Map brand positioning: correspondence analysis and MDS

How do customers see your brand compared with competitors? Which brands are seen as similar, and which attributes define each brand’s position? Perceptual maps answer these questions in one picture, and they are a staple of brand strategy presentations. This lesson covers the two most common methods.

Correspondence analysis

Correspondence analysis (CA) starts from a contingency table of counts: for example, how many respondents associate each brand with each attribute (“Which of these brands do you consider innovative?”, with multiple answers allowed). It finds the dimensions that best explain the deviations from independence and places both rows (brands) and columns (attributes) on the same map.

Reading the CA output

The example table has 7 brands and 6 attributes with 2,141 mentions. The chi-square test shows a significant association between brands and attributes (χ²(30) = 501.23, p < .001): the brands are perceived differently. The first two dimensions capture 62.3% and 20.5% of the total inertia, together 82.8%, so the two-dimensional map is a good summary. (Inertia is the total chi-square divided by n, a measure of how far the table is from independence.)

On the map, points in the same direction from the origin are associated. The strongest associations are Ember with Stylish (2.27 times the expected frequency), Brava with Affordable (2.17×), Aurora with Innovative (2.01×), Cobalt with Reliable (1.66×) and Delta with Eco Friendly (1.45×). Dimension 1 separates the innovative, stylish brands (Aurora, Ember) from the rest; dimension 2 separates the reliable brands (Cobalt) from the eco-friendly ones (Grove, Delta).

Quality and contributions

Not every point is well represented. The quality (sum of cos² on the two dimensions) shows how well the map represents each point: Grove (.981) and Ember (.964) are represented almost perfectly, but Brava only at .415, so its position on the map should be interpreted with caution. Contributions show which points define each dimension: Ember (37.0%) and Aurora (29.9%) define dimension 1. Report the inertia explained and treat poorly represented points carefully.

Multidimensional scaling

MDS starts from dissimilarities between objects: direct similarity judgements (“How similar are brand A and brand B?”) or distances computed from attribute ratings. It places the objects on a map so that the distances between points reproduce the dissimilarities as closely as possible.

In the example, eight brands were rated on six attributes, and non-metric MDS produces a two-dimensional map with Kruskal’s stress of .079. Stress measures the misfit between map distances and dissimilarities: below .05 is good, below .10 fair and above .20 poor, so this map is fair. The correlation between map distances and the input (r = .934, R² = .872) confirms a good representation. Aurora and Ember are closest, and so perceived as most similar.

Naming the dimensions

MDS dimensions have no inherent meaning; you name them. Property fitting regresses each attribute’s mean rating on the two dimensions and draws it as an arrow. Design (R² = .966) and Innovation (.870) point along the positive side of dimension 1, while Value for Money and Service point the other way, so dimension 1 is “design and innovation versus value and service”. Reliability (R² = .961) points down and to the left, so dimension 2 separates reliable brands (low on the map) from the rest. Sustainability is poorly represented (R² = .375, p = .309); the map says little about it.

Using perceptual maps strategically

• Find your competitors: brands close to yours compete for the same perception.
• Find gaps: empty regions of the map near valued attributes may be positioning opportunities.
• Track repositioning: repeat the study after a campaign to see whether the brand moved.
• Add an ideal point: ask about the ideal brand and plot it, or overlay segment preferences.

CA or MDS?

Use correspondence analysis for count data (pick-any brand-attribute association grids, cross-tabulations of survey answers). Use MDS for similarity judgements or ratings. Both give a map; both need an honest statement of how much the map explains.