Is it allowed to use a [A = -1; B = 1] recodification? Like this, would it be correct to say that a negative beta coefficient tends to reflect Group A influence on the dependent variable? (At the opposite, a positive beta would reflect Group B influence on the DV).
Many thanks in advance.
You can not say that either A or B influences the response (ore one has a higher impact than the other. The response depends on the group membership, and you can estimate the expected response for each group or the expected difference in the response between the two groups. If you code the groups as 0/1, the coefficient b1 in the model Y = b0 + b1*1GROUP directly gives you the expected difference (b0 gives you the expected response for the groups coded with 0, and b0+b1 gives the expected response for the group coded with 1). Using other codings makes the interpretation of the coefficients a bit more difficult. In your example with Y = b0 + b1*IGROUP where I is the indicator function returning -1 for A and +1 for B, the expected response for A would be given by b0-b1, the expected response for B would be given by b0+b1, and the expected difference by 2*b1. However, b0 directly estimates the mean response over both groups.
Example:
The (mean) response in group A is 12, in group B it is 8. How can you tell which group has more impact on the result?
In the usual coding, the coefficients are b0=12 and b1=-4. So we see directly that group B as a response that is 4 units lower than that of A (or vice versa: group A response is 4 units higher than group B response).
In your coding, the coefficients are b0 = 10 (the mean of 8 and 12), and b1 = -2 (half the difference between the groups). Note that the negative sign does NOT indicate that A has "more influence" than B. It is still just a difference.
You can not say that either A or B influences the response (ore one has a higher impact than the other. The response depends on the group membership, and you can estimate the expected response for each group or the expected difference in the response between the two groups. If you code the groups as 0/1, the coefficient b1 in the model Y = b0 + b1*1GROUP directly gives you the expected difference (b0 gives you the expected response for the groups coded with 0, and b0+b1 gives the expected response for the group coded with 1). Using other codings makes the interpretation of the coefficients a bit more difficult. In your example with Y = b0 + b1*IGROUP where I is the indicator function returning -1 for A and +1 for B, the expected response for A would be given by b0-b1, the expected response for B would be given by b0+b1, and the expected difference by 2*b1. However, b0 directly estimates the mean response over both groups.
Example:
The (mean) response in group A is 12, in group B it is 8. How can you tell which group has more impact on the result?
In the usual coding, the coefficients are b0=12 and b1=-4. So we see directly that group B as a response that is 4 units lower than that of A (or vice versa: group A response is 4 units higher than group B response).
In your coding, the coefficients are b0 = 10 (the mean of 8 and 12), and b1 = -2 (half the difference between the groups). Note that the negative sign does NOT indicate that A has "more influence" than B. It is still just a difference.
There are many different coding schemes for categorical variables as explained in the following link.
Edit: Oopps, actually I pasted the link into the box and forgot to click add, thanks Jochen, you are reading my mind.
http://stats.idre.ucla.edu/sas/webbooks/reg/chapter5/regression-with-saschapter-5-additional-coding-systems-for-categorical-variables-in-regressionanalysis/
Is this the "missing link"? :)
http://stats.idre.ucla.edu/r/library/r-library-contrast-coding-systems-for-categorical-variables/
- Badges
- Science topic
- Similar topics
- Mathematical Sciences
- Statistics
- Statistical Software
- SPSS