# Consumer Menu Preference: an Application of Additive Conjoint Measurement

##### Citation:

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Paul E. Green, Yoram Wind, and Arun K. Jain (1972) ,"Consumer Menu Preference: an Application of Additive Conjoint Measurement", in SV - Proceedings of the Third Annual Conference of the Association for Consumer Research, eds. M. Venkatesan, Chicago, IL : Association for Consumer Research, Pages: 304-315.
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[Paul E. Green is S. S. Kresge professor of marketing, Yoram Wind is associate professor of marketing and Arun K. Jain is a doctoral student in marketing, all in the Wharton School, University of Pennsylvania. Financial support, in part, was provided by the General Electric Educational Foundation.]

In a recent JMR article Green and Rao (1971) presented an exposition of conjoint measurement procedures and commented on the fact that application of these techniques was still in its formative stages. This note describes one such application in the area of consumer preferences for menus. Specifically, additive conjoint measurement is applied to respondent evaluations of two-, three- and four-component restaurant menus in order to derive part-worth contributions of the components: appetizer, entree, dessert and price, to the total utility of a menu.

Two main questions guided the research design [The procedure and analysis described here represents only part of the complete study, a full account of which can be obtained from the authors.] and subsequent analysis:

1. Are utilities for menu components describable by an additive utility model, i.e., where total utility is equal to the sum of component utilities?

2. Are component utilities stable over embedding conditions-two-, three-, and four-component menus? For example, is the utility for apple pie relatively the same in the context of roast beef alone as it is in the context of shrimp cocktail, roast beef and a menu price of $6.50?

We first briefly describe the additive utility model and its relationship to this application. The results of the study are then presented, followed by a short discussion of the relevance of this type of research to managerial and consumer decision making.

ADDITIVE CONJOINT MEASUREMENT

In additive conjoint measurement the researcher is interested in measuring jointly--at the level (asymptotically) of interval scales with common unit--an originally rank-ordered dependent variable and a set of independent variables. In so doing one assumes that a particular composition rule (viz., an additive one) describes the observed rank order. To illustrate, suppose a respondent is asked to rank a set of menus according to preference, each menu consisting of an appetizer, entree and dessert. Assume, further, that three different appetizers, entrees and desserts are available for making up the menus. Given three "levels" of each menu component, 27 distinct menu combinations are possible.

Each menu can be represented as an ordered n-tuple:

(1) X = (X

_{1}, X_{2}, X_{3})

where x (j = 1, 2, 3) denotes some value of the j-th factor. Other menu combinations are denoted x', x", etc.

In additive conjoint measurement we seek real-valued functions on each factor (menu component) such that utility, U(x), is expressed as:

(2) U(x) = f

_{1}(X_{1}) + f_{2}(X_{2}) + f_{3}(X_{3})

and x > x' if and only if U(x) > U(x'), where > is defined as an observable relation: "not less preferred than."

Thus, experimentally, one constructs factorial combinations of menu components, 27 combinations in the above case, and has the respondent rank order the combinations from most to least preferred. [If the number of factor-level combinations is too large for convenient ranking one can use fractional factorial designs of the type employed in this study.] One then seeks a non-decreasing monotonic function of the observed ordering and part-worth functions, f1, f2, and f3, whose values are added to produce U(x), U(x'), etc.

Specifically, we can portray equation (2) in more traditional analysis of variance terms as

(3) U(x) = B

_{0}+ B_{1}X_{21}+ B_{2}X_{31}+ B_{3}X_{32}+ B_{4}X_{32}+ B_{5}X_{23}+ B_{6}X_{33}

where B0 denotes the contribution to utility when all factors are at their first levels and B1, B2, ... B6 denote the incremental utility contributions of each factor at their second and third levels.

Additive utility theory has a long history (Becker & McClintock, 1967) but only recently have procedures been devised to measure component utilities in cases where the dependent variable is only rank ordered. One such algorithm, Kruskal's MONANOVA program (Kruskal, 1965), is used in this study.

DATA COLLECTION

There were 46 subjects who participated in this study: 23 males and 23 females, drawn from the Philadelphia area. The subjects were young adults in their mid-twenties to mid-thirties. The sample was drawn on a convenience basis. All interviewing was personally administered by trained student interviewers of the Wharton School.

Stimuli, Procedure, and Tasks

The stimuli used in the study consisted of the names of 15 common food items--5 appetizers, 5 entrees and 5 desserts, as shown in Table 1. Also shown are the price levels (for restaurant-type menus) used in the last experimental task.

In the first phase of the interview the respondent was shown a set of twenty-five 3" x 5" cards. On each card was printed a pair of menu items-a specific appetizer and entree (denoted A-E in subsequent analysis). The subject was asked to imagine that he had been invited out to dinner by a friend and could order any of the 25 "menus" he desired (without being responsible for paying the bill). He was first asked to sort the cards into three ordered categories of overall liking and then to rank the cards within each category according to overall liking. (Cards could be shifted from category to category prior to final ranking.) This two-stage procedure was then repeated for 25 appetizer-dessert pairs (A-D) and 25 entree-dessert pairs (E-D), each consisting of all appropriate combinations of the items shown in Table 1.

STIMULI AND BACKGROUND VARIABLES USED IN MENU EVALUATION TASKS

In the next phase of the interview the respondent was again shown a set of 25 cards. However, this time each card consisted of a triple of items-appetizer, entree and dessert (A-E-D). The combinations used for presentation were developed from a latin square design representing a one-fifth replicate of the full set of 125 factorial combinations. Instructions proceeded as before.

In the next phase of the interview the respondent was again shown a set of--25 cards. Each card contained a four component profile--appetizer, entree, dessert and price (A-E-D-P). The respondent was asked to imagine that this time he was responsible for purchasing his own meal. The combinations used for presentation were based on a graeco-latin square design representing a one-twenty-fifth replicate of the full set of 625 factorial combinations. Instructions for ranking proceeded as before.

RESULTS

Each subject's ranking data regarding A-E, A-D, E-D, A-E-D and A-E-D-P were analyzed separately by means of Kruskal's MONANOVA algorithm. This program finds a best fitting monotone transformation of the original ranking and component utility scales such that the sum of the part worths of each menu component equals values of the monotonely transformed ranks. The program computes stress as a badness of fit measure. Stress represents (the square root of) a normalized residual sum of squares between additive model and monotonely transformed data values. A perfect fit of model to transformed data is associated with a stress of zero. Stress values less than or equal to 0.1 are considered "good" fits from a rough, descriptive viewpoint.

In the case of tasks A-D, A-E and E-D a full factorial design was used. In tasks A-E-D and A-E-D-P the input data were treated as a fractional factorial and the missing data feature of MONANOVA was utilized. (Use of the latin square and graeco-latin square designs presuppose additivity of utilities.)

Additivity

Table 2 shows a frequency tabulation of stress by type of task.

FREQUENCY TABULATION OF STRESS VALUES FROM MONANOVA, BY TASK

As can be noted from Table 2, the number of respondents displaying stress values of 0.1 or less for A-D, A-E, E-D, A-E-D and A-E-D-P, respectively, are 31, 26, 39, 29, and 34; that is, on the average, almost 70 per cent of the subject-tasks showed correspondence with the additive utility model.

Of course, high stress (poor fit) cases are equivocal. One cannot tell whether high stress reflects noisy data or a more complex, e.g., interactive-type, model. In the cases of the two component tasks, A-E, A-D and E-D, a full factorial design is represented. If, for the moment, one assumes that the original integer ranks can be treated as numerical (cardinal) values, standard ANOVA procedures can be used to examine the menu component interaction term. Accordingly. the original integer rank numbers for the A-E, A-D and E-D tasks were submitted to separate ANOVA computations. (Since ranking data are used, each subject's mean and variance is constant; hence, sums of squares from this source of variation are zero.) Table 3 shows the results of the ANOVA calculations.

ANALYSIS OF VARIANCE SUMMARIES FOR TWO-COMPONENT TASKS

Examination of the three ANOVA summaries of Table 3 shows that the contribution of sums of squares for menu component interaction to total sums of squares is indeed small. Although not shown in the table, the ratios of sums of squares due to menu component interaction to total sums of squares are only 0.002, 0.004 and 0.003, respectively, for A-E, A-D and E-D. Moreover, the largest mean squares are associated with either main effects (menu item-values) or subject-item interaction. None of the menu-item interaction terms is "significant" at the 0.05 level; however, in view of the ranking-type input data these "tests" are considered only descriptively.

Thus, given the reasonably low stress values and the small contribution of menu component interaction to total sums of squares (treating the integer ranking data as cardinal values), it would appear that the two-component menu data, at least, are rather well represented by an additive utility model. Of course, the possibility exists that some respondents, in some tasks, could be employing more comPlex (e.R., interactive) models.

Scale Stability Across Tasks

While it may be true that additive utility models provide good accounts of most subject-tasks, it does not necessarily follow that particular component utilities are the same across tasks. Accordingly, this question was considered next. For any specific subject the experimental design used here permits one to develop four interval scales each, for appetizer, entree and dessert items: a) the two scales for each menu component, as derived from the two-component tasks A-E, A-D and E-D; b) the scale derived from the three-component task; and c) the scale derived from the four-component task. Separate analyses can be conducted for appetizers, entrees and desserts.

To illustrate, for each of the 46 subjects, four scales were available for each of the 5 appetizers. At the individual subject level these scales can be intercorrelated in order to see if scale values differ across tasks. This was done for each subject in turn. Then an average correlation (of the six distinct two-variable correlations) was computed as a descriptive summary measure of how stable each subject's scales were across tasks.

The upper panel of Table 4 shows a frequency tabulation of the results of this analysis. We note that scale stability is greatest across tasks involving entrees, followed by appetizers and desserts. [The relative stability of scales was in accordance with the relative importance of each component class, as independently reported by each respondent. That is, each respondent was also asked to rate (on an 11-point scale) the relative importance of each menu component to overall meal satisfaction.] In all cases, however, the median correlation across subjects is-0.75 or higher.

The lower panel of Table 4, summarizing inter-task correlations (averaged over subjects), indicates that these correlations are also fairly stable. [However, some tendency is noted for correlations to decrease as the embedding context becomes more complex, e.g., three-component or four-component versus two-component menus.] Again we note that stability across scales appears greatest in the case of entrees, followed by appetizers and then desserts.

Group Summary

In order to provide the reader with some idea of the substantive results of the study, MONANOVA scalings were also made of the ranks summed across the whole sample for each of the tasks separately, The part-worth scales found by MONANOVA were then translated and scaled, for comparison purposes, to unit sums of squares.

Figure 1 shows the results of these group analyses.

FREQUENCY TABULATION OF INTER-TASK SCALE CORRELATIONS BY SUBJECT AND TASK PAIR

PART-WORTH FUNCTIONS (NORMALIZED) BY COMPONENT AND TASKS

Scale stability at the group level differs somewhat by menu component. In the case of entrees all scale values are ordinally stable across tasks. We note that filet mignon is most preferred in all cases and roast pork is least preferred. Less stability is noted in appetizers, although the two highly favored appetizers, shrimp cocktail and fruit cup, remain well separated from the rest. Similarly, insofar as desserts are concerned, scale values lack stability although the two favored desserts, apple pie and vanilla ice cream, remain well separated from the remaining desserts across all tasks.

Finally, the behavior of price utility (as measured in the A-E-D-P task) in Figure 1 is of interest. As might be expected, component utility decreases with increases in menu price. Over the experimental range of this variable the relationship is almost linear.

DISCUSSION

The foregoing report illustrates how conjoint measurement--more specifically, additive conjoint measurement--can be used to develop partworth contributions of various components of a multi-component alternative to total utility. Moreover, these component utilities are (asymptotically) interval scaled with common unit, although the original dependent variable (the respondent's preferences for menus) is only rank ordered.

More elaborate utility models involving powers or interaction terms are capable of being applied within the conjoint measurement framework (Carroll, 1972). Indeed, conjoint measurement models exist for coping with responses that are expressed only categorically (Carroll, 1970), ordered or unordered.

The advantage of conjoint measurement procedures over other measurement methods lies primarily in their ability to deal with rank ordered response data. Moreover, as discussed by Krantz and Tversky (1971), conjoint measurement may be used to test alternative composition rules rather than seek scale values that are in best agreement with a prespecified composition rule (as was emphasized here). [Unfortunately, appropriate statistical tests for dealing with fallible response data (where composition rules are not perfectly satisfied ordinally) are still lacking.] One might next inquire about the relevance of conjoint measurement to consumer and managerial choice behavior. [See Green and Bao (1971) for a discussion of some of the current limitations of conjoint measurement.]

Consumer Choice Behavior

A key consideration in the study of consumer choice is that most alternatives are multi-attribute. For example, current attitude theories postulate that total affect is functionally related to a set of "evaluative beliefs." Conjoint measurement provides a way to deal directly with the question of part-worth contributions to total utility (Becker & McClintock, 1967). That is, consumers can respond to the alternatives as total entities; it is the analyst who decomposes these responses according to some utility model, additive or otherwise (Einhorn, 1970). If the composition rule holds, the analyst should be able to predict choice among new combinations placed in the existing array of multi-attribute alternatives.

A number of measurement problems--price elasticity, package design, product benefits analysis, perceived risk--would seem to be amenable to conjoint measurement designs although little empirical research has been conducted on these problems so far.

Managerial Choice Behavior

The study of managerial decision making is also characterized by multiple objectives--profits, growth, market share, environmental effects, and so on. Somehow managers "balance" conflicting objectives by means that are rarely explicated to the researcher. Here, too, it would seem that various utility models might be explored via conjoint measurement, including the study of self-explicated models (Hoepfl & Huber, 1970). With growing awareness of the complexity of modern decision making, it seems clear that future research attention will be increasingly paid to multiattribute choice problems in both the private and public sectors. Conjoint measurement could play a methodological role in the measurement tasks associated with these problems.

REFERENCES

Becker, G. M. & McClintock, C. G. Value: Behavioral Decision Theory. Annual Review of Psychology (1967) 239-86.

Carroll, J. D. Categorical Conjoint Measurement. Multilithed report. New Jersey: Bell Telephone Laboratories, 1970.

Carroll, J. D. Individual Differences in Multidimensional Scaling. In Shepard, R. N., Romney, A. K. and Nerlove, S. (eds.), Multidimensional Scaling: Theory 1 Applications in the Social Sciences. New York: Academic Press, 1972.

Einhorn, H. J. The Use of Nonlinear, Noncompensatory Models in Decision - Making. Psychological Bulletin 1970, 73, 221-230.

Green, P. E. & Rao, V. R. Conjoint Measurement for Quantifying Judgmental Data. Journal of Marketing Research, 1971, 8, 355-63.

Hoepfl, R. T. & Huber, G. P. A. Study of Self-Explicated Utility Models, Behavioral Science, 1970, 15, 408-14.

Krantz, D. H. & Tversky, Amos. Conjoint Measurement Analysis of Composition Rules in Psychology, Psychological Review, 1971, 78, 151-69.

Kruskal, J. B. Analysis of Factorial Experiments by Estimating Monotone Transformations of the Data. Journal of the Royal Statistical Society, Series B, 1965, 22, 251-263.

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##### Authors

Paul E. Green, University of Pennsylvania

Yoram Wind, University of Pennsylvania

Arun K. Jain, University of Pennsylvania

##### Volume

SV - Proceedings of the Third Annual Conference of the Association for Consumer Research | 1972

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