I am looking at dimensions of LIWC-Data (Linguistic Inquiry and Wourd Count), which, according to the authors, gives out values for word-categories such as "positive emotion", "health-related" or "swear words" as percentages of the whole text. I want to compare the relationship of only one such compositional variable (e.g. "positive emotion") with a continuous dependant variable to the correlation between a non-compositional explanatory variable with the same dependant variable. As dependant variable, I am using a continuous variable with range 1-7. As for my understanding, even if I am only interested in a subset of those LIWC-dimensions, I am dealing with compositional data, which cannot be analysed properly through regular correlation. As an alternative, is it reasonable to split the dependant variable into a binary and predict it with logistic regression? Thanks for any expertise and insights, links to papers are also highly appreciated.
No, that way you would loose too much information. You can use a fractional logit though. http://maartenbuis.nl/publications/proportions4.pdf