Perceptual Maps With Correspondence Analysis

In a recent blog entry, we wrote about a compositional approach to perceptual mapping known as discriminant analysis.  Correspondence Analysis is another method used to create a perceptual map that involves a set of objects and attributes (ex. distinctive product or service attributes by demographic group) from a contingency table that are plotted on a shared perceptual map.

Looking at the table above, we see that brand sales vary among brands and age groups.  However, identifying meaningful patterns requires standardizing the data so that meaningful comparisons can be made.

In the young adults category, the table shows that an equal amount (30 units) of each brand was purchased.  But is this what we would expect on average?  How could determine if this group actually prefers one brand over another?  In order to determine if this age group prefers one brand over another, we must compute the expected value of sales in proportion to overall product sales across all groups.

Once the above expected values are calculated, the differences across all age groups and brands must be standardized using the chi square statistic and then these associations must be converted into a perceptual map.  Once the model fit and dimensionality has been established, the researcher is faced with two tasks: interpreting the dimensions and assessing the degree of association.

The following perceptual map was created using correspondence analysis.

Perceptual Map Created With Correspondence Analysis

Discriminant Analysis, Marketing Segmentation & Perceptual Maps

Perceptual Map Created With Discriminate Analysis

Perceptual maps are used to visualize the differences and similarities in perceptions and choices between products, brands or customers.

For example, a manufacturer of salon brand hair care items wants to see whether a lifestyle variables such as being a NASCAR racing fan, education level, ethnicity and demographic variables such as personal income, sex and a number of other factors are useful in distinguishing purchasers of their products from purchasers of other salon hair care brands.   Based on this classification, customer profiles will be developed in order to plan targeted advertising campaigns.

Discriminate analysis, a multivariate technique used for market segmentation and predicting group membership is often used for this type of problem because of its ability to classify individuals or experimental units into two or more uniquely defined populations.  The discriminant score is the basis for predicting to which group (a purchaser of the manufacturer’s brand or a competitive brand) the particular individual belongs. The discriminant weights of each predictive variable (age, sex, income, etc) indicate the relative importance of each variable.  For instance, if age has a low discriminant weight then it is less important than the other variables.

With this information, a classification matrix can be developed that indicates the accuracy of our model that will be used to construct our map.  For instance, if our discriminant model correctly classified 94.5-percent of users of our brand, then only 5.5-percent were incorrectly classified.  Conversely, if the model correctly classifies 92-percent of the competitive brand users, then only 8-percent were incorrectly classified.  We consider this a strong model because the number of correct classifications is much higher than what might be expected by chance.

Other Applications of Discrimant Analysis

While our example illustrated how discriminant analysis helped classify users and nonusers of salon brand hair care products based on independent variables, other uses of discriminant analysis include the following:

Product research – Distinguish between heavy, medium, and light users of a product in terms of their consumption habits and lifestyles

Perception/Image research – Distinguish between customers who exhibit favorable perceptions of a store or company and those who do not

Advertising research – Identify how market segments differ in media consumption habits

Direct marketing – Identify the characteristics of consumers who will respond to a direct marketing campaign and those who will not

Conclusion

While discriminant analysis is often used in marketing research for marketing segmentation and predicting group membership, there are more powerful and accurate techniques available.  We invite you to learn more about our solutions by contacting us today.

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