Fellow RGers:
A recent survey statistics and methodology journal had an article on the use of splines, and as one example they used data with which I am very familiar. In that case, however, I know that they combined categories of data for which results are also needed, and at the more aggregate level, those categories could be treated as strata. Then, each stratum, with its individual separate simple model, could contribute to perhaps the best overall results, rather than use a linear spline regression for the combined data set. Each category would appear to logically best be modeled by a simple WLS regression through the origin (which has worked well for these data). However, with data grouped together, a linear spline regression or a lowess model would seem logical, if one were unaware of the categories/strata that made up that combined data set.
But I would think that there would be much better uses for spline regressions. I'm curious to hear of some applications, especially - but not limited to - your own applications, with comments on why it was a beneficial approach, and why you chose it.
Thank you - Jim
I have applied Multivariate Adaptive Resgression Splines (MARS) in modeling of rock properties as function of many other rock characteristics. MARS is a non- parametric regression that automatically models all variables and interactions. It also eliminates the non influential parameters that have no impact on the response. MARS algorithm has led to much more accurate modeling and prediction than linear regression and generalized additive regression.
It was completely implemented in R through "earth" package.
Watheq
Hello James,
Please follow the link attached
Best wishes
https://books.google.ie/books?hl=pl&lr=&id=PYbvSt8fejoC&oi=fnd&pg=PR5&dq=spline+regression+application&ots=KzNFFBh1PA&sig=9GtE5_zdE7lxYnpZAG36wLeAy6I&redir_esc=y#v=onepage&q=spline%20regression%20application&f=false
I think splines can be used when we have strong evidence of convexity for our data. Then, since by their construction are convex, they will fit well.
(Of course there is linear case but let's omit it now)
Otherwise, a simple 3rd order polynomial regression could give the same benefits.
I have applied Multivariate Adaptive Resgression Splines (MARS) in modeling of rock properties as function of many other rock characteristics. MARS is a non- parametric regression that automatically models all variables and interactions. It also eliminates the non influential parameters that have no impact on the response. MARS algorithm has led to much more accurate modeling and prediction than linear regression and generalized additive regression.
It was completely implemented in R through "earth" package.
Watheq
Jim,
I just want to correct that the main R package for MARS algorithm is "earth" and the function is also "earth".
The comparison between multiple linear regression and MARS algorithm is represented by the attached two images that have matching between measured and predicted response by MLR and MARS, respectively.
The second image shows how efficient the MARS modeling to produce accurate prediction.
Watheq -
Hi. I downloaded the two graphs above, but cannot make out the labels on the axes. What are they please?
Thanks - Jim
We used splines to produce a smooth forecast when experts have some idea about how process should develop in future, but forecasts must be updated as new data becomes available:
https://www.researchgate.net/publication/282136270_A_joint_Bayesian_forecasting_model_of_judgment_and_observed_data
Technical Report A joint Bayesian forecasting model of judgment and observed data
Jim,
The x-axes represent the depth of the formation that oil. The y1-axes is the value of rock permeability. The permeability was modeled given many other factors of rock properties such as porosity, Gamma Ray, Resistivity, Induction, etc.
Dear James,
I rarely work with spline regression as it is both nonparametric and it uses knots. It's use is sensitive to the types of data and mostly uses patterns to build models. So I think it should be used very carefully. It is obvious that if the data points have no overlap on X axis this method can go through all the points, but gives no unique parameters. The attached file is the difference between spline and a loess smoothing in a dataset of mine and a SAS contour plot example. It really shows how much misleading this method can be, if used inappropriately.
I wish it helps
About the previous post:
Obviously, the quality of approximation depends on how many knots you use. The use of so many knots is not reasonable in the above examples. In order to select a reasonable number of knots it is possible to use various special methods, e.g., methods based on the significance of spline coefficients or on the use of information criteria, such as AIC.
P.S.
In order to avoid the problems shown above, we can also use alternatives such as linear splines, Akima interpolation, Hermite splines, wavelets or trigonometric approximation.
In our paper we proposed applying liner splines to the first difference of time series and to use judgmental estimates for some future points so that spline extrapolation does not go in a wrong direction (section 2.2):
https://www.researchgate.net/publication/282136270_A_joint_Bayesian_forecasting_model_of_judgment_and_observed_data
Technical Report A joint Bayesian forecasting model of judgment and observed data
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