Timeline for Are splines overfitting the data?
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
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| Nov 13, 2018 at 12:58 | comment | added | KH Kim | (related paper. cs.northwestern.edu/~paritosh/papers/KIP/…) | |
| Nov 13, 2018 at 12:58 | comment | added | KH Kim | How about using restricted cubic splines, which constrain the functions to be linear in the outside of data points(I am reading Harrell's book). Anyway extrapolation is always suspicious. Think of an experiment which discovered the superconductivity or plasma. Theory should be proved via experiments! I think what functions to fit is more relevant to interpolation problem. Without theory, I guess you would not be able to pick just one model with predictors in error(also unknown distribution) and unknown distribution of y|x, even when you are give enough data. | |
| Feb 8, 2013 at 14:40 | comment | added | Dinre | This isn't anything new. Rather, it's the difference seen between statistics done in early stages of understanding versus later stages of understanding. The more you understand a system, the less you rely on fitted functions and the more you rely on theoretical models. | |
| Feb 8, 2013 at 14:38 | comment | added | Dinre | As noted in my answer, the danger in splines is not greater compared to a blind use of a polynomial. Both modify themselves to fit the data, rather than using known rules to govern the fitting. The use of simple polynomials is sometimes used as a way of limiting how much of an effect the data has on the fit in an attempt to come closer to approximating the unknown governing rules. All of these approaches are subject to the loss of prediction capability outside of the data range. To predict well outside the data, an appropriate model has to be applied and not just a fitted function. | |
| Feb 8, 2013 at 13:59 | comment | added | Frank Harrell | I would have to be better convinced that regression splines extrapolate more dangerously than polynomials. | |
| Feb 1, 2013 at 16:39 | comment | added | Dinre | I am not suggesting that your prediction is ruined. Creating a splined, polynomial fit will give you a good description of the survival rates you are likely to find for the age groups within your data range. What the spline approach will not tell you is what to expect for age ranges outside of or under-represented in your data. It simply means what you and I already know: predictions made based on a fitted function are limited to the scope of the data used in the creation of the fitted function. | |
| Feb 1, 2013 at 16:16 | comment | added | Max Gordon | Thank you Dinre for your answer. My research as an orthopaedic surgeon is far from theoretical frameworks, and many of the variables work as proxies for other events. Just as an example: If we look at survival between 10-30 years the line would have a bump around 18-20, at least for men, since that is the age for a driver's license in Sweden. Now as I don't have that information, or many other probably just as important factors, I'm forced to extract the most possible out of the age variable. It's not a perfect solution, but I'm not sure why it would ruin my prediction. | |
| Feb 1, 2013 at 15:32 | comment | added | Dinre | I see your point, and that is true if you are using a perfect information approach or do not have enough information about the nature of the data. Many statisticians (myself included) assume imperfect information and make an attempt to apply exclusion criteria based on known information before trying to fit the data. Dangerous outliers should then theoretically be excluded from the fitting attempt. If you don't have the known information about the nature of the data (and this is quite common), then you're stuck trying to work around the outliers. | |
| Feb 1, 2013 at 15:18 | comment | added | guy | Polynomials are far more sensitive to anomalies within the data than splines are. An outlier anywhere in the data set has a massive global effect, while in splines the effect is local. | |
| Feb 1, 2013 at 13:03 | history | answered | Dinre | CC BY-SA 3.0 |