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I'm working on a dataset that contains both continuous and dichotomous numerical features, the latter having values in the set $\{0, 1\}$. My objective is to apply feature selection to my dataset to improve the performance of my predictive models.

My approach for feature selection is correlation-based, inspired by the minimal-redundancy-maximal-relevance (mRMR) method, where I aim to identify and eliminate features that are highly correlated.

Can I use Pearson correlation to calculate the correlation between the continuous features and dichotomous features in my dataset?

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    $\begingroup$ Clearly you can calculate correlations so long as both variables show some variability. If one variable is (0, 1) that is equivalent to checking whether group means on the other variable differ. It's not clear what other kinds of pattern there might be, $\endgroup$
    – Nick Cox
    Jun 7, 2023 at 10:00
  • $\begingroup$ Specifically, though, should Pearson correlation be okay in this instance? $\endgroup$
    – Connor
    Jun 7, 2023 at 10:12
  • $\begingroup$ What is "okay"? Screening possible predictors always carries a risk that you leave out useful information. What else did you have in mind? Using rank correlation might be what you prefer on other grounds, but using mid-ranks rather than 0 or 1 for the (0, 1) variables will have no effect on Pearson correlation. That is just a linear transformation and as such leaves Pearson correlation unchanged (other than a change of sign, depending on ranking convention). $\endgroup$
    – Nick Cox
    Jun 7, 2023 at 10:20
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    $\begingroup$ Not wanting to be confrontional but "meaningful" and "reasonable" are no more of an answer! There is plenty of literature showing that almost any kind of classic correlation misses things you don;t want to miss, although that is not your question. In a nutshell my reaction is that using your strategy with (0, 1) variables too does not add much to the limitations it already has. $\endgroup$
    – Nick Cox
    Jun 7, 2023 at 10:33
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    $\begingroup$ Google "Chatterjee correlation" to get some ideas that may be interesting or useful. $\endgroup$
    – Nick Cox
    Jun 7, 2023 at 10:35

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Using the Pearson correlation would be OK because it is equal to the pointbiserial correlation, which is suitable to examine the relationship between a dichotomous and a continuous variable.

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  • $\begingroup$ While Pearson correlation in this case is equal to the point biserial correlation, this answer leaves out the important commentary by Nick Cox that this kind of screening is fraught with problems. $\endgroup$
    – Dave
    Nov 20, 2023 at 20:31

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