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Background: Although correspondence analysis is used mainly for visualizing similarities of categories of two or more nominal variables, I tried following: 39 students (from the same survey as in this question) were asked to ask their friends about smoking habits with four possible responses (I do smoke; I used to, but I do not anymore; I have tried and I have not even tried).

Then I created matrix with two columns: First is nominal variable with 39 categories (my students, in further labeled by numbers) and second one is also nominal with 4 categories (smoking levels). This data were used as an input into correspondence analysis and resulting plot can be seen below.

Questions: I am not sure about some interpretations of the plot.

  • Can we say something about frequencies of categories of second (smoking) variable? It looks for example that there is higher number of respondents near the category "I have tried". Does it mean that most of participants have only tried smoking?
  • If two respondents are close together (for example 6 and 18), does it mean that their friends have similar smoking "behavior"?
  • Where in the map are for example those respondents whose friends mostly used to smoke, but they do not anymore? Are they those who are near the label "I used to, but I do not anymore" (respondents 3, 22, ...) or those whose label has similar angle with x -axis as label "I used to, but I do not anymore" (respondents 3, 22, 30, 29, 10, 21, ...) or those whose projection to any axis is similar as projection of label "I used to, but I do not anymore" (respondents 5, 8, 2, 25 when projected to x - axis)?
  • Does the plot below say something about the degree of dependence between two variables? How should plot below look like if variables were independent?

Correspondence analysis

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I'm new to CA too and have found this article to be a great resource: http://marketing-bulletin.massey.ac.nz/V14/MB_V14_T2_Bendixen.pdf

Take a look at figure 5. I wonder if you could do the same with your plot. I would suggest you plot the individuals (1-39) and label the axes with the answer categories- the paper takes you through step-by-step on how to do this. If this works I believe your plot would tell you how similar individuals are in terms of what "types" of friends they have.

There is also a section about removing outliers- it appears to me that you might have a few outliers in the "individual" category. Once you identify an outlier (the process is presented in the paper) you can "remove" it by listing that particular row or column as a supplementary point. This point will no longer influence the analysis but will still receive appropriate coordinates and cos2 values.

Can you separate the individuals into any sort of sub-groups? Like males and females, old or young? If you're able to replicate figure 5 for your data you could then color the points for the different categories and see if there is a hidden pattern within the plot.

Good luck and let us know how you get on!

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