WILLIAM L. MOORE. RUSSELL S. WINER*. The recently developed "pick-any" approach to data collection and analysis is described and illustrated by examples ...
Constructing Joint Spaces from PickAny Data: A New Tool for Consumer Analysis MORRIS B. HOLBROOK WILLIAM L. MOORE RUSSELL S. WINER* The recently developed "pick-any" approach to data collection and analysis is described and illustrated by examples that support its face validity, reliability, and convergent validity with other multidimensional scaling techniques. Some solutions to problems that arise in applying the pick-any procedure are suggested, and potential extensions are proposed for use of the procedure in perceptual mapping applications.
M
this still assumes that the respondents are familiar with all brands in that subset. Furthermore, Farley, Katz, and Lehmann (1978) found that attribute ratings of an automobile differed significantly depending on which other makes were also rated, questioning the wisdom of this random-subset procedure. Unfortunately, in many applications, the assumption of respondent fami~iarity with all brands is unreasonable. For example, a prospective home buyer selects the relevant subset of potential housing choices from a vast range of possibilities. Similarly, a listener's choice of radio stations is restricted to a small subset of the total range of available alternatives. This use of an "evoked set" as a decisionsimplifying heuristic occurs in almost all types of buyer decisions in established product categories (Howard and Sheth 1969). In a study of seven packaged goods categories, Urban (1975) found the average evoked set to be about three. This implies that operative choice sets are idiosyncratic to each consumer in a given market. It also means that, for any specific revealed preference, selection of one alternative does not necessarily imply rejection of another--or even that it was considered at all. Empirical observations from such choice situationsi.e., where the choice set is virtually unconstrained and therefore differs among individuals-produce what Coombs (1964) referred to as "pick-any" data. For a particular respondent, a pick-any data set consists only of zeros (for brands not chosen or considered) and ones (for those chosen). In such a data format, only the ones are analyzed, since a zero does not necessarily imply rejection of that alternative. Standard MDS programs, such as KYST (Kruskal, Young, and Seery 1973), are conceptually and operationally inappropriate for handling pick-any data because they
ultidimensional scaling (MDS) has been one of the most popular topics in consumer research over the past decade (e.g., Green 1975). While MDS has proved to be invaluable in numerous applications, there are times when traditional MDS methods are either inappropriate or impractical. This paper discusses some of the limitations of these techniques and describes an alternative procedure that has proved to be useful in certain situations. The construction of joint spaces using external analysis of preference requires the collection of both perceptual and preference measures on all brands to be scaled. To provide data for the perceptual space, respondents must rate the similarity of all pairs of brands (Green and Carmone 1970) or rate each of the brands on a number of attributes (Johnson 1971; Pessemier and Root 1973; Urban 1975). To fit ideal points or preference vectors into the space, pair-comparison, rank-order, or rated preferences must then be collected on all brands (Carroll 1972). If one performs an internal analysis of preference (Carroll 1972; Sch6nemann and Wang 1972), one must still collect preference judgments on all brands or on all pairs of brands. In addition to placing fairly heavy demands on respondents' time and concentration, these data-collection procedures implicitly assume that the respondents are sufficiently familiar with all brands to provide meaningful information about each of them. While it is possible to reduce the respondent's burden (assuming homogeneity of perceptions) by requiring each individual to rate only a random subset of the brand pairs, *Morris B. Holbrook, William L. Moore, and Russell S. Winer are Associate Professors, Graduate School of Business, Columbia University, New York, NY 10027. The work was supported by the Columbia Faculty Research Fund. 99
© JOURNAL OF CONSUMER RESEARCH. Vol. 9. June 1982
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100
treat unchosen alternatives as though they have been rejected. Recently, however, Levine (1979) has developed a procedure specifically designed to analyze data in the pickany format. Levine's paper has stimulated an interest in the use of these data in a consumer context (Green and DeSarbo 1979,1981; Holbrook, Moore, and Winer 1980). The present paper explores the applicability of this technique and some of its extensions in consumer research. The underlying method is described and its use is then illustrated in two different situations. Problems encountered in its application to five different data sets are discussed and extensions of the basic method to perceptual mapping are proposed.
LEVINE'S PROCEDURE When pick-any data are collected, one has information only on which items were chosen (or preferred) and which were not. One does not know why some brands were not chosen-whether it was because they were not thought of or because they were thought of but rejected. Therefore, while the construction of a successful spatial representation of pick-any choices or preferences requires that people be positioned close to the brand(s) they have selected, there are no implications for the relative positions of brands not selected by a given individual. In other words, proximity in the space is a necessary but not sufficient condition for preference or choice. Levine (1979) addressed this problem of using pick-any data to derive a joint space. Taken individually, a brand should be located at the centroid of the people who selected it. Similarly, a person should be located at the centroid of the brand(s) chosen. Levine's solution is to solve both problems simultaneously by finding coordinates that best satisfy both centroid criteria at the same time. Specifically, if there are N respondents and K brands, E is defined as a symmetric matrix of dimension N + K with the following form:
E~[:~ :K]
where B is an N x K matrix of zeros and ones with elements bij indicating the choice of brand j by respondent i; N and K are N x Nand K x K null matrices respectively. D is defined as a diagonal matrix of order N + K with diagonal elements N+K
d ii
=
L j=1
eij
For i ~ N, d ii represents the number of brands chosen by person i, and for N + 1 ~ i ~ N + K, dii is the number of people choosing brand i - N. Finally, let x k be a column vector of N + K coordinates for the N respondents (first N rows) and K brands (last K rows) of the kth dimension of the joint space.
1
For a particular respondent (1 ~ i ~ N) or brand (N + i ~ N + K), the solution to the centroid problem is
~
N+K
= dii 1
X ik
L=
j
(1)
eijxjk 1
However, this equation can always be satisfied by placing all people and all brands at the same point. To obtain a nontrivial solution, the left side of Equation 1 is multiplied by a positive scale factor Ak : N+K
A0ik =
7
di 1
L
j= 1
(2)
eijxjk
For Ak -4= 1, Equation 2 places each individual's ideal point proportional to the centroid of the brands chosen, and each brand proportional to the centroid of the people choosing it. Equation 2 can be written in matrix form as follows: A0k
=
(3)
D-1Exk
Here, Ak and x k are the kth eigenvalue and eigenvector of the nonsymmetric matrix D -I E. For computational ease, both sides of Equation 3 can be premultiplied by the nonsingular matrix D1I2 to give: Ak
(D II2X k )
=
D II2 (D- 1E)x k
=
R(D II2X k )
(4)
where R = D - 1I2ED -112. Equation 4 is a symmetric eigenproblem where Ak is an eigenvalue and D1I2Xk is an eigenvector of R. The coordinates of the brands and respondents can therefore be obtained by calculating the eigenvectors of R and then premultiplying them by D- I12 to obtain D -1I2(D I/2X k) = x k . For small numbers of respondents and brands (e.g., N + K ~ 50), this procedure is straightforward and easily implemented using readily available computer routines. In realistic situations, however, the number of respondents (N) and/or brands (K) may become quite large, rendering the eigen-decomposition of the resulting (N + K)-square R matrix extremely expensive or even completely infeasible. Fortunately, a computational shortcut is available. Specifically, let V k = D II2X k . Because R is block off-diagonal with the form: R
~ [~,
:]
the first N rows of Vk (VNk ) are a linear function of the last K rows (VKk)' and vice versa, i.e., V Nk =
A;I
FVKk
(Sa)
V Kk =
A;IF'VNk
(5b)
In most applications, K
«
N. In these cases, VKk and
Ai can be obtained by decomposing F' F. Then VNk is found
using Equation 5a.
JOINT SPACES FROM PICK-ANY DATA
101
EMPIRICAL EXAMPLES
FIGURE A
Two empirical examples illustrate very different situations in which this method of joint space construction might be employed. The first is a situation in which it is very unlikely that any respondent is familiar with more than a small fraction of the available alternatives (radio stations in New York City). This example, where the more traditional MDS techniques are inappropriate, is especially wellsuited to the pick-any procedure. The second example involves two more familiar classes of products (soft drinks and bar soaps). Traditional MDS techniques could be appropriate here because many of the respondents are sufficiently familiar with most of the brands to be able to provide rank-order preferences or pair-wise similarity ratings. The purpose of this example is to compare the joint spaces produced by the pick-any approach and a traditional method (the unfolding option of KYST). This comparison is important because the pick-any data could be collected by means of telephone interviews, thus lowering data-collection costs and possibly permitting the use of a more representative sample.
JOINT SPACE OF STATIONS AND RESPONDENTS
a
WBLS-FM
'CJH~gh-energy • \
'\
'\
\
\
\
A study of radio listenership in the New York City area focused on determining the market structure implicit in local patterns of listening. As input into this analysis, panel data were obtained from a standard (but confidential) audience-measurement service. The panel was recruited from the New York City metropolitan area to provide information on their radio-listening habits for a one-week period. The basic information provided for each day included listening activity (stations selected) by time of day (in quarter-hour units) and whether the listening took place at or away from home. Other data concerned county, race, sex, age, and zip code. The initial sample included 1,472 respondents. Clearly, this choice situation is appropriate for pick-any analysis. Few people are familiar with many of the relatively large number of radio stations in the New York area. Therefore, choice of one station does not necessarily imply rejection of another with a similar format. Also, choice sets obviously vary between individuals. In view of these considerations, the radio listenership data were analyzed using Levine's procedure. The data were first pruned by dropping stations with few listeners from the analysis. These tended to be distant stations to which few local residents listened. Thus, if less than 4 percent of the panel listened to a station during the week, it was eliminated. This resulted in an analysis based on 25 stations and 1,380 respondents. Originally, the data from all 1,380 respondents were scaled with our pick-any algorithm. However, in order to represent the ideal points in a parsimonious manner, we decided to cluster them into homogeneous segments based on their coordinates in the joint space. Due to limitations on the available Howard/Harris (1966) clustering routine,
Low-brow
WAB;:-AMI
\
• WRVR-FM
\
I
.
WYNY-FM.
• WKTU-FM
\
/
\
\
I
.
WNEW-FMI • / WRFM-FM
I
a~
I
I
II
.WQXR-FM ·WNCN-FM
WNBC·AM
~
.WCBS-FM
WNEW-AM
e\.
.
WMCA-AM
~INS-AM
•
WHN-AM
WOR-AM·~ \ ~
\
WCBS-AM\
WPAT-M~\
I
High·brow
I
I · WXLO-FM
II I
I
I
I
\
WPLJ-FM WPIX-FM.
I
I
II@
\\
\
Radio Listenership Data
I
I
WBLI-FM
\ WVNJ-FM
•
WTFM-FM
•
• \ WPAT-FM
\
Low\ energy \
\ \
the sample was randomly split into three subsamples of equal size by taking every third person starting from the first, second, and third person, respectively. Data from each of the three groups of 460 respondents were then scaled separately. Interpoint distances between all pairs of the 25 stations were computed for each of the three analyses and correlated to obtain a measure of the reliability of the solutions. The first and third samples produced quite similar spaces: their interpoint distances had a correlation of 0.83. The second space was less similar to the first and third, with interpoint distance correlations of 0.67 and 0.65, respectively. The average interpoint distance correlation of 0.72 compares favorably with test-retest correlations of similarity spaces obtained by McCullough, MacLachlan, and Moinpour (1981) and by Summers and MacKay (1976). The joint space from the first sample is presented in Figure A. Radio stations are labeled and clusters are shown with the number of respondents in each. A rotation of the axes, as shown by the dotted lines, suggests a fairly high face validity. One axis appears to describe intellectual commitment (high- versus low-brow) with the two classical stations (WNCN-FM and WQXR-FM) at one end and top-40 stations (WABC-AM and WNBC-AM) at the other. The other axis represents a continuum from high-energy jazz/
THE JOURNAL OF CONSUMER RESEARCH
102
FIGURE B
disco stations (WBLS-FM and WRVR-FM) to low-energy "beautiful" music (WPAT-AM and WPAT-FM). Interestingly, these are the same two dimensions that appear in several studies of patterns of leisure activity (Holbrook and Lehmann 1981). As can be seen, the relative cluster sizes suggest the apathetic (185) or low-brow (125) tastes often associated with "popular culture" and the relatively narrow appeal of the classical (25) and jazz-oriented (35) stations.
PICK-ANY SPACE FOR SOFT DRINKS
Cola
Soft Drink and Bar Soap Data Data collection for traditional unfolding analyses is somewhat laborious for the respondent because rank-order, paired-comparison, or rated preferences must be obtained for all brands. The pick-any approach has the potential to ease this burden in that data can be elicited by asking only what brand(s) are considered. However, to utilize this simplified data-collection procedure, it must be shown that the joint space representations provided by the pick-any and by the traditional approaches are similar. This validation was conducted through a series of studies involving soft drinks and bar soaps. The same procedure was utilized on both products. Here, the soft drink data are discussed in detail and only a brief summary is devoted to bar soaps. Data collection for the validation study involved two steps. First, 45 MBA students were asked to "list the brands of soft drink that you would consider purchasing for your own use." Seven lines were provided for answers. The nine most frequently chosen brands were selected for analysis with the traditional unfolding methodology. No further use was made of these data. Second, another sample of 122 subjects was chosen from the same population and randomly assigned to one of two groups. Group 1 (60 subjects) received the same brandlisting questionnaire that had been used in the first step. Group 2 (62 subjects) received a list of the nine most popular brands from the preliminary phase; each subject was then asked to rank order all of the brands "according to your preferences when purchasing the product for your own use." The nine brands of soft drink listed on Group 2's questionnaire were also found to be the nine brands most frequently chosen by Group 1. A joint space was constructed for Group 1 by analyzing the choices of these nine brands with an algorithm based on Levine's procedure. Fifty-one of the 60 respondents chose at least one of these nine brands and were included in the analysis. The positions of these brands on the second and third dimensions are shown in Figure B (the first dimension is always the degenerate solution associated with X-\ = 1.0). A space of this dimensionality was chosen in accordance with advice given by Shepard (1974) on explained variance (65 percent of trace), interpretability, and parsimony. The horizontal axis is clearly a "diet-nondiet" dimension, while the vertical axis represents the "cola-noncola" dimension. This finding of a stronger diet dimension than cola dimension is consistent with other unfolding analyses of soft drink preferences
Coke
•
Diet Pepsi Pepsi • • Tab Non-Diet
Canada Dry
• • 7-UP
Dr. Pepper •
Diet •
Diet 7-UP
•Pepsi Light
Non- Cola
(Cooper 1973; Little and Moore 1975) and with spaces based on brand-switching data (Lehmann 1972). Rank-order preferences for the 58 usable responses from Group 2 were used as input to the split-by-rows option of KYST (Kruskal, Young, and Seery 1973). The resulting brand positions on the first two dimensions are presented in Figure C. The similarity of the two spaces is visually evident and is reflected by an interpoint distance correlation of 0.85. Thus, in this situation, the pick-any and the KYST methods produced quite similar results. Preferences for eight brands of bar soap were collected and analyzed in the same manner. The product positions (not shown due to lack of space, but available from the authors) had a reasonable degree of face validity. The beauty soaps, Dove and Camay, clustered together, as did the heavily scented Coast and Irish Spring. The more neutral Ivory and Dial fell in the middle of the space, while Palmolive and Zest were outliers. The interpoint distance correlation between all pairs of brands in the pick-any and KYST spaces was 0.69. This indicates a reasonable correspondence between the two spaces. Possible reasons for the reduced correspondence of results between methodologies are explored in the next section.
JOINT SPACES FROM PICK-ANY DATA
103
FIGURE C
respondents a list of brands and let them check those they would consider choosing. One drawback to this approach is that it partially violates the spirit of the pick-any method, as the choice set is prompted and not unconstrained. This does not appear to be critical, however, because the respondents can be explicitly instructed to consider only items that are familiar and to disregard any others.
KYST SPACE FOR SOFT DRINKS
Cola
Instability of Less Popular Brands Pepsi Light
•
• Diet Pepsi • Tab
Pepsi
•
Non-Diet
7-UP •
•
Diet
•Coke
Dr. Pepper
•Diet-7-UP
Canada Dry
•
Non-Cola
PROBLEMS ENCOUNTERED WITH THE PICK-ANY METHODOLOGY In a series of studies with the pick-any approach, three different but related problems arose concerning (1) questionnaire design, (2) instability of less popular brands, and (3) unequal prominence of brands.
Questionnaire Design One easily remedied difficulty was encountered when respondents failed to give full names by listing "brands" such as "cola," "store brands," or "Canada Dry." This problem was corrected through questionnaire instructions using examples of either fictitious brands or brands in other product categories. Another difficulty concerned respondents who listed only one brand. Such respondents obviously do not provide any information about the relative positions of the brands. This difficulty increases with smaller sample sizes. This problem was corrected fairly well through questionnaire instructions, i.e., by asking, "If you chose only one brand in a category and a store was out of that brand, would you purchase any other brand? If so, list the one you would consider." Another way of coping with this problem was to give the
When only a few people choose a particular brand, its position is very unstable and it tends to be placed in an extreme location in the space. For example, in Figure B, only two people chose Pepsi Light. One of these two also chose Tab and Diet 7-Up, as might be expected. However, the other also chose Canada Dry, Dr. Pepper, and Tab. Thus, the two people choosing Pepsi Light had very different choice sets. In an attempt to satisfy the centroid conditions, Pepsi Light was placed in an extreme position in the space. When the second observation is dropped, Pepsi Light falls close to Tab and Diet 7-Up. Similarly, in the analysis of bar soaps, Zest was chosen by a small number of people, and it appears that its outlying position had a bearing on the lower correspondence between the two bar soap spaces. This problem suggests that, in general, one should not attempt to interpret the space based on the outlying, infrequently chosen brands. However, it appears that this difficulty decreases in severity as the sample size increases. In the radio-listenership survey, the classical stations (WQXR-FM and WNCN-FM) were two of the three least popular stations (Figure A); yet their positions were quite stable in all the joint spaces constructed. Therefore, the problem appears to be more a function of the absolute number of people choosing a brand than of the relative proportion of people choosing it. This question might be fruitfully studied through simulations in future research. Green and DeSarbo (1979, 1981) have developed an external unfolding algorithm for pick-any data. In their approach, ideal points are positioned in an existing perceptual space by placing each at the centroid of the brands chosen by a given individual. Obviously, this eliminates the problem of brand stability because the positions of the ideal points are derived in a previous analysis. If one is willing to assume homogeneity of perceptions (which is generally done), perceptual data can be collected from a small number of respondents and the pick-any data can then be gathered for a much larger sample.
Unequal Prominence of Brands In an earlier study of the toothpaste market, all respondents listed Crest as one of their choices, so that Crest was chosen in combination with every other brand. As a result, it appeared in the center of the space. If this space is interpreted with the aid of attribute vectors, Crest would be dominated by at least one brand on any possible attribute.
104
This result would be at variance with our expectations and with previous findings by Moinpour, McCullough, and MacLachlan (1976). It is possible that the characteristics of the brands in pickany joint space should be modeled as features rather than attributes. That is, the characteristics could be represented as fixed points in the space (Green, Wind, and Claycamp 1975). Brands close to such a feature would tend to possess the characteristic in question. By contrast, when a characteristic is interpreted as an attribute, it can be represented by a vector in the space so that the brands with projections that fall farthest toward the head of the vector tend to rate highest on that characteristic. The difference in interpretation between features and attributes is thus analogous to the difference in the way ideal points and preference vectors are interpreted in a joint space. Here, the feature-based interpretation might help reduce the problem of unequal brand prominence, since the positions of features would be based on clusters of brands rather than on the locations of brands at the periphery of the space. A similar consideration arose in the study of bar soaps, where Ivory was chosen by 42 of 51 respondents and therefore appeared in the middle of the space. However, in this case, the central position of Ivory may reflect its perceived neutral position on key product characteristics, making it a good middle-of-the-road brand, i.e., acceptable to many people. To summarize, when one brand was chosen much more often than the others, it tended to be placed at the center of the space. While this did not conform to our expectation, it is possible that the expectation rather than the joint space was wrong. This problem of one-brand dominance does not appear to be too severe: it did not show up with Coke in the soft drink study or with Budweiser in an earlier study of beer choices. However, in order to examine this issue further, another questionnaire was constructed in which respondents were given a list of brands and asked to check the ones that they would consider purchasing for their own use. In this manner, the brands were made more equally prominent. This did not change the position of either Ivory or Crest: both remained in the middle of their respective spaces. However, this method did seem to reduce the problem of outliers.
PERCEPTUAL SPACES FROM PICK-ANY DATA: AN EXTENSION This method also appears to lend itself to the construction of perceptual spaces. In such an application, respondents would be asked which brands possess certain features or rate high on various attributes. For example, one could ask which brands of toothpaste are good at preventing cavities, leave your mouth feeling fresh, or have the lowest levels of abrasion. These responses could then be aggregated across people so that the resulting matrix would be a brandsby-attributes matrix rather than a brands-by-people matrix.
THE JOURNAL OF CONSUMER RESEARCH A brand-attribute intersection would contain a one if some minimal (say, one-half) proportion of respondents rated the brand high on that attribute and a zero otherwise. This methodology would make data collection much easier when constructing perceptual spaces. However, the proposed approach should be validated against traditional perceptual mapping techniques as well as against other methods of analyzing contingency data (Pessemier 1979).
CONCLUSIONS The construction of joint spaces from pick-any data has been described and illustrated with a number of examples. These results generally suggest high face validity. Moreover, when compared to other MDS techniques, the pickany methodology appears to give fairly similar results. Its split-half reliability (as measured by interpoint distance correlations) was comparable to the test-retest reliabilities found in perceptual spaces derived by other procedures. Further, while no validation tests on actual purchases have yet been carried out (cf. Moore, Pessemier, and Little 1979), it is expected that the relationship will be fairly strong. Haley and Case (1979) found that both brand choice and brand awareness scales were related to brand last purchased. Use of pick-any data greatly reduces the respondent burden and enables one to collect data for the construction of joint spaces with telephone or other inexpensive interviews. Finally, as a benefit in an age of time-sharing computer systems, the solution by eigenvalue decomposition offers greatly reduced computational time. In spite of these advantages, we have encountered a number of problems in the application of the pick-any methodology. At this point, most of them seem to be manageable through good research practices (e.g., explicit instructions in the questionnaire and adequate sample sizes). The problem of the stability of outlying brands seems to be the most severe. It appears that this problem may be overcome by presenting respondents with a list of brands and letting them check off those they prefer. Preliminary research on this data-collection technique indicates that it tends to increase the total number of brands mentioned, but does not alter the basic pattern of which brands are mentioned together. Thus, the primary effect has been to stabilize the outlying brands rather than to disturb the location of the more popular brands. However, resolution of this issue will require further research. These different data-collection methodologies should be validated against more traditional MDS approaches as well as actual market choice behavior. As a further interpretive safeguard, we recommend that characteristics of the brands in pick-any spaces be viewed as features (i.e., fixed points) rather than as attributes (i.e., continuous vectors). While this is a change from the traditional interpretation of MDS configurations, it accords with recent psychometric developments (Shepard 1974). [Received August 1981. Revised December 1981.]
JOINT SPACES FROM PICK-ANY DATA
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