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?

Thanks,

Chris

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?