Timeline for Conflicting interpretations for coefficient of log transformed predictor
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 28, 2020 at 17:17 | vote | accept | CL. | ||
| Mar 21, 2016 at 18:16 | comment | added | CL. | Thank you. In my opinion, it is a shame that so many resources (in the internet, but also printed textbooks) use an approximation without warning the reader. I see that the first rule is handy (and "sufficiently correct" for small values), but I think it is important to know the rule's limitations and the exact interpretation. | |
| Mar 21, 2016 at 18:13 | history | bounty ended | CL. | ||
| Mar 17, 2016 at 22:09 | comment | added | Dalton Hance | OP did not specify that he/she was interested in an approximation that works only when considering $d<3$. Even if he/she were, I fail to see how $1.01*\beta_1$ is more useful than $1.01^{\beta_1}$. It's a trivial difference in terms of computation and the second is more accurate, more general, and is derived directly from the form of the statistical model. | |
| Mar 17, 2016 at 21:27 | comment | added | Alex R. | You're asking to fit a peg in a square hole. If you want to talk about a 5% increase then you wouldn't use the approximation. There are plenty of situations I have encountered where you would be interested in a 1-3% increase and would like a quick estimate. This reasoning is extremely useful in assessing complicated nonlinear models. | |
| Mar 17, 2016 at 20:58 | comment | added | Dalton Hance | We are interested in the formulating the statement "For an d% percent increase in X, the expected value of Y increases by z%" from a statistical model. An approximate method based on a taylor series is very limited for making such a statement, so limited as to be completely unusable. I see no reason to prefer it, especially when we have an exact way of determining that statement. I'm not disputing the math, just saying for the purpose of inference it's not very helpful. What if we want to talk about a 5% increase in X? | |
| Mar 17, 2016 at 20:18 | comment | added | Alex R. | @DaltonHance: For $100\log(1+d/100)$, the error is bounded by $d^2/200$, which even if exponentiated is not completely unreasonable for $d\leq 3$. | |
| Mar 17, 2016 at 19:17 | comment | added | Dalton Hance | But this only holds as an approximation if $d/100$ is close to 0, which is not very useful in the context of log-log regression and interpretation of a statistical model. So it is incorrect way of talking about the effect of the predictor. | |
| Mar 17, 2016 at 18:50 | history | answered | Alex R. | CC BY-SA 3.0 |