Timeline for Interpretation of dummy variables
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
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| Jun 9, 2017 at 13:43 | comment | added | quant | @DavidWright how did will this approach of interpretation change, if i center the data before the regression ? | |
| Jun 9, 2017 at 11:34 | comment | added | quant | @DavidWright Thank you. One last follow up question. So in The case that i have 2 dummies, Male/Female and Rich/Poor, and I code $d_{g}=1$ for Male, $d_{g}=0$ for Female, $d_{money}=1$ for rich and $d_{money}=0$ for poor, I will get 3 coefficients, a(intercept), b(for gender) and c(for money). Then if i re-run the regression and I code $d_{g}=0$ for Male, $d_{g}=1$ for Female, $d_{money}=1$ for rich and $d_{money}=0$ for poor, will all the coefficients change ? Also the intercept ? | |
| Jun 8, 2017 at 17:27 | comment | added | David Wright | and unconditional probabilities like $E[Y|. .] = a + (p_{1 0} + p_{1 1}) b + (p_{0 1} + p_{1 1}) c$, and then take difference to get expected changes such as $E[Y|1 .] - E[Y|. .] = (p_{0 0} + p_{0 1}) b + \left[ \frac{p_{1 1}}{p_{1 0} + p_{1 1}} - (p_{0 1} + p_{1 1}) \right] c$. There may be some way to convert this to more compact matrix expressions; I don't know. If you are willing to re-do the regression, it would also be straightforward to fall back to Michael's suggested procedure. | |
| Jun 8, 2017 at 17:21 | comment | added | David Wright | @quant: You can extend it, but the algebra gets pretty harry. Suppose your model is $Y = a + b u + c v$, where $u = \{0, 1\}$ and $v = \{0, 1\}$ are your dummy variables for female/male and poor/rich, respectively. You can write fully conditional expectations $E[Y|0 0] = a, E[Y|1 0] = a+b, E[Y|0 1] = a+c, E[Y|1 1] = a + b + c$. Given the population fractions of each subgroup $p_{0 0}, p_{1 0}, p_{0 1}, p_{1 1}$, you can compute semi-conditional probabilities like $E[Y|1 .] = (p_{1 0} E[Y|1 0] + p_{1 1} E[Y| 1 1])/(p_{1 0} + p_{1 1}) = a + b + \frac{p_{1 1}}{p_{1 0} + p_{1 1}} c$ | |
| Jun 8, 2017 at 14:45 | comment | added | quant | How could this be extended, in the case, that apart from Male Female, there was also a dummy for e.g rich/poor, and you wanted the effect of being male regardless of being rich/poor | |
| Jun 7, 2017 at 9:00 | history | edited | David Wright | CC BY-SA 3.0 |
Fix typo
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| Jun 7, 2017 at 8:58 | vote | accept | quant | ||
| Jun 7, 2017 at 8:58 | comment | added | quant | Thank you. @Scortchi I am sorry if it was not clear enough. | |
| Jun 7, 2017 at 8:45 | comment | added | Scortchi♦ | (+1) Wonder if that's the desired interpretation of "the effect of being male, but not relative to the female". (I can't think of another that makes any sense) | |
| Jun 7, 2017 at 8:33 | comment | added | Michael L. | +1, this is the better solution once the regression is already done. | |
| Jun 7, 2017 at 8:21 | history | answered | David Wright | CC BY-SA 3.0 |