Perceptual Maps With Correspondence Analysis

Perceptual Maps With Correspondence Analysis

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 perceptual maps 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.

Cross Tabulation By Brand & Age
Age Category	Brand A	Brand B	Brand C	Brand D	Total
Young Adults (18-34)	30	30	30	30	120
Middle Age (34-50)	50	20	20	10	100
Mature (51-67)	20	40	10	40	110
Senior (68+)	40	10	50	40	140
Total	140	100	110	120	370

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.

Age Category	Brand A	Brand B	Brand C	Brand D	Total
Young Adults (18-34)	35.74	25.53	28.09	30.64	120
Middle Age (34-50)	29.79	21.28	23.40	25.53	100
Mature (51-67)	32.77	23.40	25.74	28.09	110
Senior (68+)	41.70	29.79	32.77	35.74	140
Total	0.30	0.21	0.23	0.26	470

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.