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I have a model similar to the following:

y = a + b + c + d + e;

a,b, and c are binary variables while d is other control variables and e is error term. For my whole sample, each observation has a 1 for either a,b, or c -- each observation must belong to either a,b, or c (no observations can be 0 in all three). To avoid dummy variable trap, I can run my model two ways:

y = a + b + c + d + e (no intercept)

or

y = intercept + b + c + d + e

I've read around, including here, that intercept should never be dropped unless I am sure the regression goes through the origin. That would mean I should use the second model. However, is it possible for me to drop the intercept in this situation and use the first model -- would my estimates be biased if I dropped the intercept for the first model?

Thanks!

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  • $\begingroup$ Do you have reason to believe that the predicted response line would necessarily have to be travel through the origin and be zero at some combination of your dependent variables? What is the issue with using the second model, which is quite standard? $\endgroup$
    – StatsStudent
    Commented May 13, 2016 at 22:59
  • $\begingroup$ I want to use the first model for ease of interpretation. I'm comparing the coefficients across the three groups. $\endgroup$
    – user4951834
    Commented May 13, 2016 at 23:00
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    $\begingroup$ @Tim I believe this question isn't about using an intercept at all, but about coding categorical variables. Both models listed in the question are equivalent. $\endgroup$
    – whuber ♦
    Commented May 14, 2016 at 0:43
  • $\begingroup$ I think you will find the information you need in the linked thread. (Although that thread discusses these issues in the context of logistic regression, the principles are the same.) Please read it. If it isn't what you want / you still have a question afterwards, come back here & edit your question to state what you learned & what you still need to know. Then we can provide the information you need without just duplicating material elsewhere that already didn't help you. $\endgroup$
    – gung - Reinstate Monica
    Commented May 14, 2016 at 1:01

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Yes, without in-depth knowledge of your situation, leaving out the intercept will create bias in the results. If you do not want to use one group as a baseline in the second model, consider using effects coding for your dummy variables?

Effects coding will let you compare the effect of each group to the overall mean, rather than one baseline group.

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