Term Paper on "Statistics Multidimensional Scaling MDS"

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multidimensional scaling (MDS). The next section compares MDS with factor analysis and cluster analysis. The third section identifies actual applications of MDS in the marketing research literature and the last section is devoted to a hypothetical situation in which MDS is used in a snack food market.

What is Multidimensional Scaling?

According to Young (1985), multidimensional scaling was introduced as an aid to understanding people's judgments about the similarity of members of a set of objects. In marketing applications, MDS is a technique for assessing and visually representing the preferences and perceptions of consumers. Potential customers are asked to compare pairs of products and make judgments about them. Discriminant analysis is a statistical technique used in marketing and the social sciences. ...Conjoint analysis, also called multiattribute compositional models, is a statistical technique that originated in mathematical psychology. ... The judgments can be as simple as "prefer a to B," "A is more like B. than C," or a rating of 5 given to product a on an "appealingness" scale of 1 to 7, where a, B, and C. are three products in a larger set of products.

The aggregated judgments (e.g., percentage of times preferred, average appeal rating) for each product are shown as points in space, usually two- but sometimes three-dimensional. (More than three dimensions makes for difficulty in interpreting.) the objective of MDS is to place points in multidimensional space so that the distances between points reflect as closely as possible the subjective distances obtained by surveying subjects.

An important issue in MDS is dimensio

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nality. Normally, MDS is used to provide a perceptual map of a complex set of relationships that can be scanned at a glance. Dimensions are item attributes that seem to order the items in the map along a continuum. Borgatti's (1997) example of MDS applied to dog breeds is illustrative. Borgatti proposed that an MDS of perceived similarities among breeds of dogs might show a clear ordering of dogs by size. At the same time, an independent ordering of dogs by perceived viciousness might be observed. This ordering might be perpendicular to the size dimension, or it might cut a sharper (less that ninety degree) angle.

The underlying dimensions are thought to "explain" the perceived similarity between items. In his dog example, Borgatti stated that two dogs are seen as similar because they have similar scores or locations on the identified dimensions. That is, the observed similarity between a Doberman and a German Shepherd is explained by their being perceived as nearly equally vicious and about the same size. The implicit logic of how similarity judgments are made is that items have attributes (such as size, viciousness, speed, thickness of fur, etc.) in varying degrees, and the similarity between them is due to their similarity across all attributes.

Garson (2009) pointed out that the labeling of axes in MDS is just as subjective as in factor analysis. Subjects and/or experts "eyeball" the MDS perceptual maps (scatterplots) and infer dimension labels. Where labeling is subjective and sometimes debatable, there is some objectivity to deciding on the number of dimensions. The "Stress Test" is the name given to the most commonly used statistical test of goodness of fit for a given number of dimensions. Garson noted that the statistic is the ordinary phi.

Garson (2009) cautioned that, while MDS makes fewer assumptions than factor analysis, some guidelines must be adhered to when applying the method. They include the following:

1. Include all relevant objects (products or items) in the preference comparisons on which the MDS is based. Omission of relevant items can drastically alter MDS results, as can inclusion of irrelevant items.

2. Do not allow more dimensions than objects. If there are more dimensions than objects, the MDS solution will be unstable and goodness of fit measures will be inflated. Garson's rule of thumb is that "the research design should provide for four times as many objects as dimensions, plus 1 (thus 5 objects for a 1-dimensional solution, 9 for 2-dimensional, etc.).

3. Make sure that the objects being compared/voted upon/ranked share one or more meaningful dimensions so that meaningful comparisons are possible.

4. Be aware that dimensions may change over time for the same individuals. There are some problems or questions where the market researcher might wish to examine changes over time.

5. Insure that missing values comprise only a small percentage of total cases. Large numbers of missing values can lead to misleadingly low estimates of stress. (Low values of stress indicate a good fit. Larger values of stress signal a poorer fit.)

6. Likewise, insure there are few ties. A large number of ties can also lead to misleadingly low estimates of stress.

7. Insure that there is variability in the raw data. Although MDS does not assume any particular data distribution, some variance in the data is necessary for meaningful results.

How does MDS Differ from Factor Analysis and Cluster Analysis?

In marketing applications of factor analysis, the investigator obtains underlying dimensions from responses to product attributes identified by the researcher. MDS obtains the underlying dimensions from respondents' judgments about the similarity of products. MDS does not depend on researchers' judgments. Not does it require a list of attributes to be shown to the respondents. The underlying dimensions come from respondents' judgments about pairs of products. Moreover, unlike factor analysis, MDS does not require assumptions of linearity, metricity, or multivariate normality, so sometimes it is preferred over factor analysis even for objective data.

If the raw data are metric or dichotomous, factor analysis or cluster analysis would be more efficient for the researcher's problem. On the other hand, MDS has relaxed data distribution assumptions and is robust with smaller sample size than is factor analysis, so there are instances where the researcher might prefer MDS even for objective data (Garson, 2009).

The major difference between MDS and cluster analysis is that multidimensional scaling identifies underlying dimensions, while cluster analysis identifies clusters. Thus, if a market researcher wished to group customers based on their preferences and had no need to identify underlying dimensions; he or she would probably choose cluster analysis.

How is MDS Used by Companies to Address Business Problems?

Cooper (1983) reviewed MDS in marketing research and found applications as diverse as (a) assessing how a given brand of coffee relates to other brands, (b) rating the appeal of different breakfast bakery items, (c) relating individuals' degree of concern over ecology to laundry detergent ratings, (d) evaluating law enforcement officers' judgments of the severity of different kinds of drug abuse, and (e) determining the effect, in a before an after design, of aggressive marketing's on attitudes toward a cigarette brand. These are by no means the only applications, but an indication of their variety. Applications are limited only by the creativity of the market researchers and managers.

How Might MDS Be Used in a Snack Food Market?

The following is a hypothetical situation. CW, a manufacturer of candy bars, has decided to put a new candy bar on the market. He wants to insure that it is a strong competitor with other more established candy bars. So CW hires a market research organization (MRO) to advise him on where to direct his efforts. He already knows that a good portion of candy bar buyers are in the age range 12-19 years old, so he informs MRO that that is who should be the subjects of the research.

MRO recruits 320 candy bar judges in the requisite age range (40 of each age in the range). After much discussion between MRO and CW, nine candy bar brands are selected as representing the variety of candy bars currently being marketed. The 320 judges are instructed to rate each of the nine candy bars based on past tasting experience (and not… READ MORE

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Quoted Instructions for "Statistics Multidimensional Scaling MDS" Assignment:

“

IMPORTANT - This is a group project and I am giving you the specs for the entire group project. HOWEVER, I am only to do my individual portion which is MDS, Multi Dimensional Scaling. The entire group project instrucions are as follows but I only need the 1500 word individual portion about MDS. Please read the group project instructions so that you know what the entire project entails. Thank you.

Deliverable Length: 1500-3000 words individual portion

Details: A high-end market research firm has contacted your boss and is trying to sell some business to your organization. Upper management does not want to appear incompetent, so they have asked you to research and explain three major ways multivariate statistics are used in a business.

Small Group Discussion

Research the Library and provide at least 1 example of how a real company has used each of the following multivariate techniques: factor analysis, multi-dimensional scaling, and cluster analysis. Companies that provide statistics software websites and market research firm websites usually include case studies and customer testimonials.

Read the postings of all group members and decide as a group which technique is preferred by the group and which example best illustrates the use of this technique.

For the individual portion of this project, on your own, write a 1500-3000 word summary explaining to upper management the chosen multivariate technique, MY MULTIVARIATE TECHNIQUE THAT YOU WILL WRITE ABOUT IS MDS (MULTI DIMENSIONAL SCALING) how it is different than the other 2 techniques, how at least one other real-life company has used this technique to address a business problem and how that technique might be used at your own organization.

Objective: Explain analysis of variance, multivariate statistics, and non-parametric methods

Instructor Comments

Here is additional guidance to help you earn the highest grade possible for Phase-4 Group Project:

Individual Posting

Â§ *Each small group member, including the Small Group Leader, should research on the Web about his or her multivariate analysis technique assigned by the instructor and discuss about general research findings regarding that technique.

Â§ *Notice that companies that provide statistics software web sites and market research firm web sites usually include case studies and customer testimonials.

Â§ *Write a Word Document memo between one to three page long (a detailed Word Document and not an actual E-mail for this assignment and not to exceed three full pages, single or double spaced) explaining to upper management about his or her assigned multivariate technique (assigned by the Group Leader)as well as the general research findings regarding that technique.

Â§ *Compare the assigned multivariate technique to other two techniques and explain how it is different than the other two techniques.

Â§ *Provide, at least one research-based example for this technique and how it is applied to the situation along with the related reference citation.

Â§ *Also, discuss how this technique can be applied by Company W to reach its marketing objectives in snack food market.

Â§ *Post at least three viable references (some from search engines with known authors and date of publication) that you actually use in your discussion. Notice that, in order to obtain a top grade for this project, most of your selected references must be from outside course related sources and obtained by search engines.

Â§ *Cite all references used in your discussion right after each related statement, in APA format.

Â§ *You need to show your similarity score of below 25% with your modified individual posting.

iIMPORTANT****NOTICE: Please do NOT discuss about all three techniques entirely in your individual posting. You should mainly concentrate on your assigned technique. ONLY MDS!!!!

THE INFO SUPPLIED BELOW MAY NOT BE AS IMPORTANT BUT I WANTED THE ***** TO KNOW WHAT PROJECT i AM TRYING TO HELP WITH. THE TASK BELOW IS NOT NEEDED, ONLY MY INDIVIDUAL PORTION ABOVE. INFO BELOW ONLY SHOWS THE GROUP PROJECT AND HOW I FALL INTO IT.

Final Group Project Posting

Â§ *The Group Leader should carefully follow the steps indicated below to submit the Final Group Project posting:

Â§ *The Group Leader should read the postings of all group members and ask all members about their preferred technique for Company W in order to decide as a group, which technique among factor analysis, multidimensional analysis, or cluster analysis is preferred by the majority of the group members.

Â§ *The group leader should provide one to three page Word Document posting, at most, about the research findings regarding the preferred technique along with members***** reasons for such selection. Notice that the group leader should rephrase the statements related to the preferred technique taken from the individual postings and cite related references in order to keep a low similarity score for the final posting.

Â§ *Compare the preferred technique with other two techniques, and state, in detail, about comparative advantages of the selected technique over the other two techniques.

Â§ *Provide some new research-based application example for the selected technique in detail that best illustrates the uses of this technique. Notice that this must a new example not used with individual postings.

Â§ *Provide detailed discussion as how such technique would benefit Company W with its marketing research.

Â§ *Post at least three viable references (including some from search engines with known authors and date of publication) in APA format that actually used in the final group project posting by the group leader. Notice that, in order to obtain a top grade for this project, most of the selected references must be from outside course related sources and obtained by search engines.

Â§ *Cite all references used in the posting in APA format, right after each related statement.

Â§ *Show the similarity score of below 25% along with the final group project posting by the group leader.

Â§ *Use the Small Group Discussion Board for interaction among group members and postings regarding their research progress involving their assigned technique.

Â§ *Only the Small Group Leader must post the final group project posting on *****Small Group Files***** inside your small group for grading. Please label your posting as *****Final group project posting***** and follow step stated below to submit the final group project posting for grading:

Â· Open your Small Group Web page. Then, open *****Add Files***** tab located inside your small group Web page and submit the final group project posting.

Â§ *The Group Leader should NOT discuss about all three techniques entirely in the final group project report. The discussion should concentrate on the preferred technique by the small group members and it should closely cover the indicated tasks by the instructor stated above.

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