Timeline for Converting a circular outcome variable to a linear one
Current License: CC BY-SA 4.0
23 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 22, 2021 at 17:36 | vote | accept | Abundance | ||
| S Sep 22, 2021 at 17:36 | history | bounty ended | Abundance | ||
| S Sep 22, 2021 at 17:36 | history | notice removed | Abundance | ||
| Sep 22, 2021 at 17:33 | comment | added | Abundance | @SextusEmpiricus, yes, I think that is the main tension. Since my prediction considers the closest peak, it's not possible to get an error larger than 180 that is projected backwards, so it wouldn't be circular in the first place. | |
| Sep 21, 2021 at 20:22 | comment | added | Sextus Empiricus | "I'm not sure whether this is a completely circular problem in the first place, since an outcome measure of is bounded between 180 and -180 degrees." It is not about the outcome being bounded. It is about the underlying mechanism. A clock has 60 minutes but that doesn't mean that a time estimate can not make errors larger 30 minutes (it means that you have some sort of censoring and an error of 45 minutes becomes an error of 15 minutes). What you need to consider is whether your prediction strategy can make an error larger than 180 degrees (but get's projected to a value smaller than 180). | |
| Sep 21, 2021 at 16:32 | comment | added | whuber♦ | Re the edit: although the outcome measurement is of circular type, you describe a distance on the circle. Distances are not circular. (For one thing, they have an obvious lower bound of zero.) In this sense, you don't have a question. They can, however, be richly varied. For a brief account see stats.stackexchange.com/a/201864/919. | |
| Sep 21, 2021 at 16:18 | history | edited | Abundance | CC BY-SA 4.0 |
more context into problem
|
| Sep 20, 2021 at 16:22 | answer | added | Sextus Empiricus | timeline score: 2 | |
| Sep 20, 2021 at 16:05 | answer | added | Alexis | timeline score: 5 | |
| Sep 20, 2021 at 13:55 | answer | added | Adam Kells | timeline score: 1 | |
| Sep 19, 2021 at 11:47 | comment | added | Sextus Empiricus | So the output range, if it is restricted to the range -180 to 180, doesn't tell us much about the process and whether it is circular or not. But... if all your observed data points would cluster within a small range only, ie they never reach the other side of the circle, then the range of the data is an indication that the underlying process doesn't cause wrapping due to a sum of deflection adding up to going around the entire circle. | |
| Sep 19, 2021 at 11:42 | comment | added | Sextus Empiricus | @Abundance, your output is in the range -180 to 180. But that doesn't necessarily mean that the underlying process doesn't generate -270. It is just that for the output the -270 is mapped to +90, and that is why you get output values that are only -180 to 180. Your linear model will be wrong if you consider all the cases of +90 in the output as +90 in the underlying process. It might also be partly -270. | |
| Sep 18, 2021 at 19:39 | comment | added | Abundance | I guess what I'm asking is if my outcome measures are in the range (-180, 180], so you can't have something like -270 degrees, hence no wrapping, and the outcome that I'm interested in is symmetrical about zero degrees, whether I can linearize my variable. For the purposes of my problem, an angle like 179 and -179 are equivalent, since they both deviate from zero equally. So although I'm measuring angles, I'm not sure if they are circular in the standard sense. | |
| Sep 18, 2021 at 17:47 | comment | added | Sextus Empiricus | @Abundance the circle wraps around itselve. Random movements to the right and left on the circle may not end up on the right or left. If you make three quarter steps to the left you end up one quarter step to the right. Only if you have a process that does not wrap around the circle or when the effect can be considered negligible, then you can linearize the situation without much problems (that's why you got the question whether the entire circle has observations, sometimes you the observations cluster on only a part of the circle). | |
| Sep 18, 2021 at 15:10 | comment | added | Abundance | I'm curious as to why this approach wouldn't work, it gets rid of the circular nature of the metric | |
| Sep 18, 2021 at 14:53 | comment | added | whuber♦ | The answer is a clear no: there's no continuous way of re-expressing the outcome on a linear scale. That's why there exists a theory of circular statistics in the first place. | |
| S Sep 18, 2021 at 14:09 | history | bounty started | Abundance | ||
| S Sep 18, 2021 at 14:09 | history | notice added | Abundance | Authoritative reference needed | |
| Sep 17, 2021 at 9:00 | history | tweeted | twitter.com/StackStats/status/1438789931418230790 | ||
| Sep 17, 2021 at 4:28 | comment | added | Ciaran Haines | I think that using a min/max scaler is a simplification, but a common one. | |
| Sep 16, 2021 at 14:14 | comment | added | Abundance | The full 360 degrees ... | |
| Sep 16, 2021 at 13:55 | comment | added | jcken | What range of angles are you observing? If the range is small you could treat the effect as already linear. If you're observing the full $360$ (or close to this) then yes I agree, something clever is needed | |
| Sep 16, 2021 at 13:51 | history | asked | Abundance | CC BY-SA 4.0 |