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I'm doing some analyses in which I have 1 continuous independent variable (IV) and 1 dichotomous independent variable (IV2) that's a demographic covariate. I'm now realizing that they are extremely correlated (~ .9). See image below.

enter image description here

Now what I'm wondering is there anything I can do (maybe some sort of centering strategy?) that will allow me to use both variables in my analyses? I was hoping to look at their interaction.

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  • $\begingroup$ it looks like your DV is ordinal. Is that correct? $\endgroup$
    – Peter Flom
    Commented Feb 20, 2018 at 13:14
  • $\begingroup$ Yup, a 1 to 7 Likert scale $\endgroup$
    – user166625
    Commented Feb 20, 2018 at 13:16
  • $\begingroup$ Even ignoring IV2 the distribution of IV1 looks really strange. The first thing I would want to do is to find out why that is. $\endgroup$
    – mdewey
    Commented Feb 20, 2018 at 13:26
  • $\begingroup$ More explanation would be good here: IV 2 is participant race (Black or White) and IV 1 is the proportion of people in their geographic area that are not in their group (i.e., for White person, the proportion of non-White people in their area). Thus, for White people (the pink dots) most live in areas that have a mostly White population (i.e., below 50). This is true for Black respondents, so they should have values bigger than 50. $\endgroup$
    – user166625
    Commented Feb 20, 2018 at 14:58
  • $\begingroup$ Your additional information reminds me strongly of the "predicting children's basketball ability from their grade and their height" example in the Miller & Chapman article I cite. $\endgroup$
    – Stephan Kolassa
    Commented Feb 23, 2018 at 14:09

2 Answers 2

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I'll go out on a limb here.

I don't think looking at the interaction is useful here. As in: any interpretation of the interaction between the two predictors will be deeply mistaken.

You can interpret the effect of IV1 in the range 0-50, where IV2 will typically be 0. Any IV2=1 with IV1 in this range is an extremely abnormal observation, simply because this combination is unheard of. And vice versa. Therefore, it simply makes no sense to discuss things like "if IV2=0, then IV1 has an effect of $x$, while if IV2=1, then IV1 has an effect of $y$" or similar.

I like to recommend Miller & Chapman, "Misunderstanding Analysis of Covariance" (2001), who have a number of very enlightening examples and explanations.

What I would instead do is to include IV1 only, but account for potential nonlinearities, e.g., using . Then you can discuss the relationship between IV1 and the DV over different ranges of IV1 and note what the typical value of IV2 is over these ranges.

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  • $\begingroup$ Is there some reason why I can't also use the IV2 AND use a splines approach? That is, is there some reason I have to ignore it? $\endgroup$
    – user166625
    Commented Feb 20, 2018 at 17:47
  • $\begingroup$ You have a high amount of multicollinearity. Specifically, you can almost perfectly predict IV2 from IV1, i.e., you have almost perfect separation. Your model will likely be unstable and your parameter estimates have high variance (see here). $\endgroup$
    – Stephan Kolassa
    Commented Feb 21, 2018 at 17:26
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I agree with @Stephen that the interaction is unlikely to be useful.

If you really think that the effect of IV1 will be different at different levels of IV2 (which is what an interaction tests) then you could stratify: That is, do separate regressions for the two levels of IV2. You can then compare the results (although you won't have estimates of the size of the interaction).

Since your DV is ordinal, you should probably use ordinal logistic regression, at least as a starting point.

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  • $\begingroup$ Just so I can try and compare your suggestion to @ Stephen's, wouldn't I basically get the same results by stratifying first (opposed to using splines)? $\endgroup$
    – user166625
    Commented Feb 20, 2018 at 17:48

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