Timeline for Do statisticians assume one can't over-water a plant, or am I just using the wrong search terms for curvilinear regression?
Current License: CC BY-SA 3.0
21 events
| when toggle format | what | by | license | comment | |
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| Feb 4, 2020 at 14:58 | comment | added | whuber♦ | (f1r3br4nd: Nice to see you back!) | |
| Feb 4, 2020 at 11:25 | vote | accept | f1r3br4nd | ||
| Jul 12, 2013 at 17:02 | history | tweeted | twitter.com/#!/StackStats/status/355733888095633409 | ||
| Jul 11, 2013 at 14:33 | answer | added | whuber♦ | timeline score: 60 | |
| Jul 11, 2013 at 9:54 | comment | added | Roland | I don't really understand the problem. I am most familiar with your crop yield/water example. There are (often quite complex) models available that are based on micro-meterology, soil physics, plant physiology, nutrient supply (fertilization), and so forth. You find them in the literature. If you fit an empirical model it can only approximate such a complex model over a limited range. It may be that a linear model is appropriate to answer your specific question, it may be that you need to be able to model saturation (use an appropriate non-linear function). | |
| Jul 11, 2013 at 9:30 | history | edited | COOLSerdash | CC BY-SA 3.0 |
Added plot for clarity and convenience
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| Jul 11, 2013 at 5:56 | answer | added | Matt Krause | timeline score: 10 | |
| Jul 11, 2013 at 5:39 | answer | added | generic_user | timeline score: 5 | |
| Jul 11, 2013 at 5:31 | comment | added | Stumpy Joe Pete | +1 for the provocative title and a followup that actually makes sense | |
| Jul 11, 2013 at 5:24 | answer | added | January | timeline score: 9 | |
| Jul 11, 2013 at 4:11 | history | edited | f1r3br4nd | CC BY-SA 3.0 |
Oops. Now I fixed it.
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| Jul 11, 2013 at 4:00 | comment | added | f1r3br4nd |
@JakeWestfall my problem with polynomial regression: plot(lm(y~poly(x),updown)), i.e. not everything that goes up and then down is a polynomial. Sine regression also gives odd residuals, but at least they're symmetrically distributed. My bigger problem with sine regression is that for non-cyclical data, it will make completely wrong predictions. And, if the data had ranged over a wider area of low response beyond the peak, the fitted curve would be a series of sine waves instead of a unimodal function!
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| Jul 11, 2013 at 3:42 | comment | added | f1r3br4nd | @Glen_b no, the 'kink' points aren't known, and might not exist-- it might be some sort of continuous function. And if the kink-points do exist, there is no evidence that they would be the same under different treatments. | |
| Jul 11, 2013 at 3:40 | comment | added | f1r3br4nd | (previous comment continued) so another way of putting my question is: what should I learn in order to be able to go from seeing a pattern in the data to a parametric model I can fit to future data and measure the effect of experimental variables on various parameters? What is the workflow from the exploratory phase (that apparently my subfield is largely in) to the hypothesis testing phase? | |
| Jul 11, 2013 at 3:14 | comment | added | Glen_b | Are the points where those things 'kink' known in advance? | |
| Jul 11, 2013 at 3:13 | answer | added | Glen_b | timeline score: 7 | |
| Jul 11, 2013 at 3:11 | comment | added | f1r3br4nd | @whuber thanks! Fixed the code. Regarding theoretical motivation: where do these come from in the first place? My bench scientist collaborators will happily dichotomize the predictor variables and do t-tests on them. So it falls to me find a way to stop wasting data by finding a mathematical relationship that captures the transition from "y correlates positively with x" to "y has little response to x" to "y correlates negatively with x". Failing that, I'll have to recapitulate what, e.g., Michaelis and Menten did when they found a relationship between enzyme, substrate, and product. | |
| Jul 11, 2013 at 2:59 | history | edited | f1r3br4nd | CC BY-SA 3.0 |
Fixed code typo.
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| Jul 11, 2013 at 2:54 | comment | added | whuber♦ |
(1) Your R code has syntax errors: group should not be quoted. (2) The plot is beautiful: the red dots exhibit a linear relationship while the black ones could be fit in several ways, including a piecewise linear regression (obtained with a changepoint model) and possibly even as an exponential. I am not recommending these, however, because modeling choices ought to be informed by an understanding of what produced the data and motivated by theories in relevant disciplines. They might be a better start for your research.
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| Jul 11, 2013 at 2:43 | comment | added | Jake Westfall | I have no idea what you're asking. You want to fit a non-monotonic function of $x$... what exactly is your problem with polynomial regression or sine regression again?? Also... "link function"... you keep using that word... I do not think it means what you think it means. | |
| Jul 11, 2013 at 2:29 | history | asked | f1r3br4nd | CC BY-SA 3.0 |