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JOHN R. HAUSER and FRANK S. KOPPELMAN *
Perceptual mapping is widely used in marketing to analyze market structure,design new products, end develop advertising strategies. This article presentstheoretical arguments and empirical evidence which suggest that factor analysisis superior to discriminant analysis and similarity scaling with respect to predictive
ability, managerial interpretability, and ease of use.
Alternative Perceptual Mapping Techniques:Relative Accuracy and Usefulness
Perceptual mapping has been used extensively inmarketing. This powerful technique is used in newproduct design, advertising, retail location, and manyother marketing applications where the manager wantsto know (1) the basic cognitive dimensions consumersuse to evaluate "products" in the category beinginvestigated and (2) the relative "positions" of presentand potential products with respect to those dimen-sions. For example. Green and Wind (1973) use simi-larity scaling to identify the basic dimensions usedin conjoint analysis. Pessemier (1977) applies discri-minant analysis to produce the joint-space maps thatare used in his DESIGNR model for new productdesign. Hauser and Urban (1977) use factor analysisto identify consumer perceptions and irmovationopportunities in their method for modeling consumerresponse to innovation. All of these researchers reportempirical applications in a number of product andservice categories. When used correctly perceptualmapping can identify opportunities, enhance creativi-
*John R. Hauser is Assistant Professor of Marketing. GraduateSchool of Management, and Frank S. Koppelman is AssociateProfessor of Civil Engineering and Transportation, TechnologicalInstitute, Northwestern University.
The authors thank Bruce Bagamery. Yosy Prashker. Steve Shu-gan. and Ken Wisniewski for their extensive technical assistance.Richard Johnson, Dennis Gensch, William Moore, Edgar Pessemier,Glen Urban, Paul Green. Allan Shocker, Subrala Sen, BrianSternthal. Lou Stern, Steven Lerman, and Philip Kotler provideduseful comments, criticisms, and suggestions.
The data for the study were collected under a University ResearchGrant, DOT-OS-4001, from ihe US. Department of Transportation,Peter Stopher and Peter Watson, principal investigators. The authorsIhank ihe Transportation Center at Northwestern University forthe use of these data.
ty, and direct marketing strategy to the areas ofinvestigation most hkely to appeal to consumers.
Perceptual mapping has received much attention inthe literature. Though varied in scope and application,this attention has been focused on refinements of thetechniques, comparison of alternative ways to use thetechniques, or application of the techniques to market-ing problems.' Few direct comparisons have beenmade of the three major techniques—similarity scal-ing, factor analysis, and discriminant analysis. In fact,most of the interest has been in similarity scalingbecause of the assumption that similarity measuresare more accurate measures of perception than directattribute ratings despite the fact that similarity tech-niques are more difficult and more expensive to usethan factor or discriminant analyses.
In practice, a market researcher has neither thetime nor the money to simultaneously apply all threetechniques. He/she usually selects one method anduses it to address a particular marketing problem. Themarket researcher must decide whether the addedinsight from similarity scaling is worth the addedexpense in data collection and analysis. Furthermore,if the market researcher selects an attribute-basedmethod such as factor analysis or discriminant analysishe/she wants to know which method is better forperceptual mapping and how such maps compare with
See for example Best (1976), Cort and Dominguez (1977), Day.Deutscher. and Ryans (1976), Etgar (1977), Gensch and Golob (1975),Green and Carmone (1969). Green. Carmone, and Wachspress(!977), Green and Rao (1972), Green and Wind (1973), Hauserand Urban (1977), Heeler. Whippie, and Hustad (1977), Jain andPinson (1976). Johnson (1970, 1971), Pessemier (1977), Singston(1975), Summers and MacKay (1976), Urban (1975), and Whippie(1976).
495
Journal of Marketing ResearchVol. XVI (November 1979), 495-506
496
those from similarity scaling. To answer these ques-tions, one must compare the alternative mappingtechniques.
One way to compare these techniques is theoreti-cally. Each technique has theoretical strengths andweaknesses and the choice of technique depends onhow consumers actually react to the alternative mea-surement tasks. Theoretical hypotheses are establishedin the next section.
Another comparison approach is Monte Carlo simu-lation. This useful investigative tool has been employedby researchers to explore variations in similarity scal-ing and other techniques (Carmone, Green and Jain1978; Cattin and Wittink 1976; Pekelman and Sen 1977).In perceptual mapping Monte Carlo simulation cancompare the ability of various techniques to reproducea hypothesized perceptual map, but it requires thatthe researcher assume a basic cognitive structure ofthe individual. Monte Carlo simulation leaves unan-swered the empirical question of whether the analytictechnique can adequately describe and predict anactual consumer's cognitive structure.
The comparison procedure we use is practical andis based on theoretical arguments and empirical analy-ses to identify which procedures yield results mostuseful for marketing research decisions. If the theoret-ical arguments are supported, researchers can continueto subject a technique to empirical tests in alternativeproduct categories. In this way, one gains insight aboutthe techniques by learning their strengths and weak-nesses. If and when the hypotheses are falsified newtheories will emerge.
We chose the following guidelines for the compari-son.
1. The marketing research environment should berepresentative of the way the techniques are usedempirically.
2. The sample size and data collection should be largeenough to avoid exploiting random occurrences andshould have no relative bias in favor of the tech-niques identified as superior.
3. The use of the techniques should parallel as closelyas possible the recommended and common usage.
4. The criteria of evaluation should have managerialand research relevance.
To fulfill these criteria, we chose an estimationsample and a saved data sample of 500 consumerseach, drawn from residents of Chicago's northernsuburbs. The application area is perceptions of theattractiveness of shopping areas in the northern sub-urbs and the criteria are the abihty to predict con-sumer preference and choice, interpretability of thesolutions, and ease of use.
HYPOTHESES: THEORETICAL COMPARISONWe begin with a brief synopsis of the techniques.
Because this synopsis is not a complete mathematical
JOURNAL OF MARKETING RESEARCH, NOVEMBER 1979
description, we have indicated the appropriate refer-ences.
Similarity scaling develops measures of consumersperceptions from consumer judgments with respectto the relative similarity between pairs of products.Though consumers are asked to judge similarity be-tween products, the definition of similarity usuallyis left unspecified. The statistical techniques selectrelative values for two, three, or four perceptualdimensions such that distance between products bestcorresponds to measured similarity. Green and Rao(1972) and Green and Wind (1973) provide mathemati-cal details.
For empirical studies with large sample sizes, com-mon space representations are developed such thateach consumer's / perception x,^j of product J alongdimension d is a. "stretching" of the common repre-sentation x,.^. The technique, INDSCAL (Carroll andChang 1970), simultaneously estimates the commonspace Xj^ for all / and estimates individual weightsv,.j to "stretch" these dimensions. Effectively, i,̂ ^=' v]d^ ^ d- For details see Carroll and Chang (1970).
The dimensions are named by judgment or by aregression-Uke procedure called PROFIT (Carroll andChang 1964). In PROFIT, consumers are asked torate each product on specific attributes, e.g., "atmo-sphere" for shopping centers. The ratings are depen-dent variables in a regression (possibly monotonic)on the perception measures, i,^^, which serve asexplanatory variables. The regression weights, calleddirectional cosines, indicate how strongly each per-ception measure relates to each attribute rating. Fordetails see Carroll and Chang (1964).
Factor analysis begins with the attribute ratings.The assumption is that there are really a few basicperceptual dimensions, x,̂ .̂ . Many of the attributeratings are related to each perceptual dimension.Factor analysis examines the correlations among theattributes to identify these basic dimensions. Forstatistical details see Harmon (1967) and Rummel(1970). Because concern is with the basic structureof perception, the correlations between attribute rat-ings are computed across products and consumers(sum over / andy). The perceptions of products aremeasured by "factor scores" which are based on theattribute ratings. The dimensions are named by exam-ining "factor loadings" which are estimates of thecorrelations between attribute ratings and perceptionmeasures. In applications, attribute ratings are firststandardized by individual to minimize scale bias.
Discriminant analysis also begins with the attributeratings, but rather than examining the structure ofattribute correlations, discriminant analysis selects the(linear) combinations of attributes that best discrimi-nate between products. See Cooley and Lohnes (1971)and Johnson (1970) for mathematical details. Becauseconcern is with the ability to differentiate products.
ALTERNATIVE PERCEPTUAL MAPPING TECHNIQUES
the dependent measure is "product rated" and theexplanatory variables are the attribute ratings. Theanalysis is run across consumers to find a commonstructure. The perceptions are measured by **discrimi-nant scores" which are estimates, based on the attri-bute ratings, of the perceptual dimensions, x.j^, thatbest distinguish products. The dimensions are'̂ namedby examining "discriminant scores" which are theweightings of the attributes that make up a discriminantdimension or by computing correlations that areequivalent to factor loadings. In applications, thediscriminant dimensions are constrained to be un-correlated (also called orthogonal).
Comparison of Similarity Scaling andA (tribute-Based Techniques
A major difference between similarity scaling andthe attribute-based techniques is the consumer taskfrom which the perceptual measures are derived.Attribute ratings are more direct measures of percep-tions than similarity judgments, but may be incom-plete if the set of ratings is not carefully developed.Similarity judgments introduce an intermediate con-struct (similarity) but the judgments are made withrespect to the actual product rather than specificattribute scales. A priori, if the set of attributes isrelatively complete there is no theoretical reason tofavor one measure over the other.
Another difference is the treatment of variationamong consumers. In the attribute-based techniquesa common structure is assumed, but the values ofindividual measures {x..^ or x.jj) are not restricted.In similarity scaling (INDSCAL) x..^ is restricted tobe at most a stretching of the common measure, x.^.This means that although complete reversals are al-lowed, no other change in rank order is allowed. Forexample, INDSCAL will not allow one consumer toevaluate relative sweetness in the order Pepsi, Coke,Royal Crown while another evaluates sweetness asCoke, Royal Crown, Pepsi. This restriction limits theapplicability of the similarity scaling.
Finally, similarity scaling is limited by the numberof products. At least seven or eight are needed formaps in two or three dimensions (Klahr 1969). Thereare no such restrictions for factor analysis. The re-striction for discriminant analysis is the number ofproducts minus one. This argument favors attribute-based techniques if the number of products in aconsumer's evoked set is small; it favors neithertechnique if the number of products is large. Inpractice, the evoked set averages about three products(Silk and Urban 1978).
On the basis of these arguments, if the attributeset is reasonably complete, attribute-based techniquesshould provide better measures of consumer percep-tion than similarity scaling (as implemented bv IND-SCAL).
497
Comparison of Factor Analysis and DiscriminantAnalysis
Factor analysis is based on the correlations acrossconsumers and products. Discriminant analysis islimited to dimensions that, on average, distinguishamong products. Thus factor analysis should use moreattributes than discriminant analysis in the dimensionsand therefore produce richer solutions. For example,consider Mercedes Benz and Rolls Royce. Supposethat the true perceptual dimensions are country oforigin and reliability and that only reliability affectspreference and choice. Suppose that perceptions ofcountry of origin differ among products. Suppose thataverage perceptions of reliability are the same forboth cars but individual perceptions differ amongconsumers. Discriminant analysis will identify onlycountry of origin. Factor analysis will identify bothdimensions.
On the basis of this type of argument, one expectsfactor analysis to provide a richer perceptual structurethan discriminant analysis. It should be able to usemore of the attribute ratings and should identifyperceptual dimensions that predict preference andchoice better than discriminant analysis dimensions.
EMPIRICAL SETTING: SHOPPING LOCATIONSThe empirical setting is north suburban Chicago and
the "product" category is overall image of shoppinglocations, an increasingly important area of investiga-tion in marketing. From the perspective of retailers,shopping center managers, and community planners,the sensitivity of destination choice behavior to theirnage or attractiveness of the shopping location pro-vides an important opportunity to develop strategiesto attract shoppers.
In terms of an empirical comparison of perceptualtechniques, shopping location choice provides a strongtest of the model's explanatory and predictive capa-bilities. Shopping location choice is a complex phe-nomenon, difficult to model and difficult to under-stand. If a perceptual technique does well in thiscategory, it is likely to do well in a less complexcategory. (The complexity of. the category shouldintroduce no relative bias in the model comparisons.)
We develop models based on seven shoppingareas including downtown Chicago and six subur-ban shopping centers of very different characteristics.The locations represent the types of shopping locationsavailable to the residents of the suburbs north ofChicago including large, medium, and small shoppingareas with exclusive, general merchandise, or discountorientations.
The data were collected by a self-administeredquestiomiaire. (For details see Stopher, Watson, andBlin 1974.) The attributes were measured by 16 five-point rating scales chosen in an attempt to get as
498 JOURNAL OF MARKETING RESEARCH, NOVEMBER 1979
complete a list as possible without causing consumerwearout. (They were selected and refined on the basisof literature reviews, preliminary surveys, and qualita-tive research.) The similarity judgments were mea-sured by pairwise comparisons on a seven-point scale.The respondent judged all pairs of the products inhis/her evoked set (measured by a knowledge ques-tion). Table 1 contains example instructions for theattribute ratings and similarity judgments.
The dependent measures for predictive testing wereobtained in the same survey. Choice was self-reportedfrequency of visits. Preference, also called "attrac-tiveness," was rank-order preference in which avail-abihty/accessibility was held constant. (Pretests indi-cated consumers were comfortable with this task.)Availability/accessibility was measured as map dis-tance from the consumer's residence to the shoppinglocation. The model (explained in the next section)was drawn from the retailing and transportation litera-ture and is given as follows.
Perceptions -+Preference- •Frequency of Visits
Availability/Accessibility
This two-stage model allows managers and researchersto measure the "attractiveness" of a shopping centerindependently of its location. Thus one can readilyinvestigate strategies, such as improving the atmo-sphere of a shopping center, that may be more costeffective than relocation strategies. This ability isespecially useful when relocation is not an option asis the case in many downtown shopping areas.
In the original data set, 37,500 mailback question-naires were distributed at four of the shopping loca-tions. Of these, 6,000 were returned as complete andusable questionnaires. Although this low return ratemay cause some nonresponse bias, the bias shouldnot affect relative comparisons. Because similarityscaling requires at least seven stimuli, the data werescreened to select those consumers who indicated
Table 1EXAMPLE QUESTIONS FOR AHRIBUTESCALES AND SIMILARITY JUDGMENTS
In this question, we would like you to rate each of the shopping centers on these characteristics. We have provided a range fromgood to poor for each characteristic. We would like you to tell us where you feel each shopping center fils on this range.
For example:
/
Eating
I
O°
good ;
ties
poor
1
RATINGS OF THE ATTRIBUTES OF SHOPPING LOCATIONS
Again, if all the shopping centers were equally easyto get to. how similar do you think they are to eachother? In answering this question, please think aboutyour preference to shop at them for the goods youcame to buy. Check the box which best describes howsimilar they are. Please be sure to do this for all pairsof shopping centers.
WoodfieldEdens PlazaWoodfield
andandand
Chicago LoopGolf MillPlaza del Lago
11I
[1[1II
2
I 1I 1[ I
5I 1[ 1
SIMILARITY JUDGMENTS
ALTERNATIVE PERCEPTUAL MAPPING TECHNIQUES
knowledge of and who rated all seven stimuli (1,600consumers). Any bias introduced by this screeningshould favor similarity scaling and thus favor falsifyingour hypotheses. Finally, 500 of these consumers wererandomly selected for an estimation sample and 500others for saved data testing.
One source of bias is that samples were taken atfour locations but judgments were made for sevenlocations. This sampling technique should produce nobias in the relative predictive ability of the perceptualtechniques but could bias the coefficients in thepreference and choice models. Fortunately, this biascan be corrected with choice-based sampling (CBS)estimation procedures. Manski and Lerman (1977) givetheoretical proofs and Lerman and Manski (1976)provide intuitive arguments. To test CBS empiricallyfor the data, parallel analyses were performed usingonly the four sampled shopping locations. Consistentwith the theory, all models were statistically equiva-lent. Koppelman and Hauser (1977) give details ofthese comparisons.
EMPIRICAL PROCEDURESo that other researchers can replicate the tests,
we describe in this section how the measures weredeveloped. In selecting procedures an attempt wasmade to follow common and recommended usage asclosely as possible. When potential variations occurred(rotation vs. nonrotation, direct vs. indirect similari-ties, three vs. four dimensions) sensitivity tests wereperformed.
Similarity ScalingPairwise similarities were changed to rank order
similarities and input to INDSCAL. Three dimensionswere selected on the basis of an elbow in stress values.Four dimensions were not possible with the limitednumber of products.
Factor Analysis
The attributes were standardized by individual.Correlations were computed across consumers andproducts. Four dimensions were selected by usingelbow and interpretability criteria on the commonfactor solution with varimax rotation. Limited testingwas done with three dimensions for comparability tosimilarity scaling.
Discriminant AnalysisThe attributes were standardized by individual. A
discriminant analysis was run with the product ratedas the dependent variable and the 16 attributes asexplanatory variables. The elbow rule and significancestatistics suggested at least three dimensions (97.5%of trace), possibly four because the chi square testwas still significant. Most analyses were done withfour dimensions although limited analyses were donewith three dimensions. Varimax rotation improved the
499
interpretations slightly. Dimensions are constrainedto be orthogonal.
Preference
The linear compensatory form was chosen becauseof its widespread use in marketing (Wilkie and Pesse-mier 1973), because Monte Cario simulation has shownit reasonably representative of more complex formssuch as disjunctive, conjunctive, and additive (Car-mone, Green, and Jain 1978), and because many ofthe nonlinear models such as conjoint analysis (Greenand Srinivasan 1978, Green and Wind 1975) require(more intensive) personal interviews rather than themaUback format used by Stopher, Watson, and Blin(1974).
Mathematically, this model is given by:
(1)
where/7,̂ . is individual /'srank forproducty, — indicatesnionotonic, d^j, is Ts perception of j along the /'^dimension, and w, is the importance weight of the/'" dimension. (For similarity scahng d^j, = x.^^, forfactor analysis d^j, = x^j^, for discriminant analysis
Because there is a possibility that any single prefer-ence estimation procedure for the w/s will favor oneor another perceptual model, two estimation proce-dures were simultaneously tested: preference regres-sion and first preference logit. Preference regressionis a metric technique which replaces monotonicity (~)by equality (=) and uses ordinary least squares withequation 1. First preference logit is a monotonictechnique based on estimating the probability that aconsumer will rank a product as first preference. Inlogit, maximum likelihood techniques are used todetermine w,. For a more complete description, seeMcFadden(l970). In both models, choice-based sam-pling variables are used to provide consistent estimatesof W/ (Manski and Lerman 1977).
Choice
The multinomial logit model is used to predictchoice. (The logit model is based on a probabilisticinterpretation of choice. For estimation and predictionequations, see McFadden 1970.) The dependent vari-able is frequency of visits and the explanatory variablesare distance and estimated preference, p.^, where p..is generated by equation I and the estimates, w,, oithe importance weights. That is, p^^ = ^,w,d^,.
Finally, we chose to test the "assumption of atwo-stage model by using a revealed preference logitmodel. The dependent variable was frequency andthe explanatory variables were distance and the per-ceptual measures, d^^/. Choice-based sampling varia-bles were included for consistent estimates.
500 JOURNAL OF MARKETING RESEARCH, NOVEMBER 1979
Saved Data PredictionsOne begins with the standardized attribute ratings
and similarity judgments from the saved data sample.Factor score coefficients from the estimation sampleand the attribute ratings from the saved data are usedto create factor scores, x..^ (see Rummel 1970). Dis-criminant score coefficients from the estimation sam-ple and the attribute ratings from the saved data areused to create discriminant scores, x^^J (see Cooleyand Lohnes 1971). INDSCAL is run on the saveddata similarity judgments to create similarity scores,Xy^. If anything, this procedure should favor similarityscaling. Indeed, an alternative procedure of generatingthe similarity scores from the attribute ratings providedpoorer predictive results for similarity scaling and thusis even stronger support for the hypotheses.
For each combination of models (perception, pref-erence, choice) the estimated importance weights, w,,from the estimation sample are applied to the (̂ .̂ /sto create ^, . These are rank ordered and comparedwith the actual p,^. The estimated relative weightsof yj, and distance then are used (with the relevantlogit equation) to estimate the relative frequency ofvisits. These predictions are compared with reportedfrequency of visits.
Predictive TestsPreference prediction was measured by the percen-
tage of consumers who ranked first the shopping centerthat the model predicted as first. This measure isstraightforward and is commonly reported in theUterature.
Choice prediction is more difficult to measure. First,the models predict the probability of choice whichmust be compared with frequency of choice. Thisproblem is resolved by using percentage uncertaintywhich is an information theoretic statistic that mea-sures the percentage of uncertainty (entropy) explainedby the probabilistic model (see Hauser 1978; McFad-den 1970; Silk and Urban 1978). The second problemarises because both accessibility and the perceptualdimensions (through preference) are used to predictchoice. Only the incremental gains in uncertainty dueto the perceptual measures are of interest. Becausethe information measure is additive, we use the gainin percentage uncertainty achieved by adding theperceptual dimensions to a model based on distancealone.
Other measures including rank order preferencerecovery, percentage of consumers choosing themaximum probability shopping location, and meanabsolute error in market share prediction are notreported here because each of these measures rankedthe perceptual model in the same relative order asdo the reported measures. For these statistics seeKoppelman and Hauser (1977).
EMPIRIC A L RES UL TS
Predictive TestsThe results of the predictive tests are reported in
Table 2. Preference recovery was not computed forrevealed preference logit which is estimated directlyon choice. Table 2 also reports preference and choiceprediction for models using distance and the 16 stand-ardized attribute scales as explanatory variables. Thesestatistics are computed to examine whether the per-ceptual dimensions provide more or less informationthan a full set of attribute ratings.
To better understand Table 2, it is useful to considersome base level values. The maximum value forpreference recovery is 100%, but most empiricalmodels do not obtain values even near I(X)%. Ratherthese measures should be compared with that attain-able by purely random assignment, i.e., all locationsequally likely to be chosen, and that attainable byassigning consumers to shopping centers in proportionto market share. These values are 14.3% preferencerecovery for the equally likely model and 26.7%preference recovery for the market share model.Rigorous statistical tests are not applicable in compar-ing one perceptual technique with another becausethe preference models are based on different explana-tory variables. But, intuitively, differences in prefer-ence recovery can be compared via the maximumstandard deviation. 2.2, which would result under theassumption that for a given model each observation(consumer) has an equal probability of being correctlyclassified.
The significance of the choice models can be testedbecause the uncertainty explained is proportional toa chi square statistic (Hauser 1978). All models aresignificant at the .01 level.^ The chi square's cutoff,which is less than 0.4, can also be taken as an intuitivemeasure in comparing the alternative perceptual tech-niques.
First examine the predictive tests. Factor analysisis superior to similarity scaling and discriminant analy-sis for ail preference models and both predictionmeasures. This evidence supports the hypotheses.These results are particularly significant because anyincompleteness in the attribute scales would favorsimilarity scaling over discriminant analysis and factoranalysis. Furthermore, the sample was screened tofavor similarity scaling.
The fact that factor analysis does well in comparisonwith models based on attribute scales indicates that
'- After frwiuency adjustment, 2N* relative percentage uncertaintyis a chi square statistic if the null model. i,e,. distance alone,is a special case of the tested model, i.e,. perceptions and distance.The degrees of freedom equals the difference in the number ofvariables. For the three similarity dimensions the cutoff is ,031.For the other models which coniain four dimensions, the cutoffis .037.
ALTERNATIVE PERCEPTUAL MAPPING TECHNIQUES 501
T a b l e 2PREDICTIVE TESTS'
Goodness of fit tests Saved data tests
Simitarity .scalingPreference regression1st preference logitRevealed preference logit
Factor analysisPreference regression1st preference logitRevealed preference logit
Discriminant analysisPreference regression1st preference iogitRevealed preference logit
Attribute scalesPreference regression1st preference logitRevealed preference logit
Preferencerecovery
' uncertaintyexplained(choice)
Preferencerecovery
% uncertaintyexplained(choice)
36.634.8—
50.655.0—
35.535.3—
39,655.6—
0.91.11.5
3.84.75,9
1,71.92,9
3.25.26.6
23. i22.7
47.350.8
38.140.3
41,451.6
-32.4-41.3-69.5
4.35.36.0
1.92.03.0
-3.96.46.9
'The preference test is ability to recover first preference, the choice test is percentage of uncenainty explained relative to a modelwith distance alone. To get total uncertainty, add 32.6 lo these measures. All uncertainty measures are significant at the ,01 level.
very little information is lost by using the reducedfactors rather than the full set of attributes. The poorshowing of preference regression on the attributescales is the result of multicoUinearity. The poorshowing of discriminant analysis in relation to theattribute scales supports the hypothesis that concen-trating on variations between products neglects di-mensions that are important in preference and choice.
Next, examine the saved data test. Factor analysisis still superior to both discriminant analysis andsimilarity scaling. Both of the attribute-based measureshold up well. The small improvement in the statisticsmay be attributed to random variation between datasets. Similarity scaling predicts poorly on saved data,doing worse than the naive model which assignsconsumers proportional to market share (26.7% pref-erence recovery). The model does so poorly in relationto distance alone that it adds large amounts of uncer-tainty (negative uncertainty explained) in choice pre-diction.
Thus the saved data tests support the hypotheses.Table 2 is one empirical comparison. Replications,
sensitivity, and threats to validity are examined inthe next section, but first a more qualitative analysisis used to determine whether these comparisons areconsistent with managerial interpretations of the tech-niques.
Interpretability
First examine how the perceptual dimensions fromeach technique relate to the attribute scales. These
relationships are reported in Table 3. The underlinednumbers (directional cosines, factor loadings, ordiscriminant coefficients) indicate a strong relationshipbetween the underlined attribute (row) and the dimen-sion (column). The dimension names are compositesof the underlined attributes.
Despite marked superficial similarities, the differentmodels demonstrate striking differences in interpreta-tion. Factor analysis uses all the attribute scaleswhereas discriminant analysis uses only 10 of the 16scales, and only five of those 10 have discriminantscores greater than 0.5. This outcome is consistentwith the theoretical hypothesis that concentrating onvariance between products neglects information. Notealso that the third discriminant dimension, "value vs.satisfaction," is a mixed dimension positively relatedto value but negatively related to satisfaction. Comparethis to the factor analysis solution which has nopositive/negative mixed dimension. This differenceprobably arises because value and satisfaction maybe negatively correlated among existing shoppinglocations (discriminant analysis) but not in the wayconsumers rate these locations (factor analysis).
These differences are important to the manager whowants as much control over the market as possible.For example, many of the variables left out of thediscriminant solution (e.g., "layout of the store,""return and service," "sales assistants") could beaffected by relatively low-cost changes in shoppingcenter operation. Because discriminant analysis usesfewer variables the manager can analyze fewer strate-
502 JOURNAL OF MARKETING RESEARCH, NOVEMBER 1979
Table 3STRUCTURAL COMPARISON OF PERCEPTUAL MODELS
FACTOR ANALYSIS—FACTOR LOADINGS DISCRIMINANT ANALYSIS^-DISCRIMINANT COEFFICIENTS
Fundamentalattributes Variety
Quality andsatisfaction Value Parking
Fundamentalattributes Variety
Quality andsatisfaction
Value vs.satisfaction Parking
I,
2,
3.
4,
5,
6,
7.
8,
9,
10,
11,
12.
13,
14.
15,
16,
Layout of store
Return and service
Prestige of store
Variety of
merchandise
Quality of
merchandise
Availability of
credit
Reasonable price
"Specials"
Free parking
Center layout
Store atmosphere
Parking available
Center atmosphere
Sales assistants
Store availability
Variety of stores
.267
,095
.338
.665
,307
,159
,067
.223
- .15
,03
.080
,145
.244
,173
,619
.829
.583
.528
.822
.327
.810
,337
,063
.074
.068
,308
.658
.105
.694
.561
,320
.288
,156
.343
- 0 0 1
,309
-037
,487
,599
.739
.043
.074
.034
,108
.040
,147
.204
.160
,200
.255
-,058
-,185
-.074
,049
,113
.008
,811
,560
.400
,841
,404
,319
.034
-.173
1, Layout of store
2. Return and service
3. Prestige of store
4. Variety of
merchandise
5. Quality of
merchandise
6, Availability of
credit
7, Reasonable price
8. •"Specials"
9, Free parking
10, Center layout
11, Store atmosphere
12, Parking available
13, Center atmosphere
14, Sales assistants
15. Store availability
16. Variety of stores
.067
-.094
,156
.335
-.196
-.008
- .108
- 1 0 1
,065
-.065
- ,158
- .288
.109
- .138
,089
1,291
-,110
.254
.366
.153
1.114
,170
- ,008
-.171
-,066
-.233
.087
-,020
- 1 2 3
,015
.035
-.123
-.085
.287
- .318
.295
.020
.352
.586
.225
-.007
-.334
- 0 5 5
.018
- .510
- ,168
.084
-.022
-.023
.134
- .137
-.042
-.216
.025
- .0»-.1151.714
.082
- .053
,171
.284
-.084
- .065
.145
SIMILARITY SCALING-DIRECTIONAL COSINES
Fundamentalattributes
Varietyand value
Qualityvs.
value
Parking andsatisfaction
L Layout of store
2. Rettim and service
3. Prestige of store
4. Variety of merchandise
5. Quality of merchandise
6. Availability of credit
7. Reasonable price
8. "Specials"
9. Free parking
10. Center layout
11. Store atmosphere
12. Parking available
13. Center atmosphere
14. Sales assistants
15. Store availability
16. Variety of stores
.217
.318
,297
,929
.295
.880
,485
.786
-.294
-.447
- ,199
- .463
-.099
-.052
.872
.921
.497
.122
.804
.360
.811
-.085
-.853
- 5 9 4
-.550
.036
.452
- .478
.480
.411
.429
.385
,840
.940
.515
.M4- .505
- .468
.192
.173
.782
•894
.869
.747
.872
.910
- ,236
- ,054
gies. Also, because of the mixed dimension it isdifficult to evaluate strategies that increase both satis-faction and value.
Comparing factor analysis with similarity scaling,one again sees a mixed dimension, "quality vs. value,"but the similarity scaling solution uses all 16 attributes.This mixed dimension probably results from the IND-SCAL assumption which concentrates on differences
between products at the expense of variations inconsumer perceptions. But in this case the "quahtyvs. value" is easier to understand and operate onthan "satisfaction vs. value."
Thus, of the three models, factor analysis has themost managerially useful structure. Because all modelshave strong face validity and all use the basic fiveconstructs^variety, quality, satisfaction, value, and
ALTERNATIVE PERCEPTUAL MAPPING TECHNIQUES 503
Voriety
Quality andSotisfaction
Porking
Value-2.0 -1.0
Figure 1COMPARISON OF PERCEPTUAL MAPS
Voriety
Quolity
Value vs.Salisfaction
Parking1.0 -5.0 -3 0 -1.0 0 1.0
A. Factor Analysis:Factor Scores
B. Discriminant Analysis:Group Centroids
Variety
Quality vs.Value
Porking andSatisfaction
-.4 -.3 -2 -,| 0 ,1 .2 .3 .4
C. Non-metric Scaling:Common Space Positions
STIMULI SET:
o Chicago Loop• Waodfielda EdensA Golf Mi l l
Plaza del LagoOld OrchardKorvette City
parking—we believe that the predictive and saved datasuperiority of factor analysis is due to better structurein identifying dimensions.
The second test of interpretability is the visual mapsproduced by each method (see Figure 1). These mapshelp managers identify how each shopping locationis "positioned" in the marketplace. Thus a managercan know the relative strengths and weaknesses ofeach shopping location and can identify opportunitiesin the market.
Careful inspection of Figure 1 shows consistencyamong the models when the measured constructs arethe same. For example, note the low scores forKorvette City on quality (satisfaction) and for ChicagoLoop on parking or the high scores for Woodfieldon variety and for Plaza del Lago on quality (satisfac-tion). These and many other "positionings" havestrong face validity and are consistent with prior beliefsabout the images of the seven shopping locations.But there is an important difference. Factor analysisIS better for strategy development because it separatesthe dimensions in such a way that ambiguous inter-pretations ("quahty vs. value" and "satisfaction vs.value") are avoided.
Ease of Use
A final consideration is the investment in analysistime required by the techniques. Managers and re-searchers may be willing to accept more approximate
models if the approximations allow great cost savings.Our experience indicates that the attribute-based tech-niques are relatively easy to use whereas similarityscaling is somewhat more difficult with respect toboth data collection and data analysis. Both factorand discriminant analyses use only the attribute ratingswhereas similarity scaling requires, in addition, judgedsimilarities which can be a difficult consumer task.Once the data have been collected, factor and discrim-inant analyses are readily available on standardstatistical packages (e.g., BMDP, SPSS), cost' about$10-20 to run, and require little professional time.In sharp contrast, the special programs for similarityscaling require many exploratory runs, special FOR-TRAN programs for data transfer, and a series ofstatistical manipulations and data handling to developa common space, estimate individual weights, andcompute directional cosines. A single set of runs costsabout $40 in computer time, but because variousstarting configurations and dimensions must bechecked, the effective cost is about $150. Thoughthe added direct computer costs are acceptable, theprogramming and analysis require significant profes-sional time and could be very costly to organizationsnot familiar with the programs.
^Costs vary by computer. These costs represem $510 per cpuhour on a CDC 6400. See Dixon (1975) for BMDP and Nie etaL (1975J for SPSS.
504JOURNAL OF MARKETING RESEARCH, NOVEMBER 1979
Table 4SUMMARY OF THE RESULTS OF EMPIRICAL COMPARISON
Criteria Results
TheoryGoodness of fitPrediction
(saved data)InterpretationEase of use
Factor analysis > Discriminant analysisFactor analysis > Discriminant analysis
Factor analysis > Discruninant analysisFactor analysis ^ Discriminant analysisFactor analysis ~ Discriminant analysis
Similarity scalingSimilarity scaling
Similarity scalingSimilarity scalingSimilarity scaling
indicates superior, s indicates probably superior, ~ indicates no major difference.
SummaryIn this section representative attribute-based and
simitarily scaling techniques are compared lo deter-mine which perceptual mapping technique is mostappropriate for marketing research applications. Theempirical results, which support the hypotheses, sug-gest that the most popular technique, similarity scaling,may not be the best; rather, factor analysis may bebetter on predictability, interpretability, and ease ofuse (see Table 4). These results are subject to con-firmation or qualification in other empirical applica-tions but, at the very least, this empirical test raisedissues worth further investigation by other marketingresearchers.
THREATS TO VALIDITY, SENSITIVITY, ANDREPLICATIONS
Empirical comparisons are difficult. Only by usingthe state of the art in each technique can one befair to that technique. To attempt to extrapolate thesecomparisons, one must examine causes that threatento make the results specific to the empirical sample.
Threats to ValidityNonresponse bias, choice-based sampling, repre-
sentativeness of the set of attributes, and screeningon the seven stimuli in the evoked set have beendiscussed. They should introduce no relative biasfavoring the hypotheses.
One threat to the hypotheses is potential halo effectsin the attribute scales, i.e., the attribute scales maycontain an affective as well as a cognitive component(Beckwith and Lehmann 1975). This threat is mini-mized by standardization of the attribute scales priorto analysis and by using attribute scles designed tomeasure only the cognitive component. Another threatis that the stimuli set contained at most seven products.Although this constraint is typical of real-world ap-plications, it does suggest future comparisons withlarger stimuli sets.
Sensitivity •*The comparisons among techniques are found to
remain consistent when hmited changes are made ineach technique. Rotation of discriminant solutions
improved interpretability but not predictive ability (therotated solution is reported). Use of indirect similaritymeasures did not improve either interpretability orpredictive ability. The factor and discriminant analysesused four dimensions whereas similarity scaling waslimited to three dimensions. Though this is a minorchange in the degrees of freedom in the preferenceand choice models (490 vs. 489), it could have aneffect. Limited testing showed that dropping the leastsignificant dimension in the four-dimensional solutionscaused very little shrinkage in prediction. (For exam-ple, with preference regression and discriminantanalysis the shrinkage was about one-tenth of onepercent in preference recovery.) Finally, use of al-ternative factor analysis solutions such as principalcomponents or three-way analyses might improveprediction, but such improvement would only addsupport to the hypotheses.
ReplicationsSince the orignal study, the hypotheses have been
tested on two other data sets. Using a sample of 120graduate students, Simmie (1978 found preferencerecoveries of 67.4% for factor analysis, 51.9% fordiscriminant analysis, and 14.0% for similarity scaling.Simmie also found greater consistency across groupsof students with factor analysis than with similarityscaling. Her product category was managementschools. Using a random sample of Evanston residents,Englund. Hundt, and Lee (1978) found preferencerecoveries of 67.1% with factor analysis and 48.6%with discriminant analysis. Their product category wastransportation mode choice (bus, walk, or car). Theimplications of both studies are consistent with ourresults.
IMPLICATIONS AND FUTURE RESEARCHPerceptual mapping is an important marketing re-
search tool used in new product planning, advertisingdevelopment, product positioning, and many otherareas of marketing. Strategies based on perceptualmaps have led to increased profits, better marketcontrol, and more stable growth. Furthermore, muchresearch is based on implications of market structureas identified by perceptual maps. Because of this
ALTERNATIVE PERCEPTUAL MAPPING TECHNIOUES
interest and use, it is crucial that the best mappingtechnique available be employed in these applications.
We provide and support hypotheses that factoranalysis is superior to both similarity scaling anddiscriminant analysis for developing measures of con-sumer perceptions. In particular, factor analysis islikely to be superior in categories where:
1. The number of products in the average consumer'sevoked set is relatively small (seven stimuli or less).
2. There is variation in the way consumers perceiveproducts in the category.
3. Qualitative research has identified a set of attributeslikely to represent the product category.
The presence or absence of these characteristics doesnot ensure the superiority of one technique, butwithout evidence to the contrary they can serve asguidelines.
The results of this one theoretical and empiricalcomparison are hoped to raise the issue of and theneed for continued research to identify whether factoranalysis is always superior or, if not, under whatconditions the alternative mapping techniques shouldbe used.
Confirmation of these comparisons awaits replica-tion in other categories. In addition, further explorationmay be appropriate for other preference models. Forexample, nonlinear models such as conjoint analysisshould theoretically order the perceptual models inthe same way. but empirical tests are warranted. Wehaveuseddisaggregate preference models, i.e., modelsbased on individual consumers {p.. rather than p., d^.^rather than d^^ where / indexes consumers). In'mostapplications these disaggregate models have provensuperior to aggregate models which blur individualdifferences. Because aggregate models still are usedin some marketing applications, these might be tested.For example, PREFMAP, which is a form of prefer-ence regression, can be used at both the aggregate(Pessemier 1977) and disaggregate level (Beckwithand Lehmann 1975). We hypothesize that because thesuperiority of factor analysis over discriminant analy-sis is based on individual differences, predictivecomparisons might shift and discriminant analysismight do as well as factor analysis when analysesare limited to the aggregate level.
Other research might be of a more proactive nature,searching for improvements for the weaknesses ofeach technique. Theoretical developments might makeit practical to relax the INDSCAL assumption. Furtherresearch could expand the similarity scaling solutionsto more stimuli via use of concept statements. Seg-mentation on perceptions could be used prior tosimilarity scaling or discriminant analysis to ensurethat there is little variation among consumers. Theseand other methodological developments are suggestedby the examination and comparison of the alternativeperceptual mapping techniques.
505
This area of comparative model development isimportant to marketing and deserves attention frommarketing researchers.
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