Timeline for Spearman2's rho or Chatterjee's xi correlation coefficient for non-monotonic data?
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| when toggle format | what | by | license | comment | |
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| 7 hours ago | history | became hot network question | |||
| 7 hours ago | history | edited | kjetil b halvorsen♦ | CC BY-SA 4.0 |
deleted 120 characters in body
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| 7 hours ago | answer | added | Glen_b | timeline score: 2 | |
| 12 hours ago | answer | added | Nick Cox | timeline score: 1 | |
| 13 hours ago | comment | added | Nick Cox | Sorry. but I can't follow what you want here. Is no relationship at all really your benchmark? When I see your data and fit, I just think of other ways to model the relationship and whether they differ and which summary I prefer on any number of grounds. More positively, the best check on a fitted relationship is whether other kinds of fit tell similar stories. Wanting to reduce the problem to a significance test raises more questions than it answers. | |
| 14 hours ago | comment | added | denis | @whuber, thank you, but I'm not ruling out the Spearman method; I'm just noting that the p-value is not significant. Furthermore, I used the spearman2() function, which, according to Harrell, is usable in cases of non-monotonicity (stats.stackexchange.com/questions/219224/…). What types of assumptions are you referring to? | |
| 14 hours ago | comment | added | whuber♦ | "Significant" in a statistical context usually means discernible, a quality that is often tested by adopting a probability model for the data. I take it that (a) there is a visually evident link between $x$ and $y$ but (b) you wish to make a formal test of that. Thus, it looks like you need to tell us what kinds of probability models you have in mind for the possible links. You have rejected a standard non-parametric method (Spearman) because it doesn't comport with what we can see--it's not sufficiently powerful. You can increase power only by making stronger assumptions. What are they? | |
| 15 hours ago | comment | added | denis | @Nick: So there's no reliable test to determine whether or not there's a link between these two variables? Even though the data suggests a relationship? | |
| 15 hours ago | comment | added | denis | @whuber: Yes, "correlated" in the common sense. Put another way: is there a significant link between these two variables? And yes, you're right, "s(x)" represents "y", thank you. | |
| 15 hours ago | comment | added | Nick Cox | My short answer is neither. as neither kind of correlation is tied to the kind of curve you've fitted. But I would be happy myself to start with the correlation between observed data points and predicted data values as implied by the fit. As always, there are reservations, as for example that a curve which interpolated the data points would yield a correlation of 1. (Chatterjee's correlation is to me an interesting idea with too many limitations to join the classic measures.) | |
| 15 hours ago | comment | added | whuber♦ | Do you use "correlated" in the standard sense of "arising from a bivariate distributiion with nonzero [Pearson] correlation coefficient," or in some other sense? Could you clarify what you mean by "independent...given the non-monotonic regression"? That sounds like some form of conditional independence, but is that what you intend? And, despite the labels "s(x)" and "partial effect" on your plot, isn't the vertical axis "y" itself? | |
| 16 hours ago | history | asked | denis | CC BY-SA 4.0 |