Research: Uncovering Competitive Advantages

Warren F. Kuhfeld, SAS Institute Inc., Cary N.C. Presented at SEUGI '92 by Gerhard Held, SAS Institute

Abstract Perceptual mapping methods produce plots that dis­ play product , product preferences, and dif­ ferences between customers in their product prefer­ The SAS® System provides a variety of methods for ences. Conjoint analysis is used to investigate how analyzing marketing data including conjoint analysis, consumers trade off product attributes when making correspondence analysis, preference mapping, multidi­ a purchasing decision. mensional preference analysis, and . These methods allow you to analyze pur­ chasing decision trade-offs, display product position­ ing, and examine differences in customer preferences. Perceptual Mapping They can help you gain insight into your products, your customers, and your competition. This paper Perceptual mapping methods, including correspon­ discusses these methods and their implementation in dence analysis (CA), multiple correspondence analy­ the SAS System. sis (MCA), preference mapping (PREFMAP), multi­ dimensional preference analysis (MDPREF), and mul­ tidimensional scaling (MDS), are data analysis meth­ Introd uction ods that generate graphical displays from data matri­ ces. These methods are used to investigate relation­ ships among products as well as individual differences is an area of applied data anal­ in preferences for those products. ysis whose purpose is to support marketing decision making. Marketing researchers ask many questions, CA and MCA can be used to display demographic and including: survey data. CA simultaneously displays in a scatter­ plot the row and column labels from a two-way con­ tingency table (crosstabulation) constructed from two • Who are my customers? categorical variables. MCA simultaneously displays in • Who else should be my customers? a scatterplot the category labels from more than two categorical variables. • Who are my competitors' customers? MDPREF displays products positioned by overall pref­ • Where is my product positioned relative to my erence patterns. MDPREF also displays differences in competitors' products? how customers prefer products. MDPREF displays in a scatterplot both the row labels (products) and col­ • Why is my product positioned there? umn labels (consumers) from a data matrix of contin­ uous variables. • How can I reposition my existing products? MDS is used to investigate product positioning. MDS • What new products should I create? displays a set of object labels (products) whose per­ ceived similarity or dissimilarity has been measured. • What audience should I target for my new prod­ ucts? PREFMAP is used to interpret preference patterns and help determine why products are positioned where they are. PREFMAP displays rating scale data in the Marketing researchers try to answer these questions same plot as an MDS or MDPREF plot. PREFMAP using both standard data analysis methods, such as shows both products and product attributes in one descriptive statistics and crosstabulations, and more plot. specialized marketing research methods. This paper discusses two families of specialized marketing research MDPREF, PREFMAP, CA, and MCA are all similar methods, perceptual mapping and conjoint analysis. in spirit to the biplot, so first the biplot is discussed

185 Con!lumer Consumer Consumer 3 y = A 8' Product 1 Product 2 1 1 Product o 2 o Product llj o 2 il [1 il c [! 2 11 Figure 1. Preference Data Matrix Figure 2. Preference Data Decomposition to provide a foundation for discussing these methods. decomposition (SVD).+ An approximate biplot is con­ The Biplot. A biplot (Gabriel, 1981) simultaneously structed by plotting the first two columns of A and displays the row and column labels of a data matrix B. in a low-dimensional (typically two-dimensional) plot. The "bi" in "biplot" refers to the joint display of rows When q > 2, the full geometry of the data cannot be and columns, not to the dimensionality of the plot. represented in two dimensions. The first two columns Typically, the row coordinates are plotted as points, of A and B provide the best approximation of the and the column coordinates are plotted as vectors. high dimensional data in two dimensions. Consider a cloud of data in the shape of an American football. Consider the artificial preference data matrix in Fig­ The data are three dimensional. The best one dimen­ ure 1. Consumers were asked to rate their preference sional representation of the data-the first principal for products on a 0 to 9 scale where 0 means little component-is the line that runs from one end of the preference and 9 means high preference. Consumer football, through the center of gravity or centroid and 1 's preference for Product 1 is 4. Consumer 1 's most to the other end. It is the longest line that can run preferred product is Product 4, which has a preference through the football. The second principal component of 6. also runs through the centroid and is perpendicular or The biplot is based on the idea of a matrix decom­ orthogonal to the first line. It is the longest line that position. The (n x m) data matrix Y is decomposed can be drawn through the centroid that is perpendic­ ular to the first. If the football is a little thicker at into the product of an (n X q) matrix A and a (q X m) matrix B/. Figure 2 shows a decomposition of the the laces, the second principal component runs from data in Figure 1.* The rows of A are coordinates in the laces through the centroid and to the other side of the football. All of the points in the football shaped a two-dimensional plot for the row points in Y, and the columns of B' are coordinates in the same two­ cloud can be projected into the plane of the first two dimensional plot for the column points in Y. In this principal components. The resulting scatterplot will show the approximate shape of the data. The two artificial example, the entries in Yare exactly repro­ duced by scalar products of coordinates. For example, longest dimensions are shown, but the information in the other dimensions are lost. This is the principle be­ the (1,1) entry in Y is Yll = all X bll + a12 X b12 = hind approximate biplots. See Gabriel (1981) for more 4=lx2+2x1. information on the biplot. The rank of Y is q ::; M IN(n, m). The rank of a ma­ trix is the minimum number of dimensions that are Multidimensional Preference Analysis. Multidi­ required to represent the data without loss of informa­ mensional Preference Analysis (Carroll, 1972) or MD­ tion. The rank of Y is the full number of columns in PREF is a biplot analysis for preference data. Data are A and B. In the example, q = 2. When the rows of A collected by asking respondents to rate their preference and B are plotted in a two-dimensional scatterplot, the for a set of objects-products in marketing research. scalar product of the coordinates of ai and hj exactly Questions that can be addressed with MDPREF anal­ equals the data value Yij. This kind of scatterplot is a yses include: Who are my customers? Who else should biplot. When q > 2 and the first two dimensions are be my customers? Who are my competitors' cus­ plotted, then AB' is approximately equal to Y, and tomers? Where is my product positioned relative to the display is an approximate biplot. t The best val­ my competitors' products? What new products should ues for A and B, in terms of minimum squared error I create? What audience should I target for my new in approximating Y, are found using a singular value products? For example, consumers were asked to rate their pref- "Figure 2 does not contain the decomposition that would be used for an actual biplot. Small integers were chosen to simplify the arithmetic. tSVD is sometimes referred to in the psychometric literature tIn practice, the term biplot is sometimes used without qual­ as an Eckart-Young (1936) decomposition. SVD is closely tied ification to refer to an approximate biplot. to the statistical method of principal component analysis. 186 YDPREf Anolysi! of hlo.obiles Manufaclured in 1980 solute length of a consumer's vector is unimportant. The relative lengths of the vectors indicate fit, with longer vectors indicating better fit. The coordinates Conlinenlal I Eldorado 16 for the endpoints of the vectors were multiplied by 2.5 to extend the vectors and create a better graphical

D display. The direction of the preference scale is impor­ i • I tant. The vectors point in the direction of increasing values of the data values. If the data had been ranks, with 1 the most preferred and n the least preferred, then the vectors would point in the direction of the least preferred automobiles. Consumers 9 and 16, in the top left portion of the

-I plot, most prefer the large American cars. Other con­ sumers, with vectors pointing up and nearly vertical, also show this pattern of preference. There is a large cluster of consumers, from 14 through 20, who prefer -2 24 the Japanese and European cars. A few consumers, -2 -I most notably consumer 24, prefer the small and inex­ Dinnin 1 pensive American cars. There are no consumer vectors pointing through the bottom left portion of the plot Figure 3. Multidimensional Preference Analysis between consumers 24 and 25, which suggests that the smaller American cars are generally not preferred by any of these consumers. erence for a group of automobiles on a 0 to 9 scale, where 0 means no preference and 9 means high pref­ Some cars have a similar pattern of preference, most erence. Y is an (n x m) matrix that contains ratings notably Continental and Eldorado, which share a sym­ of the n. products by the m consumers. Figure 3 dis­ bol in the plot. This indicates that marketers of Conti­ plays an example in which 25 consumers rated their nental or Eldorado may want to try to distinguish their preference for 17 new (at the time) 1980 automobiles. car from the competition. Dasher, Accord, and Rabbit Each consumer is a vector in the space, and each car is were rated similarly, as were Malibu, Mustang, Volare, a point identified by an asterisk (*). Each consumer's and Horizon. Several vectors point into the open area vector points in approximately the direction of the cars between Continental/Eldorado and the European and that the consumer most preferred. Japanese cars. The vectors point away from the small American cars, so these consumers do not prefer the The dimensions of this plot are the first two principal small American cars. What car would these consumers components. The plot differs from a proper biplot of like? Perhaps they would like a Mercedes or BMW. Y due to scaling factors. At one end of the plot of the first principal component are the most preferred Preference Mapping. Preference mapping* (Car­ automobiles; the least preferred automobiles are at the roll, 1972) or PREFMAP plots resemble biplots, other end. The American cars on the average were but are based on a different model. The goal in least preferred, and the European and Japanese cars PREFMAP is to project external information into a were most preferred. The second principal component configuration of points, such as the set of coordinates is the longest dimension that is orthogonal to the first for the cars in the MDPREF example in Figure 3. The principal component. In the example, the larger cars external information can aid interpretation. tend to be at the top and the smaller cars tend to be Questions that can be addressed with PREFMAP at the bottom. analyses include: Where is my product positioned rela­ The automobile that projects farthest along a con­ tive to my competitors' products? Why is my product sumer vector is that consumer's most preferred au­ positioned there? How can I reposition my existing tomobile. To project a point onto a vector, draw an products? What new products should I create? imaginary line through a point crossing the vector at a The PREFMAP Vector Model. Figure 4 contains right angle. The point where the line crosses the vector an example in which three attribute variables (ride, re­ is the projection. The length of this projection differs liability, and miles per gallon) are displayed in the plot from the predicted preference, the scalar product, by of the first two principal components of the car prefer- a factor of the length of the consumer vector, which is constant within each consumer. Since the goal is to ·Preference mapping is sometimes referred to as external look at projections of points onto the vectors, the ab- unfolding. 187 P"feIIlCI Ylppin! 101 AutOiobiin hnullctu"d in UBO P'lh,"CI Yapping I., blOl.hi les Yanulaclured in 1980

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-2 -2 -2 -1 Oilusi .. 1 -2 -1 OillniOi I Figure 4. Preference Mapping, Vector Model Figure 5. Preference Mapping, Ideal Point Model ence data. Each of the automobiles was rated on a 1 to 5 scale, where 1 is poor and 5 is good. The end points for the attribute vectors are obtained by projecting the far away. Figure 5 shows the results of fitting an ideal attribute variables into the car space. Orthogonal pro­ point model for the three attributes. In the vector jections of the car points on an attribute vector give model, results are interpreted by orthogonally project­ an approximate ordering of the cars on the attribute ing the car points on the attribute vectors. In the ideal rating. The ride vector points almost straight up, in­ point model, Euclidean distances between car points and ideal points are compared. Eldorado and Conti­ dicating that the larger cars, such as the Eldorado and nental have the best predicted ride, because they are Continental, have the best ride. Figure 3 shows that closest to the ride ideal point. The concentric circles most consumers preferred the DL, Japanese cars, and drawn around the ideal points help to show distances larger American cars. Figure 4 shows that the DL and Japanese cars were rated the most reliable and have between the cars and the ideal points. The numbers the best fuel economy. The small American cars were of circles and their radii are arbitrary. The overall not rated highly on any of the three dimensions. interpretations of Figures 4 and 5 are the same. All three ideal points are at the edge of the car points, Figure 4 is based on the simplest version of which suggests the simpler vector model is sufficient PREFMAP-the vector model. The vector model op­ for these data. The ideal point model is fit with a erates under the assumption that some is good and multiple regression model and some pre- and post­ more is always better. This model is appropriate for processing. The regression model uses the MDS or miles per gallon and reliability-the more miles you MDPREF coordinates as independent variables along can travel without refueling or breaking down, the bet­ with an additional independent variable that is the ter. sum of squares of the coordinates. The model is a constrained response-surface model. The PREFMAP Ideal Point Model. The ideal point model differs from the vector model, in that the The results in Figure 5 were modified from the raw ideal point model does not assume that more is bet­ results to eliminate anti-ideal points. The ideal point ter, ad infinitum. Consider the sugar content of cake. model is a distance model. The rating data are inter­ There is an ideal amount of sugar that cake should preted as distances between attribute ideal points and contain-not enough sugar is not good, and too much the products. In this example, each of the automobiles sugar is also not good. In the cars example, the ideal was rated on these three dimensions, on a 1 to 5 scale, number of miles per gallon and the ideal reliability where 1 is poor and 5 is good. The data are the re­ are unachievable. It makes sense to consider a vector verse of what they should be--a ride rating of 1 should model, because the ideal point is infinitely far away. mean this car is similar to a car with a good ride, and This argument is less compelling for ride; the point a rating of 5 should mean this car is different from a for a car with smooth, quiet ride may not be infinitely car with a good ride. So the raw coordinates must be 188 Car D.ners and Cor Origin multiplied by -1 to get ideal points. Even if the scor­ ing had been reversed, anti-ideal points can occur. If the coefficient for the sum-of-squ~res variable is nega­ 1.5 , lorge tive, the point is an anti-ideal point. In this example, there is the possibility of anti-anti-ideal points. When D the coefficient for the sum-of~squares variable is neg­ i 1.0 m ' Single. Kids ative, the two multiplications by -1 cancel, and the e Alericon , coordinates are ideal points. When the coefficient for n s , 1 Income the sum-of-squares variable is positive, the coordinates i u.s a dOlllily' are multiplied by -1 to get an ideal point. n , Married I Kias Ren t , , Single Work Correspondence Analysis. Correspondence anal­ Mediul , , , Male D.O ysis (CA) is used to find a low-dimensional graph­ I Din ical representation of the association between rows Felole I and columns of a contingency table (crosstabulation). , 2 Incoliles Japanese -0.5 , , SlIIa II It graphically shows relationships between the rows European f I Sporty and columns of a table; it graphically shows the rela­ Married' tionships that the ordinary chi-square statistic tests. Each row and column is represented by a point in -1.0 a Euclidean space determined from cell frequencies. -1.0 -0.5 0.0 0.5 1.0 1.5 CA is a popular data analysis method in France and Japan. In France, CA analysis was developed under Dimension 1 the strong influence of Jean-Paul Ben2:ecri; in Japan, Figure 6. Multiple Correspondence Analysis under Chikio Hayashi. CA is described in Lebart, Morineau, and Warwick (1984); Greenacre (1984); Nishisato (1980); Tenenhaus and Young (1985); Gifi (1990); Greenacre and Hastie (1987); and many other Such information can be used to identify target audi­ sources. Hoffman and Franke (1986) provide a good ences for advertisements. This interpretation is based introductory treatment using examples from market­ on points being located in approximately the same di­ ing research. rection from the origin and in approximately the same region of the space. Distances between points are not Questions that can be addressed with CA and MCA interpretable in MCA. include: Who are my customers'? Who else should be my customers'? Who are my competitors' customers'? Multidimensional Scaling. Multidimensional scal­ Where is my product positioned relative to my com­ ing (MDS) is a class of methods for estimating the petitors' products? Why is my product positioned coordinates of a set of objects in a space of specified there'? How can I reposition my existing products'? dimensionality from data measuring the distances be­ What new products should I create'? What audience tween pairs of objects (Kruskal and Wish, 1978; Schiff­ should I target for my new products'? man, Reynolds, and Young, 1981; Young, 1987). The data for MDS consist of one or more square symmetric MCA Example. Figure 6 contains a plot of the re­ or asymmetric matrices of similarities or dissimilarities sults of a multiple correspondence analysis (MCA) of between objects or stimuli. Such data are also called a survey of car owners. The questions included ori­ proximity data. In marketing research, the objects are gin of the car (American, Japanese, European), size of often products. MDS is used to investigate product car (small, medium, large), type of car (family, sporty, positioning. work vehicle), home ownership (owns, rents), mari­ tal/family status (single, married, single and living For example, consumers were asked to rate the dif­ with children, and married living with children), and ferences between pairs of beverages. In addition, the sex (male, female). The variables are all categorical. beverages were rated on adjectives such as Good, Sweet, Healthy, Refreshing, and Simple Tasting. Fig­ The top-right quadrant of the plot suggests that the ure 7 contains a plot of the beverage configuration categories single, single with kids, one income, and along with attribute vectors derived through prefer­ renting a home are associated. Proceeding clockwise, ence mapping. The alcoholic beverages are clustered the categories sporty, small, and Japanese are asso­ at the bottom. The juices and carbonated soft drinks ciated. In the bottom-left quadrant you can see the are clustered at the left. Grape and Apple juice are association between being married, owning your own above the carbonated and sweet soft drinks and are home, and having two incomes. Having children is perceived as more healthy than the other soft drinks. associated with owning a large American family car. Perhaps sales of these drinks would increase if they 189 Mulli/i.,"io,,1 Sculi'g 01 B.. "uges of the vectors are not important since the goal is to Heo 1Ih, project points on vectors, not look at scalar products V8 J, i" • , Mi It of row points and column vectors. It is often necessary ClOd to change the lengths of all of the vectors to improve the graphical display. If all of the vectors are rela­

Sio,le Tosling tively short with end points clustered near the origin, D i the display will be difficult to interpret. To avoid this •e • hi er problem in Figure 3, both the x-axis and y-axis coor­ , Ice Tea 'Hoi Tea I• POI In , Hoi dinates were multiplied by the same constant, 2.5, to i 0 1 Up , Coif .. o • Dr. Pepper • Iced Coff .. lengthen all vectors by the same relative amount. The , P"si C.I, • Cute coordinates must not be scaled independently.

-1 • lile • Beer Conjoint Analysis

• RUllI -2 , Scolch Conjoint analysis is used in marketing research to an­ alyze consumer preferences for products and services. -1 -I See Green and Rao (1971) and Green and Wind (1975) Di .... ion I for early introductions to conjoint analysis and Green Figure 7. Multidimensional Scaling and PREFMAP and Srinivasan (1990) for a recent review article. Conjoint analysis grew out of the area of conjoint measurement in mathematical psychology. In its were marketed as a healthy alternative to sugary soft original form, conjoint analysis is a main effects drinks. A future analysis, after a marketing campaign, analysis-of-variance problem with an ordinal scale-of­ could check to see if their positions in the plot change measurement dependent variable. Conjoint analysis in the healthy direction. decomposes rankings or rating-scale evaluation judg­ Water, coffee and tea drinks form a cluster at the ments of products into components based on qualita­ right. V8 Juice and Milk form two clusters of one point tive attributes of the products. Attributes can include each. Milk and V8 are perceived as the most healthy, price, color, guarantee, environmental impact, and so whereas the alcoholic beverages are perceived as least on. A numerical utility or part-worth utility value is healthy. The juices and carbonated soft drinks were computed for each level of each attribute. The goal is rated as the sweetest. Pepsi and Coke are mapped to to compute utilities such that the rank ordering of the coincident points, as are Postum (a coffee substitute) sums of each product's set of utilities is the same as and Hot Coffee. Orange Soda is near Orange Crush, the original rank ordering or violates that ordering as and Lemon Koolaid is near Lemonade. little as possible. Geometry of the Scatterplots. It is important that When a monotonic transformation of the judgments scatterplots displaying perceptual mapping informa­ is requested, a nonmetric conjoint analysis is per­ tion accurately portray the underlying geometry. All formed. Nonmetric conjoint analysis models are fit of the scatterplots in this paper were created with the iteratively. When the judgments are not transformed, axes equated so that a centimeter on the y-axis rep­ a metric conjoint analysis is performed. Metric con­ resents the same data range as a centimeter on the joint analysis models are fit directly with ordinary x-axis. * This is important. Distances, angles between least squares. When all of the attributes are nomi­ vectors, and projections are evaluated to interpret the nal, the metric conjoint analysis problem is a simple plots. When the axes are equated, distances and an­ main-effects ANOVA model. The attributes are the gles are correctly presented in the plot. When axes independent variables, the judgments comprise the de­ are scaled independently, for example to fill the page, pendent variable, and the utilities are the parameter then the correct geometry is not presented. This im­ estimates from the ANOVA model. The metric con­ portant step of equating the axes is often overlooked joint analysis model is more restrictive than the non­ in practice. metric model and will generally fit the data less well than the nonmetric model. However, this is not nec­ For MDPREF and PREFMAP, the absolute lengths essarily a disadvantage since over-fitting is less of a problem and the results should be more reproducible *If the plot axes are not equated in this paper, it is due to with the metric model. unequal distortions of the axes that occurred during the final printing process. In both metric and nonmetric conjoint analysis, the 190 respondents are typically not asked to rate all possible Conjoint Analysis of Teo-Iosting Data combinations of the attributes. For example, with five Tie TRAHSm Procedure Hypothesis Tests for lIMEAR(SUBJ2) attributes, three with three levels and two with two levels, there are 3 x 3 x 3 x 2 x 2- = 108 possible com­ Unimiate ANOYA Table Based on the Usual Degrees of FreedOi binations. Rating that many combinations would be SUI of Yean difficult for consumers, so typic(!.lly only a small frac­ Some OF Squares Square F Yalue tion of the combinations are rated. It is still possible Model 7 617.722222 BR.mm 32.955 0.0001 Error 10 26.717118 2.671778 to compute utilities, even if not all combinations are Tolal 17 644.500000 rated. Typically, combinations are chosen from an or­ Root MSE 1.6363917 R-square 0.95845 thogonal array which is a fractional factorial design. Dep Mean 12.166667 Ad j R-sq 0.92937 In an orthogonal array, the zer%ne dummy variables CY 13.449795 are un correlated for all pairs in which the two dummy variables are not from the same factor. The main ef­ fects are orthogonal but are confounded with interac­ Utilities Table Based 01 lhe Unol Degrees of FreedoM tions. These interaction effects are typically assumed I'portance to be zero. Staldard (I Uti I i 1\ Lobe I ut iii ty £r ror Range Variable Questions that can be addressed with conjoint analysis Intercept 12 .1666667 0.3857 INTERC£PI include: How can I reposition my existing products? Lnon: No 0.7222222 0.3857 7.008 CLASS.mONNO What new products should I create? What audience L!IOn: Yes -0.7222222 OJ857 CLASS. L£UONYES should I target for my new products? Ielperalure: Hot 0.5000000 0.5455 12.129 CLASS. TEUPHOI Ielperature: Iced 1.0000000 0.5455 CLASS.mPIC£D Ielperalure: 'arl -I. 5000000 0.5455 CLASS.l£MPWARU Consider an example in which the effects of four at­ Sleetness: 1 leaspoon 3.1666661 0.m5 55.195 CLASS.SlmU tributes of tea on preference were evaluated. The Sleetness: 2 leaspaons 4.1666667 0.5455 CLASS.SlmU attributes are temperature (Hot, Warm, and Iced), Sleetness: No Sugar -7.3333333 0.m5 CLASS.SWEETNO sweetness (No Sugar, 1 Teaspoon, 2 Teaspoons), Strength: Uoderote 1.Bmm 0.5455 25.067 CLASS. SIR£NCUO Strength: Strong 1.5000000 0.5455 CLASS.SlRENCSI strength (Strong, Moderate, Weak), and lemon (With Strength: leak -l.3mm 0.5455 CLASS. SIRENm Lemon, No Lemon). There are four factors: three with three levels and one with two levels. Figure 8 contains Figure 8. Conjoint Analysis the results. Sweetness was the most important attribute (the im­ portance is 55.795). This consumer preferred two tea­ Multidimensional Preference Analysis. The spoons of sugar over one teaspoon, and some sugar was SAS/STAT procedure PRINQUAL performs multidi­ preferred over no sugar. The second most important mensional preference analysis and outputs the coordi­ attribute was strength (25.067), with moderate and nates for plotting. Nonmetric MDPREF, with trans­ strong tea preferred over weak tea. This consumer's formations of continuous and categorical variables, is most preferred temperature was iced, and no lemon also available. was preferred over lemon. Preference Mapping. The SAS/STAT procedure TRANSREG performs preference mapping and out­ puts the coordinates. Nonmetric PREFMAP, with transformations of continuous and categorical vari­ Software ables, is also available. Multidimensional Scaling. The SAS/STAT proce­ The SAS system includes software that implements dure MDS performs multidimensional scaling and out­ these methods. SAS/STAT@ software was used puts the coordinates. Metric, nonmetric, two-way, and to perform the analyses for all of the examples. three-way models are available. SAS/STAT software, including changes and enhance­ ments, is documented in SAS Institute (1989, 1992). Scatterplots. The Base SAS procedure PLOT can The perceptual mapping is described with more math­ plot the results from these analyses and optimally po­ ematical detail in Kuhfeld (1992). sition labels in the scatterplot. PROC PLOT, includ­ ing the changes and enhancements for label plotting, Correspondence Analysis. The SAS/STAT pro­ is documented in SAS Institute (1990, 1991, 1992). cedure CORRESP performs simple and multiple cor­ PROC PLOT uses an algorithm, developed by Kuh­ respondence analysis and outputs the coordinates for feld (1991), that uses a heuristic approach to avoid plotting. Raw data or tables may be input. Supple­ label collisions. Labels up to 200 characters long can mentary classes are allowed. be plotted. 191 A macro, using SAS/GRAPH® software, was used to methods may suggest how to reposition your product create graphical output from PROC PLOT. In the to appeal to a broader audience. They may also sug­ macro, PROC PLOT creates a printer plot, which gest new groups of customers to target. Preference is written to a file that the user can edit to modify mapping is used as an aid in understanding MDPREF label positioning. Then the macro reads the edited and MDS results. PREFMAP displays product at­ plot and creates the final graph .. There are options tributes in the same plot as the products. Conjoint to draw vectors to certain symbols and draw circles analysis is used to investigate how consumers trade off around other symbols. This macro is available free of product attributes when making a purchasing decision. charge. Send requests to Sue Glenn. For electronic mail, use [email protected]. If you do not have ac­ The insight gained from perceptual mapping and con­ cess to electronic mail, use: Sue Glenn, Applications joint analysis can be a valuable asset in marketing de­ Division, SAS Institute Inc., Cary NC, 27513-2414. cision making. These techniques can help you gain insight into your products, your customers, and your Conjoint Analysis. The SAS/STAT procedure competition. They can give you the edge in gaining a TRANSREG can perform both metric and nonmetric competitive advantage. conjoint analysis. PROC TRANSREG can handle both holdout observations and simulations. Holdouts are ranked by the consumers but are excluded from References contributing to the analysis. They are used to vali­ date the results of the study. Simulation observations' Carroll, J.D. (1972), "Individual Differences and are not rated by the consumers and do not contribute Multidimensional Scaling," in Multidimensional to the analysis. They are scored as passive observa­ Scaling: Theory and Applications in the Behav­ tions. Simulations are what-if combinations. They are ioral Sciences (Volume 1), in Shepard, R.N., combinations that are entered to get a prediction of Romney, A.K., and Nerlove, S.B. (Editors), New what their utility would have been if they had been York: Seminar Press. rated. The SAS/QC® procedures OPTEX and FACTEX, Eckart, C., and Young, G. (1936), "The Approxima­ along with the ADX menu system, can generate or­ tion of One Matrix by Another of Lower Rank," thogonal designs for both main-effects models and Psychometrika, 1, 211-218. models with interactions. Nonorthogonal designs­ Gabriel, K.R. (1981), "Biplot Display of Multivari­ for example, when strictly orthogonal designs require ate Matrices for Inspection of Data and Diagno­ too many observations-can be generated with the sis," Interpreting Multivariate Data, V. Barnett SAS/QC procedure OPTEX. Nonorthogonal designs (Editor), London: John Wiley & Sons, Inc. can be used in conjoint analysis studies to minimize the number of stimuli when there are many attributes Gifi, A. (1990), Nonlinear multivariate analysis. and levels. Chichester UK: Wiley. Other Data Analysis Methods. Other procedures Green, P.E. and Rao., V.R. (1971), "Conjoint Mea­ that are useful for marketing research include the surement for Quantifying Judgmental Data," SAS/STAT procedures for regression, ANOVA, dis­ Journal of Marketing Research, 8, 355-363. criminant analysis, principal component analysis, fac­ tor analysis, categorical data analysis, covariance anal­ Green, P.E. and Srinivasan, V. (1990), "Conjoint ysis (structural equation models), and the SAS/ETS® Analysis in Marketing: New Developments with procedures for econometrics, time series, and forcast­ Implications for Research and Practice," Journal ing. of Marketing, 54, 3-19. Green, P.E. and Wind, Y. (1975), "New Way to Mea­ sure Consumers' Judgments," Harvard Business Conclusions Review, July-August, 107-117.

Greenacre, M.J., and Hastie, T. (1987), "The Geo­ Marketing research helps you understand your cus­ metric Interpretation of Correspondence Analy­ tomers and your competition. Correspondence analy­ sis," Journal of the American Statistical Associa­ sis compactly displays survey data to aid in determin­ tion, 82, 437-447. ing what kinds of consumerS are buying your products. Multidimensional preference analysis and multidimen­ Greenacre, M.J. (1984), Theory and Applications sional scaling show product positioning, group pref­ of Correspondence Analysis, London: Academic erences, and individual preferences. Plots from these Press. 192