I am reading the book by correspondence analysis in practice by Michael Greenacre.It has the following example.
enter image description here

How do we find what row profiles are associated with column profiles.
In the book it says enter image description here

I do not understand what this means and how the row column association is found.So does this mean I have to project the row profiles into each of the column profiles (which are the vertices of the map) and then if this projection value is large then that particular row profile is associated with that column profile. Is it how the interpretation done?

But can't we just look at the bi plot and say if a particular row profile and column profile are displayed close together they are associated? As in this bi plot enter image description here where the red triangles represent eye colour and the black dots represent hair colour, can't I say brown eyes and black hair color are associated as they are closely mapped and so is blue eyes and blond hair.

or do i have to make row profiles projected on to column profiles. In that case how to calculate these projection values?
if someone can guide me as to determine which row profiles are associated with column profiles I would be grateful.

  • $\begingroup$ Straight euclidean distances between row and column points correspondense analysis (CA) biplot approximately relate the chi-square distances under "symmetrical" normalization of inertia. If the normalization is "principal" the projections of you citation correctly relate them. This answer, although not an answer to your question, describes algorithm of (CA) and the normalizations of inertia in it. $\endgroup$ – ttnphns Feb 21 '16 at 15:00
  • $\begingroup$ I might recommend you to post your data and the SPSS syntax you used to do the CA. Possibly me or somebody else could look in your example deeper then. $\endgroup$ – ttnphns Feb 21 '16 at 15:02
  • $\begingroup$ @ttnphns The first example I took from Michael Greenacre book. It doesn't include any data. just the map is given. In the book it talks about the dot product and I don't understand what it means by take a fixed reference direction and then line up the projections of all rows on this axis.... $\endgroup$ – sam_rox Feb 22 '16 at 4:10
  • $\begingroup$ It is clear in your citation. Project Zoology point on D line. The distance from that projection point to point D is the similarity between D and Zoology. $\endgroup$ – ttnphns Feb 22 '16 at 7:10

The scatter plot of two dimensions can be interpreted. Items which are in the same direction from the centroid are associated.

(It is worth also noting that distances between row points are valid and distances between column points are valid, but distances between row and column points are not.)


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