Common mistake 1 with Perceptual map

Reading an empty region as a gap in the market. It is a combination of attributes nobody associated with any brand, which is very often a combination nobody wants.

Common mistake 2 with Perceptual map

Comparing the two clouds’ distances literally, or reading absolute coordinates. Only the relative geometry means anything, and the sign of an axis is arbitrary.

Common mistake 3 with Perceptual map

Mapping a table that failed its chi-square. The map will look every bit as convincing as a real one.

Common mistake 4 with Perceptual map

Redrawing the map after dropping a brand or attribute and treating the new positions as a change in the market. The solution is recomputed from scratch and the axes can rotate or flip entirely.

EconStatsCraft › Perceptual map

Perceptual map

Puts brands and the attributes people associate with them in the same picture, by correspondence analysis of the cross-tabulation. A brand near an attribute is associated with it more than an average brand is.

What it needs

Brand
Attribute

The intuition

A perceptual map turns a table of brands against attributes into a picture in which brands that are seen similarly sit close together, and the attributes that separate them point in the directions that matter. It is a compression of a contingency table onto two axes, chosen so that as much of the association as possible survives the flattening.

When to use it

Brand positioning and competitive structure: who is seen as what, who is close to whom, and which attributes distinguish the market. The standard exhibit in a brand-tracking study.

Where the estimator comes from

Correspondence analysis works on the standardised residuals of a contingency table N with grand total n: let P=N/n with row and column masses r and c, and form S=D_r^{-1/2}(P-rc')D_c^{-1/2}. The singular value decomposition S=UDV' gives principal coordinates F=D_r^{-1/2}UD for rows and G=D_c^{-1/2}VD for columns. The total inertia \sum_k d_k^2 equals the chi-squared statistic of the table divided by n, so the percentage of inertia on each axis is literally the share of the table\'s chi-squared association that the axis carries.

The model

\frac{p_{ij}-r_ic_j}{\sqrt{r_ic_j}}=\sum_{k}\sqrt{\lambda_k}\,u_{ik}v_{jk},\qquad \text{inertia}=\sum_k\lambda_k=\frac{\chi^2}{n}

What it assumes

A contingency table - counts of associations. Correspondence analysis is built for counts; a table of average ratings wants PCA or factor analysis instead, and this app has both.
That the brands differ at all. A chi-square test of independence is reported first, and if it does not reject, the map is drawing noise - which will still look meaningful, and is why the test comes before the picture.
That two dimensions carry most of the inertia. If they do not, a flat map is hiding the structure rather than showing it.
That the attributes were not chosen to flatter one brand. Correspondence analysis maps the table it is given, so an attribute list drawn from one brand's marketing will place that brand centrally and well-connected by construction.

Statistical properties

Distances between ROW points are interpretable, and distances between COLUMN points are interpretable, but the distance between a row point and a column point is not - only its direction and length from the origin. Reading brand-to-attribute distance off the plot is the standard error.
The percentage of inertia on the two displayed axes tells you how much you are seeing. Below about 70% the map is hiding structure and a third axis matters.
A point near the origin has an average profile - it is not distinctive - rather than being average on every attribute. That is a subtly different and often-missed reading.
Correspondence analysis is descriptive. There is no significance test on the positions, and small differences on the map should not be interpreted.
Axes have no inherent meaning. They are named by inspecting which attributes load on them, and that naming is interpretation rather than result.
Multiple correspondence analysis extends this to more than two categorical variables, at the cost of inertia percentages that are pessimistically low and need Benzecri or Greenacre adjustment.

How to read the output

Distances between BRANDS are meaningful, and distances between ATTRIBUTES are meaningful. A single brand-to-attribute distance is the weakest reading on the chart, because the two clouds have different scales - the honest statement is directional: this brand lies toward that attribute.
The axes have no names until you name them, and naming them is interpretation, not output.
A brand near the origin is not "average" so much as undifferentiated: its attribute profile is close to the market’s overall profile.
The inertia percentages are the honest fit statistic. Two dimensions explaining 60% means 40% of the association structure is not on the page at all, and brands that look adjacent may be far apart in the dimension you cannot see.

A worked reading

Six brands by eight attributes. The first two axes carry 78% of the inertia, so the picture is a fair summary of the table. Two brands sit close together on the right, near the direction of "reliable" and "good value"; a third sits alone at the top near "innovative". The distance between those two right-hand brands is meaningful - they are perceived similarly. The distance from either of them to the word "reliable" is not, and the correct reading is that both lie in the same direction from the origin as that attribute, which is a statement about association rather than about proximity.

Symptom → diagnosis → what to do

If you see this	It means	Do this
Two axes carrying under 60% of inertia	The map is a poor summary	Show a third axis or abandon the picture
A brand at the origin	An unremarkable profile	Not "average on everything"
One outlying category dominating an axis	A rare category with a distinctive profile	Consider making it supplementary
Reading brand-to-attribute distance	Not interpretable in this scaling	Read direction from the origin instead
Map contradicting a known positioning	Small counts in that cell	Check the contingency table first
Axes flipping between runs	Sign is arbitrary in an SVD	Not an error

Common mistakes

Reading an empty region as a gap in the market. It is a combination of attributes nobody associated with any brand, which is very often a combination nobody wants.
Comparing the two clouds’ distances literally, or reading absolute coordinates. Only the relative geometry means anything, and the sign of an axis is arbitrary.
Mapping a table that failed its chi-square. The map will look every bit as convincing as a real one.
Redrawing the map after dropping a brand or attribute and treating the new positions as a change in the market. The solution is recomputed from scratch and the axes can rotate or flip entirely.

Where to read this properly

Greenacre, Correspondence Analysis in Practice (2017).
Benzecri (1973), Analyse des Donnees.
Hoffman and Franke (1986), "Correspondence Analysis: Graphical Representation of Categorical Data in Marketing Research", JMR 23(3).

Related Marketing research

Conjoint analysis · MaxDiff (best–worst scaling) · TURF - reach of a product line · Price sensitivity (Van Westendorp) · Market basket analysis · Scale reliability (Cronbach’s alpha) · Key driver analysis

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Each example is simulated from a known model, so you can check whether the estimator recovers the truth - and nothing here is anyone's private data.

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Perceptual map

What it needs

The intuition

When to use it

Where the estimator comes from

The model

What it assumes

Statistical properties

How to read the output

A worked reading

Symptom → diagnosis → what to do

Common mistakes

Where to read this properly

See also

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