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Usage of the Multidimensional Scaling in Exploring a Firm's Image and Competitiveness Mersid Poturak, M.A.
Ali Goksu
International Burch University Faculty of Economics, Management Department Sarajevo, Bosnia and Herzegovina
[email protected]
International Burch University Faculty of Economics, Management Department Sarajevo, Bosnia and Herzegovina
[email protected]
Abstract— Multidimensional scaling is a statistical technique which is used to provide a visual representation of similarities or dissimilarities between data. In multidimensional scaling, objects are represented as points in a usually two dimensional map, in way where data that are perceived to be very similar to each other are placed near each other on the map, and those data that are perceived to be very different from each other are placed far away from each other on the map. The purposes of this paper are: (1) to explain, in a nontechnical fashion, the theory and procedures underlying metric multidimensional scaling; (2) Presentation its usage through example where one selected company uses perceptual mapping techniques to identify its position in a perceptual map of major competitors in the market, with an understanding of the dimension comparisons used by potential customers; Keywords- Multidimensional Scaling, similarity, dissimilarity, individual differences, ideal points
I.
INTRODUCTION
The visualization of multivariate abstract data is a fundamental task in many fields. From bioinformatics to the financial sector, there is a great deal of interest in data that have no inherent mapping to a 2D or 3D space. Graphical means of conveying such information are subsequently relied upon to provide insight into patterns and relationships. [2] Some objects are more similar (or dissimilar) to each other than others. For example, red and pink are more similar than red and green. MDS represents the similarity or dissimilarity data among the objects by mapping the points (representing the objects) into a multidimensional space in such a way that the distances between them best accord with the observed (dis)similarity data between the objects. In the above example, the points representing red and pink are located closer in the space than the points representing red and green. By virtue of MDS, we can visually inspect the (dis)similarity data among the objects and investigate the principle underlying the organization of the (dis)similarity data. [3] A critical requirement of the production of such a representation is the means to generate layouts of the multivariate data in a lower dimensional space. The created visualization should preserve relationships existing within the data and should be comprehensible enough to allow the user to perceive such patterns. [4]
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Multidimensional scaling (MDS) is one means of mapping a data set onto a smaller number of dimensions, so that it may be visualized in a more manageable form. [4] This paper will describe MDS in more detail before discussing its usage in exploring a firm's image and competitiveness. A later section outlines example where one selected company uses perceptual mapping techniques to identify its position in a perceptual map of major competitors in the market, with an understanding of the dimension comparisons used by potential customers. Multidimensional Scaling can be simply defined as a set of data analysis techniques for analysis of similarity or dissimilarity data. It is used to represent (dis)similarity data between objects by a variety of distance models. [3] Multidimensional scaling (MDS) permits customers’ perceptions of competing products’ similarities and dissimilarities to be represented graphically and for the dimensions to be interpreted in terms of key product attributes. II.
LITERATURE REVIEW
There are many studies which purpose was to describe MDS. On the other extreme some researchers used this method for different type of data and different studies [5]. It then lay fallow and essentially unused until "revived" and modernized in the 1950s by Torgerson [6] and others, stimulated in large part by the development of modern digital computers-which made the complex methodology computationally feasible, especially in the multidimensional as well as nonmetric cases. The early history of MDS in marketing research is described in three review articles: Green [10] discusses several issues (e.g., computer program differences, the metric versus nonmetric controversy, multidimensional psychophysics) and problems facing the future of MDS methodology in designing new products; Green and Rao (1977) describe the major types of nonmetric scaling techniques and illustrate solution recovery; and Cooper, [7] provides a comprehensive review of marketing applications and also discusses trends in the use of this methodology in the future. The earliest application of MDS in marketing research appears to have been conducted by a psychometrician. Torgerson (personal communication) applied MDS in the late
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1950s to a practical problem involving consumers' perceptions of a new set of patterns designed by a New England silverware manufacturer. Steffire (1969) is probably the earliest marketing researcher to use MDS systematically-in his case mostly as a graphic device to present consumers' perceptions of brand similarities in a spatially powerful manner to businesspeople. His three-dimensional representations of MDS results, which he called "tinkertoys," provide effective devices for communicating the findings of his company's studies. The tinkertoys show interrelationships among real and/or hypothesized brands of coffee, paper products, soaps, and so on, as defined in terms of important perceptual dimensions. [8]
with specific techniques, including conjoint analysis, multidimensional scaling and structural equation modeling but in this study we will use only one of these datasets for MDS application.
Neidell [9] in his study "The Use of Nonmetric Multidimensional Scaling in Marketing Analysis" explained in a nontechnical fashion, the theory and procedures underlying nonmetric multidimensional scaling. He presented an example of its use; and speculated on some marketing applications.
Moreover, the intent is to create a single overall perceptual map by combining the positioning of objects and subjects and making the relative positions of objects and consumers for segmentation analysis much more direct.
Green [10] presented an overview of multidimensional scaling methods as applied to the analysis of similarities and preference data. They reported the results of an empirical comparison of three computer-based programs proposed for the multidimensional scaling of rank order preference data. DeSarbo and Manrai [11] presented multidimensional scaling (MDS) methodology which operationalizes the Krumhansl (1978) distance-density model for the analysis of asymmetric proximity data. Venna and Kaski [12] show experimentally that one of the multidimensional scaling methods, curvilinear components analysis, is good at maximizing trustworthiness. They then extend it to focus on local proximities both in the input and output space, and to explicitly make a user-tunable parameterized compromise between trustworthiness and continuity. The new method compares favorably to alternative nonlinear projection methods. Silva and Tenenbaum [13] in their paper, they discuss a computationally efficient approximation to the classical multidimensional scaling (MDS) algorithm, called Landmark MDS (LMDS), for use when the number of data points is very large. They then provided an elementary and explicit theoretical analysis of the procedure, and demonstrate with examples that LMDS is effective in practical use. Groenen and Velden [14] discuss what kind of data can be used for multidimensional scaling, what the essence of the technique is, how to choose the dimensionality, transformations of the dissimilarities, and some pitfalls to watch out for when using multidimensional scaling. In Zhang (2010) article, author introduced the basic concepts and models of MDS. He then discuss a variety of (dis)similarity data and their scale levels, and the kinds of MDS techniques to be used in specifc situations such as individual differences MDS and unfolding analysis. III.
THE HBAT PROBLEM – AN ILLUSTRATIVE EXAMPLE
In this example, HBAT uses perceptual mapping techniques to identify the position of HBAT in a perceptual map of major competitors in the market, with an understanding of the dimension comparisons used by potential customers. It then analyzes those market positions to identify the relevant attributes that contribute to HBAT's position, as well as those of its competitors.
In our example, the objects of study are HBAT and its nine major competitors. To understand the perceptions of these competing firms, mid-level executives of firms representing potential customers are surveyed on their perceptions of HBAT and the competing firms. The resulting perceptual maps hopefully portray HBAT's positioning in the marketplace. This study includes nine competitors, plus HBAT, representing all the major firms in this industry and collectively having more than 85 percent of total sales. Moreover, they are considered representative of all of the potential segments existing in the market. All of the remaining firms not included in the analysis are considered secondary competitors to one or more of the firms already included. In the HBAT study, metric methods are used. The multidimensional scaling analyses are performed exclusively with metric data (similarities, preferences, and attribute ratings) The HBAT study is composed of interviews with 18 mid-level management personnel from different firms. From the research objectives, the primary goal is to understand the similarities of firms based on firms' attributes. Thus, focus is placed on similarity data for use in the multidimensional scaling analysis. Similarity judgments were made with the comparison of paired-objects approach. The 45 pairs of firms [(10 X 9)/2] were presented to the respondents, who indicated how similar each was on a 9-poin scale, with 1 being "not at all similar'' and 9 being "very similar." The results are tabulated to each respondent in a lower triangular matrix. The process of developing a perceptual map can vary markedly in terms of the types of input data and associated analyses performed. In this section, we discuss the process of developing a perceptual map based on similarity judgments. The INDSCAL method of multidimensional scaling in SPSS was used to develop both a composite, or aggregate, perceptual map as well as the measures of the differences between respondents in their perception. The 45 judgments from the 18 respondents were input as separate matrices.
In order to closely present the characteristics of the MDS in this part of our study we will use HBAT dataset developed with many of the techniques. There are several datasets used
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A.
Creating the perceptual map The two-dimensional aggregate perceptual map is shown in Figure 1. To see how the similarity values are represented, let us examine some of the relationships between HBAT and other firms. In Table 2, we saw that HBAT is most similar to firm A and least similar to firms C and G. As we view in perceptual map, we can see those relationships depicted-HBAT is closest to firm A and farthest away from firms C and G. Similar comparisons for other highly similar pairs of firms (E and G, D and H, and F and I) show that they are closely positioned in the perceptual map as well.
challenge in statistics, machine learning, information retrieval, and knowledge discovery. Traditional multidimensional scaling has proved to be an outstanding approach to these problems, either by itself, or as part of a larger scheme dealing with cases where the data are nonlinear or deficient. This paper has presented a method of performing multidimensional scaling. MDS is a distinctive technique providing overall comparisons not readily possible with any other multivariate method. As such, its results present a range of perspectives for managerial use. The most common application of the perceptual maps is for the assessment of image for any firm or group of firms. As a strategic variable, image can be quite important as an overall indicator of market presence or position. In this study, we found that HBAT is most closely associated with firms A and I, and most dissimilar from firms C, E, and G. . REFERENCES [1] [2]
[3] [4]
[5] [6] [7] [8]
Figure 1. Perceptual map of HABAT and its competitors
Differences can also be distinguished between forms based on the dimensions of the perceptual map. For example, HBAT differs from firms E and G primarily on dimension II, whereas dimension I differentiates HBAT most clearly from firms C, D, and H in one direction and firms F and I in another direction. All of these differences are reflected in their relative positions in the perceptual map, and similar comparisons can be made among all sets of firms.
[9] [10]
[11]
[12]
IV.
CONCLUSION
[13]
Dimensionality reduction and successful visualization of the essential organization of a data set constitute a major
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[14]
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