Multivariate deals with the mathematical application of statistics

Multivariate analysis can be used in many ways in business. While I will focus on three specific techniques; factor analysis, multidimensional scaling, and cluster analysis, I feel it is best to give you a brief, high-level, definition of multivariate analysis in order to familiarize you with the subject.

“Multivariate analysis deals with the mathematical application of statistics to a regression function to determine the effects of changes in a group of variables on other variables in the function. As a result, multivariate analysis can suggest, with a degree of predictive capability, what can be expected to happen when those variables change. (J. Simley, 2017)

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Simley goes on in to state, “multivariate analysis is primarily a mathematical approach to decision making.” This is exactly why I will demonstrate to you how three companies have each use a variation of multivariate analysis in their own dealings.

 

Multivariate analysis: Multidimensional scaling (MDS)

 

The technique I recommend it is the Multidimensional scaling (MDS) technique. “Multidimensional scaling (MDS) is a set of related statistical techniques often used in information.” (J. Saini, 2008) A more applicable definition of MDS comes from the research company, DJS Research, who explain it as “Multi-dimensional scaling (MDS) is a statistical technique that allows researchers to find and explore underlying themes, or dimensions, in order to explain similarities or dissimilarities (i.e. distances) between investigated datasets.” Simplifying this definition, MDS can simply be used to compare companies, products, etc. For example, our company could be compared to several competitors and a survey developed asking correspondents to rank each company on the same criteria, such as price of services of products, quality of those services and products, etc. MDS can also be used for market segmentation, new product development, advertisement assessment, and distribution channel decisions. (M. Pawlicki, 2015) As you can see, this technique could be exceptionally beneficial in terms of understanding the company’s overall brand or product perception and finding ways to improve or adjust that position.

The data collected from this technique is displayed on a scatter graph but can also be displayed in a three-dimensional example, though it may create complications in terms of understanding the data as quickly or effectively.

One company which has used this type of research is Coca-Cola.  “The Coca-Cola Company has utilized techniques such as MDS to understand how consumers perceive their products as well as those of competitors and. as a result reaped rich rewards by maintaining an iron grip on the U.S. carbonated soft drink market that was estimated to be about $70 billion in 2009.” (The Marketing Research, 2015)

 

Multivariate analysis: Factor Analysis

 

To demonstrate how this technique is used we look at a German data analysis group, the IFaD or the Institute of Applied Data Analysis. The IFaD had the need to help a spirits manufacturer plan the best possible product positioning for a new herb liquor product within a very competitive market. In order to accomplish this the company utilized the factor analysis technique. “Factor analysis is a technique for reducing the complexity of high-dimensional data” (Jackson, J. E. 1981). The IFaD developed the following questions for their study:

Do the items allow key rating dimensions to be derived, permitting a compressed presentation of the results?

Are all the items sufficiently clearly distinguishable, so that these dimensions can be unambiguously classified?

Does the list contain redundancies, so that the length of the survey can be reduced by deleting some items?

Do the items contain the required information (test validity of contents)?

These questions are examples of the type of questions that WidgeCorp could develop in correlation with the utilization of factor analysis. For example, referencing the possible sales of cold beverages, a very similar system of questions and following analysis could be developed. In this case, IFaD identified 16 variables which would be used to answer the aforementioned questions.

According to the report created by IFaD, these variables were then each placed on a 7 point rating scale where 1 = “does not apply at all” and 7 = “applies completely”. According to the IFaD, “The factor analysis generated the following three fundamental dimensions,”, comprised of taste/effect, tolerability, and disturbance. This solution is one that is logical on both a technical and content point of view, according to IFaD

.  IFaD measured the following results, displayed in the table below, which shows the results of the variances in their research from most to least. These variances total to 100%.

While the factors have beem listed and displayed in order to show how much variation the explain in the study, they can also be explained by eigenvalue. “The eigenvalue is a measure of how much of the variance of the observed variables a factor explains.  Any factor with an eigenvalue ?1 explains more variance than a single observed variable.” (M. Rahn, 2017)

Paraphrasing the IFad report, when utilizing the factor analysis technique, the process extracts latent features otherwise known as principal components which incorporate the maximum share of remaining variances and that, as a whole, there may be as many latent features discovered as there are observable features. In matter of this study 16 of these features were identified and tested.

                This all relates to our company as it illustrates how we could take a wide variety of variables and accurately measure them in order to understand how they affect the overall solution.  This technique could also be used for other very complex concepts which could affect our company such as socioeconomic factors and dietary patterns of our buyers in order to better understand them by organizing data and comparing concepts which may not be directly measured against one another and may have a large amount of variable like in the example above. Again, like in the example above, it also allows for a large list of variables to be simplified into smaller groups of “interpretable underlying factors.”( M. Rahn, 2017)

                The primary reason that this is not the chosen technique is that it is a rather complex type of technique and one that requires a great amount of effort from start to finish. Questions, or hypotheses must be developed, variables defined and measured, etc. This technique may also delve into far to much complexity and specificity in terms of much of the market research that our company may complete where we may only want to understand a simple overall perception of our company in comparison to a competitor or one product vs another.

 

 

Multivariate analysis: Cluster Analysis

In terms of business, cluster analysis is a process of multivariate analysis which is used for organizing data in “natural” clusters or groups. Penn State University describes cluster analysis saying of the technique, “We use the methods to explore whether previously undefined clusters (groups) may exist in the dataset. For instance, a marketing department may wish to use survey results to sort its customers into categories (perhaps those likely to be most receptive to buying a product, those most likely to be against buying a product, and so forth).” Another example of how to explain this type of technique would be if our company separated all of our customers into 5 separate groups based on their unique purchasing habits over the period of say, one year, and then developed unique marketing and sales strategies directed at each of these “clusters”.  The primary benefit of clustering is that it can be utilized to organize large amounts of data into easy to understand groups which can identify previously unidentified patterns or clusters without the need to first develop a specific hypothesis which must then be tested and proven/disproven. (G. Vohra, 2011)

                The primary reason this technique is not the chosen technique is that it may be too undefined as there is no set guidelines on how to define clusters. This means that clusters may be poorly defined or be of little to know value and therefore not provide helpful or accurate data.  In addition, “Dolnicar and Gru¨n (2009) identify several problems of the factor-cluster segmentation approach:

1. The data are pre-processed and the clusters are identified on the basis of transformed values, not on the original information, which leads to different results.

2. In factor analysis, the factor solution does not explain a certain amount of variance; thus, information is discarded before segments have been identified or constructed.

3. Eliminating variables with low loadings on all the extracted factors means that, potentially, the most important pieces of information for the identifi- cation of niche segments are discarded, making it impossible to ever identify such groups.

4. The interpretations of clusters based on the original variables become questionable given that the segments have been constructed using factor scores.”