Canonical correlation is defined in terms of standardized scores of variables in both sides. Conceptually discrete variables cannot be used. However I have seen many people have used discrete variables with canonical technique. Is this a correct use?
It is not incorrect to use truly discrete variables, but care must be taken. To be used correctly, the variables must be coded so they are binary while at the same time making sure to not over-specify the model. For example, if you have a variable with two responses (e.g., yes and no), you can let X = 1 if yes and X = 0 if no. Only one variable would be used. If you had a variable with three options (e.g., yes, no, or maybe), you would have to use two variable. Let X = 1 if yes, 0 otherwise. Let Y = 1 if no, 0 otherwise. In other words, use two dummy variables. This would be the similar for additional options. For example, if four options, there would be three variables, if five options, there would be four variables, etc. On the other hand, if the variables are actually continuous, but you are using discrete levels (for example, the variable is population and you are using 1 = 1 to 50,000; 2 = 50,001 - 100,000; 3 = 100,001; etc), then you can use one variable and the actual indicators (i.e., 1, 2, 3, etc.). However, the larger the groupings, the more information that is lost in the process.
In OLS or Quantile regressions James' answer is 100% correct. I agreed. However, my worry about Canonical correlation is that it requires transformation of all variables into standardized values before calculating weights and correlation coefficient. How can standardized values be calculated sensibly for a dummy variable? Nevertheless I have seen use of dummies in canonical context quite often.
Thanks for answers. But I am not convinced. Sorry.
Yes. You are correct. It is clear in following link.
Thanks for replies.
http://www.mvstats.com/Downloads/Supplements/Canonical_Correlation_6e.pdf
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