## Wednesday, 31 August 2011

### Mapping Techniques

Mapping Techniques
Multidimensional Scaling (MDS)
MDS is really a broad name for a wide variety of algorithms. At the heart of all of the methods, though, is a desire to produce a map in a low dimensional space (normally two dimensions) that shows similarities between products. Some of the more common names of MDS algorithms include ALSCAL, INDSCAL, MDPREF, MDSCAL, ASCAL, KYST, and PREFMAP. For the purposes of this exposition, the differences between these models are not important.
The data input requirements for MDS are generally not stringent. Most techniques use aggregate data, while methods exist to utilize individual data. The data are referred to as similarities data, but the popular computer programs are capable of handling a number of types of input, such as correlations or distances.

There are several ways to collect brand similarity data. The most straightforward is to ask respondents directly to rate how similar two brands are on a scale, where a "1" indicates two brands are identical, and a "9"indicates that two brands differ widely. Many respondents find this level of abstraction difficult to deal with, though. Repertory grid is a particularly useful technique for developing similarities. In repertory grid, respondents are presented with three products and asked to indicate which is most unique (or alternatively which two are most alike)4.
The following simplified example of MDS will provide an understanding of the basic processes involved behind an MDS analysis. Let's look at highway distances between five U. S. cities: Seattle, Miami, Kansas City, Los Angeles, and New York. The table below shows the mileage between each pair of cities.
 Seattle Miami Kansas City Los Angeles New York Seattle 0 Miami 3454 0 Kansas City 1994 1516 0 Los Angeles 1190 2817 1728 0 New York 2975 1350 1220 2913 0

Notice that only half of the matrix is necessary in that the distance between Seattle and Miami is the same as the distance between Miami and Seattle.
The goal of MDS is to take these 10 pairwise distances and place them on one map. Let's begin by looking first at the Seattle-Miami distance, 3454.

Compositional Methods
Factor Analysis (FA)
Factor Analysis produces maps that look like MDS plots. Factor analysis was widely used in the 1970s to produce maps which, like MDS, positioned brands relative to other brands. Unlike MDS, though, factor analysis maps are composed. That is, they are "made up" based on ratings of brands on several attributes, rather than just overall similarities between brands.
While decompositional methods might ask respondents to indicate how similar two brands are, compositional methods would ask respondents to rate each brand on several attributes5. For example, a respondent might be asked to rate brands on the following set of attributes:

·        Medical Quality
·        Technological Innovativeness
·        Claims/Billing Accuracy
·        Value for the Price
·        Strong Presence in the Community

Additionally, respondents might be asked to indicate how important each attribute is. Factor analysis is then used to reduce the number of dimensions under investigation.
Factor analysis is a data reduction technique that summarizes and combines attributes based on the correlations of those attributes6. The results of factor analysis are new variables (factors) that are made up of linear combinations of the original variables. Factor analysis was used in primarily two ways to construct maps. Some researchers would factor analyze the attribute importance and then, using those functions, create factor scores for each product studied. Other researchers would factor analyze the actual ratings of all products and then create factor scores for each product. The results of either map have been empirically shown to be similar, although they won't always.
Technically, the problem with this approach is that factor analysis seeks to combine variables (create factors) that explain the greatest amount of the total variance. There are two types of variance: within brand variance and between brand variance. The between brand variance represents the true perceptual differences between one brand and another. The within brand variance is a function of the amount of agreement by respondents about a particular brand. For instance, if respondents' perceptions agree about a particular brand, the within brand variance will be small. However, if there is great disagreement about the perceptions of a particular brand, the within brand variance will be high. The issue becomes that these two sources of variation are combined by factor analysis, that is, they are confounded8. Thus, the differences in product ratings are ignored until after the factor equations are derived and are incorporated only to produce each brand's factor scores9.
Early studies showed that the factor analysis approach was superior to other compositional methods such as discriminant analysis (Hauser and Koppleman, Simmie). Limitations with those studies were discovered and the evidence now suggests that factor analysis is not theoretically or empirically superior (Moore, Huber and Holbrook). Today, factor analysis is rarely used.

Discriminant Analysis (DA)
Another compositional approach which enjoys more acceptance today among many researchers is discriminant analysis based perceptual mapping. Like factor analysis, discriminant analysis uses ratings data of brands on attributes. Also like FA, DA seeks to explain (maximize) variance of the ratings. Unlike FA which uses the total variance (within brand and between brand variance), DA maximizes the ratio of between brand to within brand variance. Put another way, only the actual differences between brands drives the solution in DA, while lack of agreement about brands' ratings (within brand variation) also drives FA. So one benefit of discriminant analysis is that the technique discriminates between brands.
Another benefit of discriminant analysis is that it includes the attributes in the map. Unlike the MDS and FA techniques which only position brands relative to other brands, discriminant analysis shows brands and attributes. The brands are positioned in the space as points (as they are in the two techniques above), and the attributes are represented as vectors emanating from the origin of the map. This is sometimes called a point and vector solution. Therefore, DA illustrates the relationship between attributes (their correlation to other attributes), how much each brand is seen as embodying each attribute, and how similar competing brands are perceived to be. The figure below shows an example point and vector perceptual map from discriminant analysis.

Source - mv-research.com

Deepak Sharma
Marketing-2