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I have a dataset were I know that there are nominal independent variables (IV) with multicollinearity (by theorethical knowledge about the IV).

These IV have been created from a categorical variable via dummy coding (leaving the first one of the categorical values to be predicted by the intercept). Specifically, I use this pandas function with drop_first=True.

Therefore, I also know that these IV are mutually exclusive i.e., if one of the IV is present in an example the other will not be present.

Can I estimate linear regression coefficients with these IV and will it be statistically sound?

Thanks in advance :-)

IVs could look like this

Possible: 
IV1    IV2    intercept
  1      0            1
  1      0            1
  0      1            1
  1      0            1
  1      0            1
  0      0            1 


NOT POSSIBLE:

IV1    IV2    intercept
  1      1            1
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    $\begingroup$ Can you explain your problem further? Are the variables mutually exclusive? $\endgroup$
    – mkt
    Commented Sep 2, 2019 at 11:13
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    $\begingroup$ It would still help if you edited your question to add more details about your problem. $\endgroup$
    – mkt
    Commented Sep 2, 2019 at 11:20
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    $\begingroup$ Clarify what you mean by the IV cannot be present at the same time in any of my observations $\endgroup$
    – Fr1
    Commented Sep 2, 2019 at 12:28
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    $\begingroup$ Are simultaneous zeroes possible for both IV1 and IV2? $\endgroup$
    – mkt
    Commented Sep 2, 2019 at 13:43
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    $\begingroup$ There's still a lot you're leaving out that would help to answer this. What are IV1 and IV2? What is this third variable you are omitting? What is your goal? Can you combine IV1 and IV2 into 1 predictor, or is there a good reason to keep them separate? $\endgroup$
    – mkt
    Commented Sep 2, 2019 at 13:55

1 Answer 1

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When reference level coding is used, the dummy variables that encode the different levels of the variable are not collinear. You can use these dummies as covariates in a regression model. Your results will be valid (assuming no other problems).

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