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I am doing a regression analysis where several of my independent variables are categorical measures of severity. I code them as dummies and exclude the least severe variable. The more severe the category the lower the dependent variable with y always equal (or nearly equal) to zero when the most severe category is in place. For clarity call the categorical independent variable S with four categories 4 being the most severe. So

y = a + S2 + S3 + S4 +e

A reviewer has suggested that if S3 is equal to 1 (e.g. the second most severe restriction is in place) then my observation would be expected to have a lower y than observations with S2=1, but a higher y than observations with S4=1. He/She suggests that these competing effects will act in opposite directions leading to a lack of significance for S3. Moreover, He/She suggests that the only appropriate choice is to model only the observations where S4 does not equal 1.

Intuitively this does not make sense to me, the model should use the dummies in comparison with the reference category not the other dummies, and since the dummies are exclusive the effect will be one-direction.

Nevertheless, the reviewer's other comments lead me to believe he/she generally knows what they are talking about. Was this just an embarrassing misstep on their part or do I have much more to learn about categorical variables?

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  • $\begingroup$ What were your results when you did the regression? It sounds like the reviewer is commenting on those results. $\endgroup$
    – Peter Flom
    Commented Aug 30, 2012 at 15:50
  • $\begingroup$ S4 had a large negative effect (significant), S2 had a small positive effect (not significant) and S3 had a small negative effect (not significant). I have another explanation in mind about why S2 and S3 might not be significant, but am searching for some clarification on the methodological suitability of modeling my categorical variable as I have. $\endgroup$
    – csfowler
    Commented Aug 30, 2012 at 16:32
  • $\begingroup$ Choice of reference group can matter. Given these results, I would use S4 as the reference group, rather than S1. Then S1, S2 and S3 will all be positive, making for easier interpretation. (Note that the models will mean the same thing. Another example of where relying on significance can lead you astray) $\endgroup$
    – Peter Flom
    Commented Aug 30, 2012 at 17:23
  • $\begingroup$ @Peter Flom. Thanks for your comments. It is probably a failure of my explanation, but I don't think your suggestion gets me there. The reference category (S1) is akin to "no treatment," and S2, S3, S4 are increasingly severe treatments. They (2,3,4) should all have a negative effect on y (which is censored at zero). The reason for the mixed results for S2 and S3 is probably that a)they are not terribly effective, and b)they are probably more likely to be put in place where y is high. Switching the reference category would, I suspect, just confound explanation. $\endgroup$
    – csfowler
    Commented Aug 30, 2012 at 20:59
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    $\begingroup$ Nope. What "should" happen isn't relevant here. Given your results, using S1 as a reference would make it clearer what did happen. And "no treatment" is usually the best reference category, anyway. $\endgroup$
    – Peter Flom
    Commented Aug 30, 2012 at 21:07

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