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.
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No, that way you would loose too much information. You can use a fractional logit though. http://maartenbuis.nl/publications/proportions4.pdf
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$\begingroup$ Thanks, I will definitely look into it. But would that mean that by looking at Pearson's correlations between LIWC-Data and Narcissism, the researchers in researchgate.net/publication/… are using their own tool in an inappropriate way? $\endgroup$– MarkusApr 26, 2020 at 19:26
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$\begingroup$ Hey, I edited my question to specify the particular comparison I want to make. Is fractional logit still applicable? $\endgroup$– MarkusApr 26, 2020 at 20:37
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$\begingroup$ I am reluctant to use the word "inappropriate" in this context. Statistical models are not black and white; they are all wrong, but some are more useful than others. The concrete worry I would have here is that correlation measures the strenght of the linear association, and I would expect these proportions to be rather small, leading to quite a noticable non-linearity in the associations. $\endgroup$ Apr 27, 2020 at 6:28