Timeline for Does taking the logs of the dependent and/or independent variable affect the model errors and thus the validity of inference?
Current License: CC BY-SA 3.0
17 events
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| Nov 25, 2017 at 19:15 | comment | added | DeltaIV | @Bill thanks a lot! Yes, it's that - it contains a "Retransformation Bias" section. | |
| Nov 25, 2017 at 19:12 | comment | added | Bill | Here (I think) is what I linked to: herc.research.va.gov/include/page.asp?id=cost-regression | |
| Nov 25, 2017 at 18:59 | comment | added | DeltaIV | @Bill thanks! I didn't know its name. I'm reading your answer. The link you provide there is broken - gives me a 404 error. I guess it linked to some paper. Is there any other paper you would suggest me to read? | |
| Nov 25, 2017 at 18:51 | comment | added | Bill | Chris Haug's point is called the re-transformation problem. There are a number of questions and answers on that topic on the site. I've answered several questions generally on that topic, you can find one here: stats.stackexchange.com/questions/55692/… | |
| Nov 25, 2017 at 18:49 | comment | added | Bill | I googled it and found someone saying that it is in games, so that's the evidence. I've never used vuong's test in R, so I don't know which implementation is the best. | |
| Nov 25, 2017 at 18:47 | comment | added | DeltaIV |
@Bill "evidently"? It's not evident at all, since a Google search returns at least 4 different packages apparently including this test, and none of them is the games package. Anyway, good to know it's there - sometimes there are different versions of a test with the same or similar name (e.g., Wilcoxon). Since I don't know anything about this test, I'll go for the games package you suggest.
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| Nov 25, 2017 at 18:41 | comment | added | Bill | Vuong's test is a test for non-nested models. If you have two different functional forms, and you wonder "which is better," that is what it is designed to test. Here is wikipedia: en.wikipedia.org/wiki/Vuong%27s_closeness_test It is in the games package, evidently. | |
| Nov 25, 2017 at 18:41 | comment | added | DeltaIV | @ChrisHaug what you say seems very interesting. Could you expand the comment into an answer? It would be great if you could show a real-world example where you believe log-transforming will lead to a valid model (and it would be even greater if you could also include an example where it doesn't :). What I criticize, of the usual approach, is that people log-transform simply because that makes the regression curve a line - that really isn't a good reason to log-transform, if then inference becomes invalid! We're doing statistics, not curve fitting. | |
| Nov 25, 2017 at 18:35 | comment | added | DeltaIV |
@Bill thanks a lot for the inputs. GAM doesn't use polynomials but penalized regression splines, which don't have all the problems of polynomials (see for example "An Introduction to Statistical Learning" by James et al.). Actually, one of the spline basis available by mgcv can be represented as a sum of terms of the type $x^2\log(x)$ - I may try them. What's Voung's test? Can you provide more details? Do you know if it's implemented in a R package?
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| Nov 25, 2017 at 17:54 | comment | added | Bill | I don't know gam, and the documentation refers to a book I don't have. However, based on the behavior of the thing, I assume it tries to approximate an unknown function using polynomials. Polynomials do a poor job of approximating shapes like y=ln(x), and this, perhaps, explains the poor performance of gam here. The ringing Hugh Perkins mentions does not come from a step function or insufficient smoothing here (again I suspect) but from the fact that polynomials ring when approximating logarithmic functions. Your data looks logarithmic, not polynomial to me. You can test with Vuong's test. | |
| Nov 25, 2017 at 14:52 | comment | added | Chris Haug | When you "transform" the variables, you are fitting an entirely different model. The related confidence intervals are valid if the transformed model is valid (e.g. in your first example, if the errors really are multiplicative on the original scale), they just differ because they are different models. You have to be careful if you then need to invert the transform: $\hat{\beta}_0\tilde{X}^\hat{\beta_1}$ is not an unbiased prediction for a new $Y$ (it is median-unbiased, though). | |
| Nov 24, 2017 at 18:57 | history | edited | DeltaIV | CC BY-SA 3.0 |
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| Nov 23, 2017 at 8:04 | history | edited | DeltaIV | CC BY-SA 3.0 |
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| Nov 23, 2017 at 1:31 | history | tweeted | twitter.com/StackStats/status/933508253585113088 | ||
| Nov 22, 2017 at 23:25 | answer | added | Hugh Perkins | timeline score: 2 | |
| Nov 22, 2017 at 20:08 | history | edited | DeltaIV |
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| Nov 22, 2017 at 19:30 | history | asked | DeltaIV | CC BY-SA 3.0 |