Correspondence Analysis

"Correspondence analysis is a technique for displaying the rows and columns of a data matrix (primarily, a two-way contingency table) as points in low dimensional vector spaces." (Greenacre 54). A two-way correspondence map displays (jointly) the "data cloud" representing the row profiles as well as the "data cloud" representing the column profiles of the table and illustrates the "correspondence" between these two data clouds. Distances between row data are measured in chi-square distances as are distances between column data points, while distances between the data clouds are not defined in any easily understood way. Thus, one should be very cautious in interpreting such a map. (Greenacre, 65) In general, one should not make the "unfolding model" assumption that, for instance, a column data points (e.g. Brands) lying near a row data point (e.g. Attribute 1) are "highest" or "most associated" with that data point. Neither does the "vector" interpretation necessarily apply, since the nature and metric of the stretching of the row and column points (and, hence the geometric relationship between them) is not easily interpretable.

The above cautions being said, it is the opinion of this author that the "vector" interpretation in general terms of more and less association between data points is a permissible one and will not lead one far astray. That is, the more a brand tends to lie in a similar direction away from the centroid as an attribute, the higher should be that brand's profile on that attribute.

The first paragraph discussion is in reference to the 'joint display' scaling option. The CGS scaling purports to allow true interpoint comparisons to be made, but this scaling, in turn, has been criticized (see references). In effect, the CGS scaling stretches the second (vertical) axis relative to that shown by the joint display. In the 'asymmetric scalings' the plotted column points are the weighted centroids of the row points or vice versa.

It should be noted that a map sharing certain characteristics of a correspondence map (that is that the map is of the 'profiles' of the data, with the overall size effect being removed) can be produced by requesting a BiPlot with the "Dev. from expcted value" option.

Correspondence map interpretation

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