well and seemed interpretable in terms ofa phosphate dimension and two cleaning powerdimensions. The analysis of dimensional weightsfor the five groups demonstrated that the higher abuyer’s ecological concern, the more salient is theecological dimension in perception and the greateris the perceived similarity of brands that are eco-logically nondestructive.Rao (1972) induced individual differences through

experimental manipulation of the amount and kindof explicit information provided as a basis for sim-ilarity ranking of 12 cars. The 2x2x2 design(with two empty cells) varied: brands identified ornot, semantic descriptions provided or not, andprofile descriptions provided or not. The cell withno brands identified, no semantic description, andno profile description was deleted from the designfor obvious reasons; and the condition containingboth semantic descriptions and profile descriptionswas deleted to avoid information overload. Thethree-dimensional INDSCAL solution was inter-

preted as (1) l~ax~ri®~s~~ss9 (2) domestic versusforeign manufacture, and (3) size. The absence ofbrand name de-emphasized salience of the originof manufacture; whereas without semantic descrip-tions the luxuriousness was de-emphasized; andwithout the profile information size was de-

emphasized. The nature of the information in eachcategory made these findings quite reasonable. The



433

salience differences were still significant after 10covariates were introduced to account for (nonex-perimental) individual differences among subjects.

Ritchie (1974) studied the nature of individualdifferences in perception of 12 leisure-time activ-ities. Over three trials he found that there was sig-nificantly less variation within individuals in IND-SCAL saliences than between individuals. How-

ever, when he formed five perceptual groups using~~h~s®r~9s (1967) hierarchical clustering on dimen-sional weights, he found that the five groups didnot differ between groups in interest or participa-tion in the activities and for the most part did notdiffer in the 18 Rokeach measures of personal val-ues. The problem here may stem from Ritchie’suse of hierarchical clustering on differences in di-mensional weights. Two individuals on a vector,just differing in length from the origin, will havethe same perceptual configuration. They will differonly in the extent to which the scaling model fitsthe approximate individual scalar products matrix.So differences in perception are better measuredby the angle in radians between the vectors for twoindividuals.

Preferences

Preference is a key concept for understandingthe linkage of perceptions to choices. Four ap-proaches to preference research are considered inthis section:

1. The huge marketing literature on conjoint anal-ysis merits its own review and is just brieflymentioned here.

2. The analysis ofmicropreference structures in-vestigates how individual level utility scalescan be developed from preference judgments.

. Internal analysis of preferences attempts to usethe preference judgments alone to developconfigurations of brands. Some internal anal-ysis techniques attempt to array directions ofincreasing preference into the brand maps (i.e.,vector preference model); whereas other in-ternal analyses of preference attempt to rep-resent the brand perceptions, along with idealpoints for individuals or groups, in a joint space.

4. External analysis of preferences attempts tomap preference vectors or ideal points ontopredetermined perceptual maps to create jointspace representations.

Although the first two approaches are treated insubsections of their own, the last two approachesare considered in three subsections on joint spaceanalysis.

Conjoint analysis. Green and Rao (1971b) in-troduced the marketing research community to con-joint measurement. They tied the general conjointanalysis model to the specific nonmetric MDS modelby multidimensionally scaling law enforcement of-hc~rs9 judgments of the severity of different formesof drug abuse. Green, Wind, and Jain (1972) used~l~P~~F9 Chang and Carroll’s (1968) internal

analysis of preferences, to represent preference het-erogeneity in what was basically a conjoint analysisstudy of dessert preferences; and Green and Devita(1975) used R4DPREF on an interaction preferencetable to provide a graphical aid for interpretinginteraction effects in an extended conjoint analysismodel.

Micropreference structures. Bechtel and

0’Connor (1979) developed analysis of variance(AN OVA) tests for micropreference structures (cf.Bechtel, 1976). The first test on the graded pairedcomparison preference ratings (i.e. ~ ratings of thestrength and direction of preferences) attempts todetermine individual level utility scale values forthe objects. In an application to soft drink prefer-ences from Cooper (1973), 51 of the 52 respon-dents had statistically significant utility scales. Theywere then retained for further tests, which at-

tempted to determine if individual utility scales

were mediated by a vector model using perceptualattributes. In this case the perceptual attributes werethe first dimension scale values (a cola versus non-cola dimension) for the soft drinks from a metricscaling of similarities (cf. Cooper, 1972) and themean familiarity ratings of the soft drinks. Underthe hypothesis of a common perceptual configu-ration using these two attributes, the ANOVA modelrejected the fit of the vector model at the individuallevel in this example. The preferences seemed tooidiosyncratic to be predicted from a common per-ceptual configuration.



434

Bechtel and 0’Connor (1979) also provided asegment-based analysis of Dutch schoolchildren’snational preferences. The preference measures camefrom the logit of the proportion of children in seg-ment i preferring nation j to nation k. The overallutility scale was statistically significant, as were

the segment utility scales for Grades 2 through 6.66~Jtility scales broaden strikingly with increasingage, indicating better preferential discriminationamong older children&dquo; (p. 255). There was also asmall, but statistically significant, amount of sys-tematic unscalability. (Systematic unscalability wasalso significant in the aggregate of soft drink pref-erences.)

Bechtel’s ( 1976) tests allow for very fine grainedassessment of the fit of particular multiattributestructures to individual or segment preferences.Bechtel (1981) further developed this logit pref-erence model.Joint space analyses. The typical integration

of similarities and preferences is illustrated by Green,Carmone, and Fox (1969), who used TORSCA onsimilarity judgments among 38 television programsand followed with Carroll and Changes (1967; Car-roll, 1972) external analysis of preferences (PREF-MAP). The Doyle and ~cC~e~ (1973) study of themarket structure of convenience foods and f~er~y9s s(1975) study of potato side dishes are similar ex-amples.

Best (1976) took a much closer look at jointspace modeling as a potential theory of individualchoice. Although price considerations did not enterhis study, Best did track choices among eight softdrinks over a 12-week period (i.e., 2 weeks to

adjust to the apparatus and two 5-week consump-tion periods). At the midpoint of each consumptionperiod, conditional rank order similarity judgmentsand rank order brand preference were collected.From the first consumption period a readily inter-pretable three-dimensional INDSCAL solution wasselected. PREFMAP was used to imbed ideal pointsfor all 77 individuals.

Inspection of the relation of ideal distances andchoice proportions from the first period led to thespecification of five different mathematical func-tions relating distance from the ideal point to prod-uct choice. Ten people were represented with a

disjunctive model (i.e., the brand closest to theideal point dominated the choices). Forty-five peo-ple were represented by a hyperbolic model (i.e.,choice probability tapered off dramatically withincreasing distance from the ideal point). Four peo-ple were represented by a conjunctive, relevant setmodel (i.e., all brands within a certain distancefrom the ideal point had an equal probability ofbeing chosen). Four people were represented by alinear model. A polynomial model was needed torepresent 10 people; these people were dieters whohad nondiet ideal points for preferences. Brandsvery near their ideal points had a low probabilityof being chosen, as did brands that were very faraway. The diet brands nearest the nondiet ideals

had the greatest probability of being chosen. Fi-nally, four people were represented by a randommodel.

Thus, 73 of 77 models provided sensible cali-bration results. Although brand preferences wherestable over consumption periods, brand choices werenot. Fifty-seven of the 73 provided significant pre-diction of future brand choices. The drop-off waspartly attributable to six individuals who went offtheir diets in the second consumption period.

Huber (1975) compared five models for pre-

dicting preferences for different levels of tea andsugar in iced tea. All models were developed on16 experimental compounds in a lattice design (basedon the logs of the sugar concentration and tea con-centration) and were used to forecast preferencesfor seven validation examples within the lattice,

The three best models were an ideal point modelmapped onto the physical space, a naive model thatsimply averaged preferences for the four nearestneighbors, and an additive part-worth model. Nottoo far behind in forecasting ability were an idealpoint model in a psychological space and an ad-ditive model weighted by perceptual scale values.For all but the naive model it was possible to com-pare metric versions for the forecasts of each modelwith corresponding nonmetric versions. Althoughthere was considerable congruence between the re-sults within models, the metric version producedconsistently superior results.

Marketing researchers developed alternatives tothe multiple regression approach of PREFMAP.



435

Srinivasan and Shocker (1973) developed a linearprogramming technique for the external analysis ofordinal preference judgments, which they termedLINMAP (see ~®pl~i~s9 Larreche, & Massy, 1977,for a typical application). Pekelman and Sen (1974)developed a mathematical programming model thatwas very similar to LINMAP.

Explicit versus implicit i~~~d p®in~.~ injoint space~ep~°~.~e~~~gi®~,~. Another approach to joint spaceanalysis requests that the respondent explicitly ratean ‘~~d~~l&dquo; product along with the other objectsbeing compared, as was done by Kinnear and Tay-lor (1973). The ideal point for the respondents isthe position of the ‘6ide~l&dquo; product in the percep-tual space. Day (1972) compared cognitive con-sistency theories of attitude structure and multidi-mensional scaling using this approach. Specifically,he was interested in comparing the representationof preferences obtained from Lehmann’s (1971a)ideal distance model (based on specific attributemeasurements) with two nonmetric joint space rep-resentations : one with an explicit 6 ‘id~~l&dquo; productalong with the other objects and the otherrepresentation obtained through external analysisof preferences.The heuristic comparison between Lehmann’s

model and the nonmetric MDS approaches favoredMDS &dquo;because they [l~~S approaches] demandless complex and fragmented data from respon-dents&dquo; (p. 284). The explicit versus implicit idealpoint comparison revealed a modest displacementbetween the average explicit and average implicitideal points. l~®~a~~~r~ the rank orders of the pref-erences from the two points were almost perfectlycorrelated. Further, Lehmann obtained consider-able variation in preferences depending on the spe-cific usage context, i.e., preference judgments werenot context-free.

Holbrook and Williams (1978) compared theINDSCAL representation of 12 female singers col-lected with and without explicit ideal points. Theirconcern was with the affective halo that sometimessurrounds multiattribute judgments of brands (Fry& Claxton, 1971, went so far as to average scoresfor only those respondents who did not prefer abrand in order to avoid halo effects in the attribute

space they compared to their MDS representation).

Holbrook and Williams found that the inclusion of

an explicit ideal point did not distort the configu-ration of the other 12 singers. A clear two-dimen-sional interpretation (i.e., ethnic membership andcontemporaniety of style) appeared in both config-urations. The 66 intersinger distances correlatedaround .95.

The explicit ideal point approach is quite inter-esting but does create some problems. It is inap-propriate to consider one person’s judgments in-volving explicit ideal points to be comparable toother respondents. Averaging across respondentscan distort the position of the explicit ideal pointeven if the positions of the other products are un-disturbed.

Recent developments in joint space analy-sis. Some of the more recent applications of jointspace analyses have come from I~®~re9 Holbrook,and their colleagues. Moore, Pessemier, and Little(1979) applied Schonemann and ~I~~~’s (1972)unfolding model in three product classes: cake mixes,household cleaners, and toothpastes. They usedPessemiefs dollar metric for graded paired com-

parison preferences in which respondents estimatea monetary value for the difference in their pref-erence (cf. Pessemier, Burger, Teach, & Tigert,1971). After development of the configurations,interpoint distances in the joint space were used toestimate purchase probabilities. They noted the ten-dency of the dollar metric to underpredict prefer-ences for more preferred brands and to overpredictthose for less preferred brands. Using a powertransformation of the scale values to predict pur-chase probabilities corrected substantially for thebias. The corresponding predictions were made fromthe nonmetric unfolding option of KYST. For

toothpastes and cake mixes the Sch6nenxann andWang (1972) model produced statistically superiorpredictions. For household cleaners KYST was

slightly, but not significantly, better.Holbrook, I~®®r~9 and Winer (1982) applied

Levine’s (1979) procedure for developing joint spacesolutions from &dquo;pick any&dquo; data. In marketing re-search this is like a ~r~le~~~t9’ set model in whicha consumer picks from a large list or simply recallsall the brands he or she would consider purchasing.In ~~~ir~~9s model p~rs®r~9s ideal point is located



436

at the centroid of all the brands he or she picks,and a brand is located at the centroid of all the

people who pick it. Holbrook, Moore, and Winer(1982) applied the model to the representation ofradio listenership data, a large stimulus set, whichno one person could judge individually. They scaled1,380 respondents based on 25 radio stations, dem-onstrating the utility of the method when most othermethods are inappropriate or impractical. They alsoapplied the analysis to soft drinks and comparedthe representation to that obtained using KYST.The results were quite similar when both tech-niques could be applied. The problems that can beencountered with Levine’s (1979) technique stemsfrom (1) individuals who only rate one brand; (2)instability of the much less popular brands (sincetheir positions may be underdetermined); and (3)the pulling of the most popular brand to the centerof the configuration (e.g., Crest was in almost

everyone’s relevant set and thus positioned at thecentroid of the respondents).Moore (1982) and Moore and Holbrook (1982)

studied the predictive power of joint space modelsusing &dquo;hold out&dquo; brands and hold out concepts.This approach, which was also used in the vali-dation of the Pekelman and Sen (1974) mathe-matical programming model for attribute weights,tries to validate the predictive ability of a jointspace representation by assessing how well pref-erences or choices for different brands can be fore-cast once they are placed into existing joint spaceconfigurations. Moore and Holbrook found a markeddeterioration in predictive power when joint spaceswere derived on real objects and used to predictnew concepts. They have suggested conjoint anal-ysis as a more sound approach.Moore (1982) found that perceptual spaces built

from discriminant analysis used with external vec-tor models performed better across frequently pur-chased goods, compact cars, and services. Whereasthe conjoint model or multiple discriminant anal-ysis may be superior in these applications, the useof holdout brands is questionable. Without a modelfor how preferences change over the sets of brandsor concepts that form the judgment contexts, oneshould be wary of holdout brands. Their use ba-

sically assumes what is rarely true, i.e., that pref-

erences and choices are context free (cf. Cooper& Nakanishi, 1983). New-product models, dis-cussed at the end of this review, need to deal spe-cifically with this issue. Even in a new-productcontext, however, it is most often only one addi-tional choice alternative that the context must ab-

sorb, not six breeds of dogs, as in Moore and Hol-brook our an unspecified number of frequentlypurchased goods, compact cars, and unnamed ser-vices, as in Moore (1982).

1~~~P~~t Segmentation

Johnson (1971) said, &dquo; market s~~~cent~t~~~analysis refers to examination of the structure of amarket as perceived by consumers, preferably us-ing a geometric spatial model, and to forecastingthe intensity of demand for a potential product po-sitioned anywhere in the space&dquo; (p. 13). Accord-ingly, Johnson discussed the uses of S and othermapping techniques in a manner very similar tomarket structure analysis, product positioning anal-ysis, and any of the joint space methods previouslydiscussed.A more traditional approach to market segmen-

tation has been presented by Wind (1978). Heindicated that the classic price discrimination modelprovides a major theoretical rationale for the seg-mentation concept. Most simply, the price discrim-ination model rests on downward sloping demandcurves in a plot of price (y) versus quantity (x).Even at a high price, some individuals would de-mand a product. As price drops, the quantity de-manded would increase. With a single fixed pricefor a product, there is no ability to retrieve the&dquo;consumer surplus&dquo; (i.e., the area in the plot abovethe price line but below the demand curve). Fromthis point of view, market segmentation becomesa strategy for differentiating consumers so as toretrieve as much as possible of the consumer sur-plus. Thus, Wind’s discussion of the uses of MDSfocused more on the grouping of consumers thanthe positioning of products. The same physicalbundle of benefits may need different packaging,promotion, advertising, pricing, and distributionthrough different retail outlets to attract differentconsumer segments. He foresaw great potential for



437

the use of overlapping clustering in this domain.Young, Ott, and Feigin (1978) differentiated

segmentation on generic benefits from product-usage-purpose segmentation and from styling seg-mentation. The latter case is for products in which&dquo;the style, looks, appearance, or image is the

overriding criterion of marketing success&dquo; (p. 410).It is in this type of segmentation that they deemedmultidimensional scaling more appropriate.

Market Structure Using AsymmetricData

Lehmann’ (1972) study of market structure us-ing brand switching data demonstrated the differentemphasis transition data gave to a nonmetric MDSsolution. The emphasis on interbrand substituta-bility gives results more akin to preference map-pings than to similarity scalings (cf. Cooper, 1973).Lehmann’s (1972) analysis, however, actuallyeliminated the asymmetries by forming a weightedaverage. MDS analyses that maintained the basicasymmetries of brand-switching data are a veryrecent development. Harshman, Green, Wind, andLundy (1982) recently introduced the DEcompo-sition into Directional ~®l~p®r~~~ts (I~~DI~®1~)model to the marketing literature. They reported areanalysis of part of the free-association data fromGreen, Wind, and Jain (1973) and an analysis ofcar trade-in data from the 1979 model year. Brand-

switching data are very important in marketing re-search, and the DEDICOM model should enjoywide use. It is, however, quite different from thespatial MDS model that marketing researchers havecome to understand in that it requires ratio scaledata. Although some discussion of its applicabilityto interval scale data is presented, marketing re-searchers would be well advised to apply DEDI-COM to the obvious and available frequency-of-purchase data or transition probability data. As ahybrid between MDS and factor analysis, the useof interval scale data calls for ’ ’factoring’’ the dou-ble-centered score matrix. The model for the fac-

toring of double-centered score matrices is verycomplex (Tucker, 1956, 1968). There should bemany applications of DEDICOM in marketing us-ing the data for which it is primarily intended. The

analysis of trade-in data for cars is an excellent

example of the kind of thinking required to un-derstand asymmetric flows.

New Product Planning

Although the comprehensive new-product modelsare discussed at the end of this review, there isother research worth noting here. Morgan and Pur-nell (1969) are often cited for their research

on isolating openings for new products in mul-tidimensional space. They actually used factor

analysis and cluster analysis to get their productspaces. Lehmann (1974) investigated the usage ofTORSCA on linear and polynomial intercorrela-tions as an alternative to factor analysis in a newproduct setting. Albers and Brockhoff(1977) struc-tured the new product positioning issue as a mixedinteger programming problem (cf. Pekelman & Sen,1974) . Roberts and Tay lor ( 1975) used multivariateanalysis of variance (~A~10~A) to show that de-sign effects of new products can be traced by 1~~~5and are open to statistical confirmation. Silk and

Urban (1978) just mentioned the role of MDS innew product development; their illustration of theASSESSOR model used constant sum scaling ofpreferences, rather than MDS.

Pncmg

The two pricing studies reported here rely on theLancaster model (1966a, 1966b, 1971), Ryans’s(1974) description of Lancaster’s approach wassimply:

In contrast to the traditional economic theoryof consumer demand, which treats the prod-ucts themselves as the basic unit of analysis, 9Lancaster’s theory is based on viewing prod-ucts as bundles of product characteristics.

Lancaster assumes that these characteristics

are objective, measurable attributes of the

product. (p. 435)Ryans proceeded by invoking the limited infor-mation-processing capacity of consumers. Durablegoods have many objective, measurable character-istics, and the consumer will probably rely on onlya few &dquo;perceived&dquo; characteristics. These per-



438

ceived characteristics were represented with non-metric MDS in Ryans’s study.

Lancaster further assumed that &dquo;individuals do

not differ in their assessment of the amount of

characteristics possessed by a given product&dquo;(Ryans, 1974, p. 435). Ryans dealt with this be-haviorally unrealistic assumption by forming clus-ters that were perceptually homogeneous and byanalyzing each cluster separately. Ryans’s modelassumed that a consumer buying a durable goodpurchased a brand and the other goods and servicesthat together maximized his/her total satisfactionwhile meeting his/her budget constraint. Thus, anymoney conserved is used for utility-generating pur-poses. The analysis group rated 12 electric blenders.The three validation groups rated 13 blenders, withthe last blender presented with three different pricesbut with the other product characteristics the same.The similarity ratings on which the product spacewas developed were collected before the price in-formation was introduced. After the introduction

of price, rating scale judgments were collected,followed by preference rankings.The data collection procedure allowed the testing

of two assumptions. The first assumption is thatthe introduction of a dynamically continuous in-novation (i.e.9 a new product with a combinationof features that are also present in possibly differentamounts in .other products in the market) will notaffect consumers’ perceptions of the characteristicsof other products. A good congruence between the12-product MDS solution and the 13-product so-lution supported this assumption. The second as-sumption was that price would not act as a surrogatefor quality and thereby affect the perceived amountsof the other characteristics possessed by the newproduct. That is, the different price tags would notresult in different attribute ratings for the sameproduct. Only the attribute scale dealing with highprice versus low price varied significantly over val-idation groups. Ryans (1974) estimated a quadraticutility function (PREFMAP-Model 1; Carroll, 1972)on the positions of the brands in a three-dimen-sional space from M-D-SCAL-5M. The utilityfunction and price were used to predict the rank-order preferences for the new product among the12 other products. The STRESSes of the solutions

for the various clusters seemed somewhat high, andthe overall predictions of rankings from the quad-ratic utility formulation seemed modest. The bestprediction, however, occurred in the proportionsof first, second, and third rankings, which is thearena of greatest interest.

Hauser and Simmie (1981) postulated a simpli-fied lens model of consumer decision making.Physical features and psychosocial cues lead to per-ceptions, which in turn lead to preferences. Con-straints such as budgets join preferences in leadingto choice, and choice feeds back to perceptions.Expressing the belief that good models exist forthe other linkages, Hauser and Simmie concen-trated on the mapping of physical features ontoperceptions. To generalize the notion of an efficientfrontier in perceptual space for the &dquo;rational con-sumer&dquo; requires the heroic assumption that an ab-solute origin can be found for the spatial represen-tation. ‘1’h~.s9 in the case of ~~~.l~esi~s9 gentlenessand efficacy dimensions could be transformed intogentleness per dollar and efficacy per dollar. The&dquo;per dollar&dquo; notion is needed in their analysis tomake possible the definition of an efficient frontierfor the decisions of a &dquo;rational consumer.&dquo; Sincethe origin ofMDS configurations is arbitrary, MDSdoes not seem to be a candidate for constructingthe perceptual spaces on which the Hauser andSimmie arguments are based. Neither, then, arethe spaces derived from factor analysis or multiplediscriminant analyses. These are not techniques thatyield ratio scaled dimensions.

Although the issue of locating the origin to theperceptual space makes it difficult to understandthe applications of rational consumer theory, oneof Hauser and ~’ ’e9s (1981) theorems deals withconsumers, rather than with the convenient fictionof &dquo;rational consumers.&dquo; Their third theorem states:

If the consumer evaluates products in percep-tual space, then any consumer analysis thatdoes not consider the perceptual mapping, F(from physical characteristics to perceptualpositions), could identify &dquo;consumer opti-mal&dquo; combinations of product which are notefficient .... (p. 41)

This theorem, which they prove by counterexam-ple, has very important implications. Although,



439

for the &dquo;rational consumer&dquo; optimality in the per-ceptual space implies optimality in the space ofphysical characteristics, for the real consumer theperceptual analysis holds primacy. Whenever per-ceptions mediate preferences, the perceptual spaceis the place in which optimality analysis shouldoccur.

Understanding the impact of pricing on brandperception is problematic within the traditional MDSframework. Price as an attribute of a brand seemsmuch easier to study experimentally by using con-joint measurement designs or by using multiattri-bute choice models (cf. Cooper & Nalcanishi, 1983).One area seemingly ripe for investigation is howprice sensitivity might vary with perceptual posi-tion (e.g., proximity to an ideal point). Such astudy would parallel Clarke’s (1978) analysis ofadvertising effectiveness by perceptual position,discussed below in the section on advertising.

Branding

Although selection of a brand name for a newproduct is one of the tasks Stefflre (1968) and oth-ers have undertaken within a MDS framework, nostudies have been published, to the author’ knowl-edge, which deal solely with other aspects of theproblems of branding.

The selection of trademarks is an area in whichthe relation of visual images and the semantic im-age they connote could be important. The Young,Ott, and Feigin (1978) study indicating the utilityof MDS in segmentation based on style or imageseems to highlight some potential uses of MDS inevaluating trademarks. The Green and lN4c-Mennamin (1973) approach to advertising prob-lems, discussed below in the section on advertis-

ing, could also be used for many problems in

branding. aThe Rao (1972) study, which included a manip-

uation of whether or not brand information was

provided along with semantic descriptions or pro-tile description, indicated some potential uses ofMDS in determining the benefits of various brand-ing policies. e

Channels of Distribution

Products flow from the manufacturer to the con-sumer through the channels of distribution. Thestudies that deal with this topic focus mainly onthe relations among different retail outlets. Thoughmarket segmentation by types of retail outlets is

very clearly within the 6 ‘price discrimination’&dquo; ap-proach to segmentation (cf. Wind, 1978), no I~17Sresearch was found on this topic.

l~~c~~y and Olshavsky (1975) studied the dif-ferences between cognitive maps of retail locationsbased on MDS of proximity judgments and thosebased on hand drawings. They found that althoughhand-drawn maps were more like physical mapsthan are MDS maps, the MDS maps related more

closely to preferences and actual shopping behav-ior. Olshavsky, MacKay, and Sentell ( 1975) foundthat distances from MDS maps correlated better

(more negatively) with shopping behavior that diddistance from actual maps.The classic example of a necktie that sells at one

price in a department store and at a much higherprice in a men’s speciality store, indicates someinteresting possibilities for MDS research involv-ing channels of distribution. Part of a product orbrand image might interact with the images of dif-ferent retail venues. Research that required judg-ments on the compatibility of brands with differentretail outlets could lead to joint space representa-tions or master configurations that would be usefulfor marketing decision making.

Personal Selling

Only two MDS studies related specifically topersonal selling. Turner (1971) used nonmetric MDSto infer the number and kinds of criteria that in-dividual salesmen used in evaluating their cus-

tomers. Such an analysis becomes very similar toKlahr’s (1969) study of the evaluation criteria ofcollege admissions officers. Green and Mc-Mennamin (1973) took a different approach in oneof their examples of market position analysis. Alarge computer firm hosted a study that first mappedthe physical characteristics of the computer and itscompetition into what they called a &dquo;performance



440

space.&dquo; The similarity judgments on the computermodels were collected from salesmen, customers,and noncustomers:

The sales personnel’s perceptions agreed mostclosely with the objective (performance) po-sitioning of the computer models. However,the finn’ customers’ perceptions disagreed insignificant ways with the sales personnel’sperceptions, suggesting that the sales peoplewere not emphasizing certain performancecharacteristics of the company’ line that wouldenhance customer satisfaction. (p. 502)

Interpretation of the separate analyses suggestedspecific differences in orientation of customers andnoncustomers.

Advertising

There are three areas in which MDS has been

used as part of advertising research. The first in-volves how MDS can be used to track the effec-

tiveness of advertisements in repositioning orchanging a brand image. The second area dealswith the compatibility of attributes or slogans withthe perceptual image of a brand and the competitivebrands. The third area deals with how advertisingeffectiveness varies with perceptual position.

In the first area there are two studies: Smith and

Lusch (1976) and Perry, 9 ~zr~~li and Perry ( ~ 976) .Smith and Lusch (1976) tried to use nonmetric

MDS to assess how advertising can position a brand.Liggett & Myer wanted ~~~ cigarettes to be con-sidered a &dquo;full flavored&dquo; cigarette. They changedthe tobacco blend, filter9 and package design, andlaunched a &dquo;massive advertising campaign&dquo; (p.39). The promotion occurred in selected West Coastcities, which enabled Smith and Lusch to studyperceptual positions before and after with a controlgroup. Smallest Space Analysis (SSA; Guttman,1968) on the similarity ratings before the campaignconfirmed that L~t~ was generally not positionedamong full flavored brands. Compared to the ’ran-dom movements&dquo; for the before-and-after mea-

surements of the control group, there was no sig-nificant shift in the position of ~~~ 6 weeks afterthe advertising campaign began.

Perry, Izraeli, and Perry (1976) used SSA totrack changes in Israelis’ perceptions of Canada asa vacation spot before and after the introduction ofdirect Sights to Canada. In this study considerablechange in perception was obvious.

The differences between the two studies are in-

structive. Five months elapsed between measure-ment occasions in the vacation study. Only 6 weekselapsed between measurement occasions in the cig-arette study. The increased time alone could pro-duce perceptual changes. The first measurement

occurred before the air route was established in thevacation study. Thus, the advertising program forvacationing by air to Canada was much more dis-tinctive than the ads for a reblended cigarette. Onlypeople who indicated that they either had traveledabroad during the last 2 years or had intended todo so in the subsequent 2 years were included inthe Perry et al. (1976) study. This is a very specificand select audience. (Although only smokers wereused in the Smith and Lusch, 1976, study, this wasa much less exclusive group.) Finally, no controlgroup was available in the Perry et al. (1976) study.Though the perceptual changes seem large and sys-tematic, Perry et ~l . did not compare the changesto random movement. The Hanno and Jones (1973)jackknife technique could have been used to testchanges against random movement.

In the second area, dealing with the compata-bility of brand images and slogans, Green andMcMennamin (1973) briefly described three stud-ies in which MDS addressed such advertising prob-lems. The first case dealt with the evaluation of 15

potential new slogans for a soft drink. MDS showedthat 1 of the slogans &dquo;were perceived as moreclosely associated with the images of one or morecompetitive brands than the firm’ own brand&dquo;’ (p.5~2) . In the second case a cereal marketer foundthat an advertising campaign emphasizing the goodtaste and high nutritional value succeeded in po-sitioning their cereal closer to the &dquo;good tasting&dquo;cereals than any of the other high nutrition cereals.In the third case, five potential advertising copyideas for an over-the-counter drug were evaluatedin an MDS study of physicians, since physicians’recommendations were the source of the early pur-



441

chases of the drug. The firm’ favorite appeal wasperceived by the physicians as being more relevantto the leading (competitor’s) product. The mostpopular appeal was thought, before the study, tobe too &dquo;soft sell.&dquo; Green and li4ch4ennamin (1973)proceeded by providing a detailed illustration ofhow market position analysis could help developan advertising strategy for fabric softeners. As in-dicated earlier, this approach could be useful inproblems related to branding.

Finally, one of the most fascinating uses ofMDSin marketing was Clarke’s (1978) merging ~f I~DSand econometric analysis to expand the scope ofcompetitive advertising models. He conjectured:

... it would seem that the advertising of twobrands which are considered close substitutefor each other should affect each other’ sales

more than would the advertising of the thirdbrand which is not viewed by consumers as anear substitute. (p. 1,687)

He described a situation in which Products A and

B are close together in a product space and ProductC is relatively far away. A differential cross-elas-ticity (i.e., the advertising expenditures of ProductB should have a different impact on sales for Prod-uct A than the advertising expenditures of ProductC would have on Product A) would be expected.For the case in which an ideal point has beenimbedded in the product space, relative distance tothe ideal point replaced interproduct distances inClarke’s (1978) analysis. He developed an adver-tising modification function involving expendituresand either interproduct distance or distance to theideal point. This is a ratio scale analysis but doesnot encounter Hauser and Simmie’s (1981) prob-lem with arbitrary origins, since Clarke (1978) usedratio distances within the configuration, not scalevalues for products on the axes. Clarke derivedself-elasticities and cross-elasticities for advertis-

ing expenditures which do account for perceptualpositioning. He also derived an expression for op-timal advertising expenditures. His theoretical de-velopments overshadowed his empirical demon-stration. The illustration dealt with 9 anonymousbrands in a 100-brand market. Similarities werecollected from students some 10 years after the last

data in the econometric stream were gathered. Suchan illustration showed only that the estimates couldbe produced. There is almost no substantive ex-

planation for the fact that particular brands enjoyeddifferentially effective advertising.

Fact and Analysis

Marketing researchers have made many meth-odological contributions to MDS research. This

section reports contributions to understanding re-sponse rate, time, and accuracy; validity, reliabil-ity, and stability; and robustness of data collectionprocedures as well as robustness of the scaling al-gorithms.

Data Collection-Response Rate, andAccuracy

~Teidell9 s ( 1972) comparison of data collected bytriadic combinations, rotating anchors (i.e., the

conditional rank order task), and semantic differ-ential scales was in much the same style as earlierresearch on unidimensional methods (cf. Green-berg & Collins, 1966; Kassarjian & Nakanishi,1967; van de Sandt, 1970). Neidell (1972) foundrotating anchor points were comparable to semanticdifferential ratings in terms of quality and quantityof responses in mail surveys. Both methods were

better than triadic combinations of these criteria.

Henry and Stumpf( 1975) and Mclntyre and Ryans(1977) added consideration of time and accuracyto their analysis of different data collection tech-niques for MDS. Henry and Stumpf (1975) variedset size and studied rank ordering, triadic compar-ison, and anchor point rankings. All were com-pared in terms of time, and the last two were com-pared for accuracy in terms of the number of

intransitivities. There was no significant differencein accuracy, but the time analysis ranked anchorpoint methods as fastest, followed by rank orderingand triadic comparisons. Mclntyre and Ryans ( 1977)compared graded paired comparisons to the con-ditional rank order task used by Henry and Stumpf(1975). Graded paired comparisons turned out tobe faster, without significant loss of accuracy. Graded



442

paired comparisons were perceived by respondentsto be a less boring and a less difficult task.

CoMection&horbar;VaMdity~ Reliability, andStability

Summers and l~~~I~~y (1976) found only a mod-est correlation of judgments (rank order similari-ties) over a 1-month period, only modest congru-ence in the individual perceptual spaces over thistime period, and only modest ability of individualsto select a mapping of their own judgments froman aggregate map. Narayana (1976), on the otherhand, found no significant difference in soft drinkperceptions over 10 weeks. The major differencebetween these two studies indicates that if it isdesirable to emphasize stability, single analysisshould be done (e.g., INDSCAL) over occasions,as did Narayana, and changes should be looked forin weights. If it is desirable to emphasize instabil-ity, raw judgment vectors should be correlated, asdid Summers and l~~cl~~y, or individual level per-ception spaces should be matched.

Moinpour, T~I~~~ll~~~h, and h4acLachlan (1976)showed that if there can be control for structuralshifts in frames of reference, INDSCAL analysisof shifts in salience over time can be an effective,conservative method for tracing the impact of per-suasive communications. Day, Deutscher, and Ryans(1976) added level of aggregation to their study ofreliability. High reliability with relatively poor fitsindicated substantial heterogeneity among respon-dents. Their coefficient of reliability compared therank order correlation of the original rankings andthe later rankings with the rank order correlationof the first ranking and the repeated judgments,assuming their worst possible values. Deutscher(1982) has reviewed these reliability studies in moredetail.

of Data Collection Techniques andll/’IDS Algorithms

Green and Rao ( l ~71 ~) studied the ability ofindividual differences models to recover syntheticconfigurations. The letter &dquo;R&dquo; was represented as15 points in a two-dimensional space. Fifteen sub-

jects were simulated by differentially shrinking orstretching the configuration. Into each configura-tion eight &dquo;property vectors&dquo; were imbedded at

random angles from the origin, and the eight re-flections of those vectors were also imbedded. The

6 ‘r~ti~~9’ of each point on each vector became oneof the 16 elements in each individual’s profile.Excellent recovery of the interpoint distancesbetween pairs of profiles could be obtained fromthe ratings using multiple discriminant analysis,factor analysis of scalar products, INDSCAL anal-ysis, TORSCA on the average distances, and

l~-~~~CA~. IV using the individual differences,nonmetric option. For comparison, the ratings weredowngraded to zeros and ones, with mean or higherratings receiving the one. This was to simulate theeffect of ~tef~re’s (cf. Brown et ~l. , 1968) datacollection procedures. For the zero-one data inter-point distance, correlations between final and orig-inal configurations ranged from about .76 to about-.02, with factor analysis of scalar products andh4-D-SCAL IV showing the worst recovery.

Green (1975b) summarized earlier simulation re-sults on the recovery of structure in structureless

data and reported that the simple integer-rank trans-formations of dissimilarities prior to nonmetric MDSwas effective in minimizing the impact of strangetransformations of distances. Regarding metric MDShe found that selection of the appropriate additiveconstant did have a pronounced impact on the re-covery of structure. Rao and Katz (1971) simulated

large data sets collected by seven different pro-cedures. Although no method recovered structureperfectly, the pick-k-and-order methods producedbetter recoveries than the subjective groupingmethods (e.g., sort into k group;) . Individual dif-ferences models produced poorer recoveries thanthe group scaling methods, and nonmetric groupmethods performed better than metric group meth-ods.

Whipple (1976) compared data collection met-ods and nonmetric MDS algorithms. Four prefer-ence rankings and one triadic preference ranking,bipolar ratings, attribute-cued rankings (e.g., theobjects are ranked on the attribute of product safety),rotating anchor point rankings, and triadic prox-imity comparisons among seven children’s toys



443

formed nine data sets, which were scaled using fivenonmetric MDS routines, i.e., elastic MDS (EMD;~C~~~, ~ 1966), M-D-SCAL 5, TORSCA, SSA-1,and KYST. Young and Appelbaum (1968) showedall these routines to be minimized by the same setof scale values even though the objective functionsvaried for some. A KYST analysis of the 21 in-

terpoint distances from each of the 45 solutions(i.e., 9 times 5) showed that there was no algo-rithmic difference, that all the preference rankingsolutions clustered together, and that the bipolarratings all clustered tightly, as did the attribute-cued rankings and the direct judged proximities.

Green and Maheshwari (1970) simulated con-ditional rank order data from an underlying con-figuration and varied the method of analysis (TOR-SCA versus direct unfolding using 34-D-SCAL IV),the extent of ties in the data, and the level of noise.A three-way ANOVA on Fisher’s Z from the re-covery correlations showed significant interactionsbetween level of ties and level of error; significantinteraction between method of analysis and levelof error; and significant main efiects for analyses,level of ties, and level of error. Jain and Pinson(1976) used l~~.I~®~.1~ to investigate the effectsof order of presentation, attentional instructions,and degree of commitment. In judging eight U.S.cities, no significant differences were found.

£4iscellany

Day and Heeler ( 1971 ) compared principal com-ponents analysis, hierarchical clustering, and non-metric MDS as a basis for clustering. The clusterswere to be used as a matching device for in-storeexperiments (cf. Green, Frank, & Robinson, 1967 a).Principal components was chosen over nonmetricMDS &dquo;because it was more economical and did

not appear to distort the data excessively&dquo; (p. 346).Hauser and Koppelman (1979) favored factor anal-ysis over discriminant analysis and over similarityscaling for producing perceptual maps. They usedpredictive validity, interpretability, and ease of useas their criteria. Although some part of their con-clusion seems application specific (i.e., modelingshopping center images), the controversy regardingthe best method for perceptual mapping continues.

Worthy of mention is the early exchange of ar-ticles and letters to the editor on distance measuresin cluster analysis (I~®rris~r~9 1967; Shuchman,1967) and nonmetric MDS (Green, Frank, & Rob-

inson, 1967b; Green & Rao, 1969). In response tothe very high expectations set by these early dis-cussions of MDS, Green, Frank and Robinson

(1967b) ended by noting, ‘6~~ tried to build a doghouse. Already you want to throw a convention init!&dquo; (p. 841).

New ~~°®d~~~ l~~d~ls

Understanding of the use of MDS in compre-hensive new-product models is aided by the delin-eation of stages given in Shocker and Srinivasan’s(1979b) review of product concept generation andevaluation studies. They discussed five stages: (1)determination of the relevant product-markets, (2)identification of the determinant attributes, (3) cre-ation of the perceptual product spaces, (4) mod-eling individual or segment decision making, and(5) evaluation of/search for new product concepts.Since the first four of these directly involve MDS,they will be discussed in turn.

of Relevant Product-Markets

The determination of relevant product-marketsis the stage of defining or articulating the marketin which the new product must compete. Srinivasanand Shocker (1973) suggested use of Stefflre ’ (cf.Brown et al. 1968) product by usage matrix, whichcould be multidimensionally scaled to articulate themarket. A possibly useful analysis here would beLevine’s (1979) analysis of &dquo;pick-any&dquo; data (cf.Holbrook, l~®~re9 ~ Winer 1982). Although theanalysis was developed for preference data, its

adaption to market definition seems promising. Asindicated earlier, respondents would be asked toselect all the products they would consider pur-chasing. Products would be positioned at the centerof all the respondents who selected them. Productsclose together would tend to be those that were themost intcrsubstitutable.

Srinivasan and Shocker (1973) suggested non-metric MDS of similarities for market determina-



444

tion. Many illustrations of this type of applicationhave been reviewed earlier, but several methodo-logical problems remain. To allow consumers togenerate the market definition should incline re-searchers to specify an overly large list of potentialcompetitors. At this early stage of development,the focus should be broad. Paired comparisons,conditional rankings, ratings, or other standard datacollection techniques would take a great deal oftime with long product lists and would lead to agreat deal of missing data or ratings of unfamiliarproducts. The pick-any format of Levine’s proce-dure resolves some of these problems and meritsmore study.

of the Determinant Attributes

Determinant attributes are traditionally definedas those attributes that distinguish the product al-ternatives and are probably determinants of brandchoice. One should be cautious in emphasizing thefor determinant attributes to distinguish amongexisting alternatives. If an important attribute doesnot distinguish among existing alternatives, newalternatives might be positioned so as to be distinctalong that attribute.MDS has obvious uses here. Along with other

techniques, MDS was fused for this purpose byLehmann (1971b), Wind (1973, 1977), Srinivasanand Shocker (1973), Urban (1975), and Hauser andUrban (1977). The advantage of MDS in this con-text is that it allows the researcher to discover the

relevant attributes. The similarities question is

probably the most neutral question in the socialsciences. It allows the respondent to bring a per-sonal frame of reference to the judgment task, ratherthan having one imposed by a prescribed list of

attributes on which the product alternatives are rated.With this neutrality comes the potential problemsof interpretability, the possibility that the resultswill be a mixture of class and quantitative variation,rather than a strict dimensional representation, andthe possibility that dimensions relevant for simi-larities judgments are not relevant for choice.The solution of these problems does not come

from accepting only a few dimensions in an MDSspace. The emphasis of marketing researchers on

low dimensional MDS representations could meanthat only the obvious will be discovered. It wouldbe wise to remember the words of 1=Ier~~l~it~s of

Ephesus, &dquo;If you do not expect it, you will notfind out the unexpected, as it is hard to be soughtout and difficult.&dquo; 9

Creation of Perceptual Product Spaces

The creation of perceptual product spaces canbe achieved by factor analysis, discriminant anal-ysis, direct measurement of &dquo;determinant attri-

buts,&dquo; or MDS. Wind (1973, 1977), Hustad, Mayer,and Whipple (1975), Urban (1975), and Hauserand Urban (1977) used MDS. All except Urbanassumed that different market segments have com-mon perceptual frames of reference. Urban con-sidered clustering individuals on their INDSCALweights, clustering factor scores, or determiningclusters by obverse factor analysis or by the Tuckerand Messick (1963) model. Shocker and Srinivasan(1979b) considered a common framework obliga-~~~0 6 ‘this is because evaluation and/or search for

desirable new concepts requires that it be feasibleto evaluate a large number of candidates efficiently.... Such tasks are difficult, and would be virtuallyimpossible were it necessary to coordinate multiplecustomer spaces with a single ~a~a~f~~t~zr~r’s space&dquo;(p. 167).The emphasis on low dimensionality and the ro-

tational determinancy of techniques such as IND-SCAL may not be the allies of the marketing re-searcher in the creation of perceptual product spaces.What would be beneficial is a representation ofindividual differences that had some perceptual di-mensions common to all and some dimensions that,although relevant to some subsets of individuals,were not relevant to others. Such a representationcould create distinct, perceptually homogeneoussegments but with a sense of which dimensionswere shared over segments and which dimensionswere not. Although it might be possible to achievethis representation with a high dimensional IND-SCAL solution, it seems that something from thefamily of individual differences models for MDS(Tucker, 1972; Tucker & Messick, 1963) wouldbe more suited for the task. Evaluation of new



445

concepts in this overall higher dimensional repre-sentation might present some problems, but thereis no reason to expect them to be insurmountable.

Modeling or Segment DecisionMaking

Srinivasan and Shocker (1973) imbedded ideal

points into the product space with their LINB4APprocedure. They modeled the probabilities of allchoices as a decreasing function of distance fromthe ideal point and modeled first choice as the prod-uct nearest the ideal point. Hustad et al. (1975)mapped preferences using PREFMAP but did notmodel choice (cf. p~ss~mi~r9 1975; Pessemier &Root, 1973). Pessemier (1975) mapped his dollarmetric preferences into the product space withPREFMAP and implicitly used a Luce (1959) modelto represent choice (cf. Pessemier, 1975; Pessemier~ R®®t9 1973). Wind (1973, 1977) imbedded idealpoints with PREFMAP and indicated that proba-bility of purchase was a decreasing function ofdistance from the ideal point. Urban (1975) alsoused PREFMAP or LINMAP as a basis for pre-dicting long-run market share. Hauser and Urban(1977) used the same preference mapping but usedthe multinomial logit model to forecast market share,as did Hauser and Koppelman (1979) and Hauserand Simmie (1981).The linkages from perceptions of preferences to

choice probabilities or market shares are importantfor marketing research. Forecasts of market-levelactivity (e.g., market share) are best done by pro-cedures that integrate consumer-level measure-

ments (e.g., MDS results) with market-level mea-surements (e.g., price, promotional expenditures, 9availability). This would seem to make the mul-tinomial logit model a robust choice, since infor-mation from numerous sources could be combinedwith MDS results into market forecasts. A verylarge stumbling block, however, is the independ-ence from irrelevant alternatives (IIA) assumptionsthat goes along with traditional applications of themultinomial logit model. Particularly in a newproduct context, it seems more reasonable to modelexplicitly the effects of changes in the composition

of choice sets than to assume, in essence, that thereare no effects.

Batsell (1980, 1981) has been working on anMDS approach to the IIA problem. As did Clarke(1978) in his work on differential advertising cross-el~sticities Batsell (1980,1981) has used inter-brand distances as a measure of substitutability whichcombines with a measure of utility to predict choiceprobabilities. Currim (1982) described his own andother recent attacks on the problem of the IIA as-sumption. Cooper and Nakanishi (1983) have shownhow simply standardizing variables in each choicesituation overcomes the IIA assumption in logitmodels or multiplicative competitive interaction(MCI) models.

Problems and Prospects

MDS does not answer all the questions which amarketing researcher can pose. Within a less thancomprehensive mandate, there seem to be threediscernible directions for MDS in marketing re-search.

The first is toward a finer grained inspection ofindividual and group perceptions. One of the lin-gering problems in this direction concerns dataomitted through prudence rather than through ca-price. If individuals are not familiar enough withsome collection of choice alternatives to make

judgments about them, it is prudent not to forcethese judgments. Levine’s (1979; cf. Holbrook,1’~®®r~, ~ Winer, 1982) &dquo;pick any&dquo; MDS modeldeals well with this issue within its scope of ap-plicability. How relevant set membership is mod-eled, however, and its impact on spatial represen-tations, requires more general attention. ThoughHauser and Koppelman (1979 have cast this as aspecial problem for MDS, it is no less a problemfor factor analysis or discriminant analysis. This ispart of a larger problem concerning the represen-tation of individual differences. As marketing re-searchers move toward basing perceptual spaces onvery large samples of consumers, a more richlyarticulated representation of individual or segmentdifferences will be useful. This will be true for

fundamentally symmetric MDS problems as wellas fundamentally asymmetric MDS problems.



446

The second direction deals with merging MDSwith other consumer-based measurements (e.g.,normative beliefs), then, in turn, merging con-sumer-level measurements with market-level mea-surements. Although the former data base is pri-marily cross-sectional (e.g., over individuals orsegments), the latter is primarily a longitudinal database. Some of the potential of this merger is com-municated by Clarke’s (1978) work. In addition topromotions expenditures, there are other market-level influences (e.g., price and distribution). Alongitudinal analysis of market-level variables mightbe done to estimate parameters in an MCI modelor in a multinominal logit model. These parametersmight then be used in a cross-sectional analysis inwhich parameters for the consumer-level variablesare estimated. With market-level choice as the cri-

terion, and the reality of scanner data as a purchase-by-purchase account of market activity, there is

much to be explained.The third direction deals with the representation

of change on a broader scale than the introductionof a new product into an existing market. The cur-rent new-product models and methods might nothave allowed marketing researchers to forecast thevideo game and home computer revolution. For

products that essentially create new markets thereneeds to be study of the structure and intersubsti-tutability of product classes or, as in Ritchie (1974),of the relations among alternative uses of leisuretime.

In his 1975 review of MDS in marketing, Green(1975 a) wondered whether or not MDS had ful-filled its early promise. With 8 more years of ex-perience, it seems that it has. The new generationof textbooks on MDS (Coxon, 1982; Davison, 1983;Schiffman, Reynolds, & Young, 1981) promise toprepare the next generation of MDS researcherseven better than the pioneers. As long as MDS isnot expected to solve all the complex problems ofthe field, it should continue to be a powerful anduseful methodology in the arsenal of marketingresearchers.

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Acknowledgment

I would like to acknowledge gratefully the stiggestionsof the special editors, Mark Davison ~MJLawr~~cc Jones;the comments of Domiaiique Hanssens, Robert Meyer,and Allan Shocker; the help of Dan Jacobs in editing;and the special efforts of Jaime 7&dquo;OM~MC-~~~, PairiciaMcNally, anJLMCy Gonzalez M manuscript preparation.

Authors Address

Send requests for reprints or further information to LeeG. Cooper, Graduate School of Management, Universityof California, Los Angeles CA 90024, U.S.A.



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