A Discussion of Papers in the &Quot;Current Issues in Multidimensional Scaling&Quot; Session

Vithala R. Rao, Cornell University
ABSTRACT - This note summarizes the discussion of the three papers presented in the session on "Current Issues in Multidimensional Scaling. In addition to presenting a comment on the papers, this note raises several technical issues ant possibilities for future research.
[ to cite ]:
Vithala R. Rao (1982) ,"A Discussion of Papers in the &Quot;Current Issues in Multidimensional Scaling&Quot; Session", in NA - Advances in Consumer Research Volume 09, eds. Andrew Mitchell, Ann Abor, MI : Association for Consumer Research, Pages: 406-407.

Advances in Consumer Research Volume 9, 1982      Pages 406-407


Vithala R. Rao, Cornell University


This note summarizes the discussion of the three papers presented in the session on "Current Issues in Multidimensional Scaling.

In addition to presenting a comment on the papers, this note raises several technical issues ant possibilities for future research.


The three papers in this session implicitly dealt with the question of how product information is linked to the various stages of the choice process. One paradigm that could help synthesize these papers is described below.

Product Information --> Similarities (perception) --> Preferences --> Choice

Under this view, the focus of each paper may be restated as follows:

Paper By: Gutman et al.

Focus: Study of similarities at one point in time with the purpose of describing a method of data collection for deriving the market structure of a large number of stimuli.

Paper By: Hutchinson and Farrand

Focus: Study of criterion-specific similarities and preferences obtained in repeat tasks with no intervening stimulus with the purpose of examining the psychological validity.

Paper By: McCullough et al.

Focus: Study of similarities and preferences using data collected at two points in time with messages (manipulated according to a 2x2 factorial design) as experimental variables with the purpose of looking at stability.

It would be useful to summarize the information on the sample sizes and substantive context of the studies reported.


The papers have not concerned themselves with the issue of how the stimuli are chosen and how the sample of stimuli employed in the respective studies is representative from the substantive point of view. In this context, the facet theory of Louis Guttman [1971] could be very useful to researchers in consumer behavior. Additionally, these studies were conducted using convenience samples; thus, their conclusions cannot be generalized.

The papers, however, are concerned with some basic issues of validity and stability within the context of their experiments

The analysis methods utilized in these studies generally represent many of the recently developed multidimensional scaling and related techniques. In particular, the techniques such as POLYCON, INDSCAL, LINMAP and ADTREE were used.

Some detailed comments on each paper are presented in the following sections. This discussion concludes with a brief statement of research possibilities in the general area covered by the papers.


The problem studied in this paper should be of great interest to consumer researchers engaged in studies of information processing and applied researchers looking at market segmentation issues. The paper presents a novel method of data collection that uses sorting task; the method should be particularly useful when one uses a large number of stimuli.

This discussion will raise three aspects: (i) derivation of market structure; (ii) technical issues on methods employed; and (iii) substantive conclusions drawn.

Derivation of Market Structure: One important issue that needs elaboration in this paper is the relative usefulness of the market structures derived from judgmental data as opposed to behavioral data (as collected in a panel). It could be argued that structures derived from behavioral data are more meaningful for managerial decisions. Some current research is focused on the issue of how to infer market structures and, therefore, consumer choice processes from observed behavior under certain assumptions; see Rao and Sabavala [1981].

Even if judgmental data are employed (as done in this paper), one needs to explicitly state the assumptions made at the individual level and implications of aggregating individual data. This paper does not adequately cover this issue of aggregation. Without a complete statement of the underlying assumptions and tests for validity of the assumptions, one could misinterpret the derived market structures.

Technical Issues: Scaling of the second order distance measure raises a question on the appropriateness of stimulus space derived in the analysis. If the Sik is related to an underlying space of stimuli, [xit] according to a squared Euclidean distance, then the measure, aij (derived from Sik, values) is a complicated function of the x values. In this context, the authors should explore the implications of multidimensional scaling of the [aij] matrix.

The authors could perhaps achieve their objective by scaling some direct measures such as those described in Bishop et al. [19751.

The measure used for describing inter-respondent similarity needs further justification. Further, the paper does not clearly identify the set of methods with which the method proposed is expected to compete.

Some ways of validating the results obtained and conclusions of such validation should be incorporated in the paper.

Substantive Issues: The authors should articulate the conceptual model leading to the judgments obtained. The construct of "familiarity" with stimuli could play a significant role in such conceptualization

The possibility of degenerate solutions in this analysis and its implications should be addressed in the paper.


This paper presents an intriguing idea of using combinations (mixtures) of existing products in the stimulus set in order to examine the psychological validity of perceptual and preference judgments. This idea will be useful in developing methods for assessing the positions of new products in existing product spaces. The implications of this approach are not fully exploited in this paper.

The study is highly exploratory; no substantive conclusions can be drawn. The test employed for assessing "psychological validity" is not clear. Some technical comments may, however, be made. First, the authors could have done some predictive testing by withholding two stimuli and predicting where they should fall in the space or tree. Second, the INDSCAL method could have been employed on all data (both test and retest) which would enable them to study the reliability of judgments. Third, the results from ADTREE require more interpretation. At times, the paper seems to confuse the terms, similarity and preference.

The issue of stability was not explored in depth. The authors need to employ a richer conceptual model and an error theory for changes of stimuli locations to examine this issue.

In summary, the paper presents a useful idea which requires extensive research in order to have an impact on studies of preference and perceptions.


The problem examined in this paper is highly significant for studies on similarities and preferences. The issues of determining structural changes and predicting what changes would occur require the specification of a model that relates stimulus locations and subject weights to experimental variables. Contrary to this approach, this paper is more descriptive of the changes rather than providing an explanation of the reasons why.

Readers of the paper ought to pay special attention to the definitions of various terms such as salience, weight, utility, characteristic, attribute and dimension. Unfortunately, the terminology employed in this paper is not generally consistent with that employed in the literature.

The particular analysis reported in the paper has some problems. Since the group space (derived from INDSCAL) is used in the estimation of v-coefficients according to LINMAP, the estimated v-coefficients will need to be adjusted for the idiosyncratic saliences as determined in the INDSCAL. This argument would imply use of ratios of weights of LINMAP ant INDSCAL saliences in ascertaining the effect of information on preferences.

Some alternative ways of analysis include: (a) comparison of data directly; and (b) a 4-way INDSCAL method for analyzing data from all subjects.

The data in this study could have been used for predictive testing as well.


The three papers discussed here are largely descriptive; advanced methods of analyses have been used for describing the data. In order to move this line of research to a higher level of generalization and abstraction, one may find the following directions of research to be worthwhile.

(i) To develop conceptual models for describing changes in perceptual spaces and preference structures and utilize them for analyses of data.

(ii) To develop an appropriate error theory for testing the significance of estimated changes; and

(iii) To perform predictive testing and validate the models.

Further, attention has to be paid to the issues of collecting data from representative samples of subjects and sampling of stimuli. The latter aspect requires more attention if consumer researchers wish to derive a general theory of perceptions and preferences as contrasted to models for describing such data.

Finally, the new techniques of constrained scaling could be valuable in models of change in perceptions and preferences. The method involves estimation of parameters of stimulus space or ideal points subject to constraints that various parameters (of stimulus space or ideal points or weights) are linearly related to prespecified variables; see Carroll et al. (1980).


Bishop, Y.M.M., Feinberg, S.E., ant Holland, P.W. (1975), Discrete Multivariate AnalYsis, Cambridge, MA: The M. I. T. Press.

Carroll, J. Douglas, Pruzansky, Sandra, and Kruskal, Joseph B. (March 1980), "CANDELINC: A General Approach to Multidimensional Analysis of Many-Way Arrays with Linear Constraints on Parameters," Psychometrika, Vol. 45, No. 1, 3-24.

Guttman, Louis (December 1971), "Measurement as Structural Theory," Psychometrika, Vol. 36, 329-347.

Rao, Vithala R., and Sabavala, Darius J. (June 1981), "Inference of Hierarchical Choice Processes from Panel Data," Journal of Consumer Research, Vol. 8, 85-96.