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I am using correspondence analysis (CA) to analyze a contingency table.

In the columns I have statements about some brands (characteristics) and in the rows I have the brands. My aim is to obtain in CA standard coordinates for the statements and principal coordinates for the brands.

The issue is that the variance of one statement (i.e. column in the contingency table) is significantly explained by both the first and second dimension. It would be ideal if the dimensions only accounted for the variation of unique brand statements. E.g. dimension X only accounts for the the variation in brand statements Y through Z. Not, brand statements Y through Z are both significantly explained by dimensions X and U. This leads to a somewhat convoluted interpretation of the brands in relation to the statements.

I know that with continuous variables there is exploratory factor analysis that rotates the principal components solution to minimize the shared variance of the variables between the factors (i.e. dimensions in CA) so that the analyst can uncover latent constructs in the data.

Is there an analogous method to do this using CA? Are there any implementations in R?

ttnphns
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RTrain3K
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  • I'm not sure about your terminology: shared variance between the factors (or columns). Principal axes or column points? The question isn't quite clear to me, orthogonal dimensions can't "share variance". Anyway. If you are speaking of analytic rotation of principal axes (such as varimax) - well, you may do it in CA (I can't suggest a R package, I don't use R). CA is a special modification of biplot while biplot and PCA are twins. So, if a rotation is sometimes done in PCA, it is as well done in CA. If you need. – ttnphns Nov 22 '16 at 17:45
  • ...In CA, where often we consider only 2 first principal dimensions, manual rotation of the axes by eye control is easily done, so things like varimax may be unnecessary. – ttnphns Nov 22 '16 at 17:45
  • interpretation of the row principal coordinates in relation to the standard coordinates Your edit didn't make it much clearer. What is to interpret a coordinate? We usually "read" a coordinate, but "interpret" the essence of a dimension (by coordinates on it of objects with known properties). – ttnphns Nov 22 '16 at 18:12
  • @ttnphns I clarified the question a bit (I hope). In the columns I have statements about brands and in the rows I have brands. The issue is that the variance of one column is significantly explained by both the first and second dimension. It wold be ideal if the dimensions only accounted for the variation of unique columns (brand statements). From what I gather, this is what is attempted with exploratory factor analysis with continuous variables. – RTrain3K Nov 22 '16 at 18:16
  • @ttnphns clarified it one more time. – RTrain3K Nov 22 '16 at 18:30
  • The issue is that the variance of one column is significantly explained by both the first and second dimension OK, that sounds to me like this: the column point (brand_j) is loaded quite heavily by two principal dimensions, = under principal normalization of column points the point is somewhere in a corner of the map. Well, if so, see my comments earlier: you are absolutely free to rotate axes so that the point leans closer to an axis you choose. Like in PCA or FA, you are in right to rotate. – ttnphns Nov 22 '16 at 18:37
  • Or you have, as I see after your edit, statements, not brands, as columns. That doesn't change the principal logic. – ttnphns Nov 22 '16 at 18:44
  • @ttnphns, that's great that it's possible. I could not find an R package that can rotate the CA solution. However, I can calculate CA in R step-by-step. So, how would I rotate the solution? Is there a formula? Is it an optimization problem? Are there any sources you can direct me to? Thanks! – RTrain3K Nov 22 '16 at 19:35

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