# Statsmodels spline

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Does anyone have a workaround for this dependency? Is the LSQunivariate interpolate function a good proxy? There is no direct workaround. The old stats. The old code has been left in the sandbox in case someone wants to reuse parts for a new implementation.

I never tried to figure out the details of the old bspline code. But I think they can be reused for many cases. I started to work on pure python smoothing splines and penalized splines but haven't looked at it in more than a year. Currently, I use the scipy.

I have essentially a time series of unevenly spaced observations along the X axis, and at each time step, I'd like to use knots located in a fixed space to spline-smooth over.

So the knots aren't necessarily located at the observation points, but I could maybe make do with uniform spacing. As fortran is indecipherable to me. Building a general purpose spline tool box is a lot of work.

A lot of it is numerical optimization for a large number of knots, for example linear algebra to take account of the banded structure, and functions to add and drop knots without recalculating everything. What's a rough count for the number of knots that you would be using? If your number of knots is not too large, then, I think, using specialised code for banded matrices doesn't matter so much.

The scipy wrappers have several low level function.

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You can set your own knots if you don't do it already and Chuck posted a recipe how to get the basis functions out of it although that didn't sounded to be the most efficient way.

The more difficult parts: imposing constraints endpoint, periodic, and similar on the splines makes it into a non-linear optimization problem searching for the location of knots needs efficient updating adding and dropping knots. I haven't looked at the functional time series case yet.

If you keep the number of knots constant and not too large, then almost all the work will be in updating the penalized least squares parameter estimate, especially if you have a long time series. Skip to content. Dismiss Join GitHub today GitHub is home to over 40 million developers working together to host and review code, manage projects, and build software together.

Sign up.Patsy offers a set of specific stateful transforms for more details about stateful transforms see Stateful transforms that you can use in formulas to generate splines bases and express non-linear fits. B-spline bases can be generated with the bs stateful transform. The spline bases returned by bs are designed to be compatible with those produced by the R bs function.

The following code illustrates a typical basis and the resulting spline:. In the following example we first set up our B-spline basis using some data and then make predictions on a new set of data:. The next section describes more specialized functions for producing different types of cubic splines. Natural and cyclic cubic regression splines are provided through the stateful transforms cr and cc respectively.

Here the spline is parameterized directly using its values at the knots. These splines were designed to be compatible with those found in the R package mgcv these are called crcs and cc in the context of mgcvbut can be used with any model. Note that the compatibility with mgcv applies only to the generation of spline bases : we do not implement any kind of mgcv -compatible penalized fitting process.

Thus these spline bases can be used to precisely reproduce predictions from a model previously fitted with mgcvor to serve as building blocks for other regression models like OLS. In the following example we first set up our spline basis using same data as for the B-spline example above and then make predictions on a new set of data:. Note that in the above example 5 knots are actually used to achieve 4 degrees of freedom since a centering constraint is requested.

Smooths of several covariates can be generated through a tensor product of the bases of marginal univariate smooths. For these marginal smooths one can use the above defined splines as well as user defined smooths provided they actually transform input univariate data into some kind of smooth functions basis producing a 2-d array output with the i, j element corresponding to the value of the j th basis function at the i th data point.

The tensor product stateful transform is called te. The implementation of this tensor product is compatible with mgcv when considering only cubic regression spline marginal smooths, which means that generated bases will match those produced by mgcv.

Recall that we do not implement any kind of mgcv -compatible penalized fitting process. In the following code we show an example of tensor product basis functions used to represent a smooth of two variables x1 and x2. Note how marginal spline bases patterns can be observed on the x and y contour projections:.

Following what we did for univariate splines in the preceding sections, we will now set up a 3-d smooth basis using some data and then make predictions on a new set of data:. Overview Quickstart How formulas work Coding categorical data Stateful transforms Spline regression General B-splines Natural and cyclic cubic regression splines Tensor product smooths Model specification for experts and computers Using Patsy in your library Differences between R and Patsy formulas Python 2 versus Python 3 patsy API reference patsy.

The following code illustrates a typical basis and the resulting spline: In [1]: import matplotlib. Warning Note that the compatibility with mgcv applies only to the generation of spline bases : we do not implement any kind of mgcv -compatible penalized fitting process. In [12]: plt. In [16]: plt. Note The implementation of this tensor product is compatible with mgcv when considering only cubic regression spline marginal smooths, which means that generated bases will match those produced by mgcv.

Read the Docs v: latest Versions latest stable v0.GitHub is home to over 40 million developers working together to host and review code, manage projects, and build software together. Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Already on GitHub? Sign in to your account. Currently this is handled directly in the model and results classes. To make this more generic we need some additional information for terms that are created by statsmodels, or by the user, in which case the user needs to provide the information. Current example is polynomial trend in tsa models, and seasonal dummies in VECM.

Another usecase would be if we use patsy for individual terms but then want to combine this term into a full exog used in the models.

Related would be a drop methods for formula terms. One problem with formula terms is that those are not independent of each other, e. This is mainly a convenience feature for users, e. GAM will allow partial prediction, i. Another application is margins with respect to a non-linear function in an explanatory variable that is a linear combination of basis functions like polynomials or splines, which we don't have yet. One problem in GAM is how to combine the given linear component exog with the created spline basis functions.

It's not a problem with numpy arrays, but we don't have the extra info that we get from pandas, i. Then we need a more generic and reusable solution to this. Skip to content. Dismiss Join GitHub today GitHub is home to over 40 million developers working together to host and review code, manage projects, and build software together.

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### Example of Multiple Linear Regression in Python

Stack Overflow for Teams is a private, secure spot for you and your coworkers to find and share information. I need to do group by smoothening of sales percentage values which could be erratic due to out of stock situations.

I have my data in a Pandas dataframe. Here is the code I am trying:. Here I am passing np. However I am getting error:. You dont need to select the column you want, because transform already turns it into a Series, which you cant index like that.

Also, UnitvariateSpline returns a 'fitted' object which you need to call again with your desired x-output to get some actual values.

## 一文读懂回归样条（regression splines），附Python代码

Learn more. Spline smoothening using statsmodel within Python pandas dataframe Ask Question. Asked 3 years, 1 month ago. Active 3 years, 1 month ago. Viewed times. Here is the code I am trying: from scipy. Active Oldest Votes.

Rutger Kassies Rutger Kassies Sign up or log in Sign up using Google. Sign up using Facebook. Sign up using Email and Password. Post as a guest Name.This article is based on a chapter from Hastie, T.

The elements of statistical learning: data mining, inference, and prediction. New York: Springer. Popular linear models for classification and regression express the expected target as a linear function of the features. This approximation is a convenient and sometimes a necessary one. Convenient, as linear models are easy to interpret and necessary, as with scarce data linear models might be all we can fit to it without overfitting.

However, the true underlying function will typically not be linear. Capturing this nonlinearity in the model might, therefore, yield more predictive and explanatory power. Such models take the form. Some widely used basis functions are:.

The rather lengthy Python code chunk below fits some simple piecewise polynomials to simulated data and plots them nicely. Note that most of the code is for plotting. The upper left panel shows a piecewise constant function with three basis functions:. The upper right panel shows a piecewise linear fit.

One problem with the piecewise linear model is that it is discontinuous at the knots. This is not desired, as we would like the model to produce a unique output Y for every input X. Therefore, in most cases one would prefer to have a continuous model, such as the one in the lower left panel. It can be obtained by enforcing continuity at the knots through incorporating proper constraints into the basis functions:. Piecewise polynomials, even those continuous at the knots, tend not be smooth: they rapidly change slope at the knots.

To prevent this and increase their smoothness, it is enough to increase the order of the local polynomial and require the first two derivatives on both sides of the knot to be the same. A function that is continuous and has continuous first and second derivatives is called a cubic spline and can be represented with the following basis functions:.

The code chunk below fits this cubic spline to the previously simulated data. The cubic spline above seems to fit well to the data. However, there is a danger associated with using this technique: the behaviour of cubic splines tends to be erratic near the boundaries, i.

To smooth the function near the boundaries, one can use a special kind of spline known as a natural spline. A natural cubic spline adds additional constraints, namely that the function is linear beyond the boundary knots.

There will be a price paid in bias near the boundaries for this rather crude approximation, but assuming linearity near the boundaries, where we have less information anyway, is often considered reasonable. For this practical example, we will use the statsmodels package for fitting the splines and patsy for defining formulas.

Hastie et al. Both splines look similarly, but notice how the natural spline is linearly stable at the right edge of the plot as opposed to the cubic spline!GitHub is home to over 40 million developers working together to host and review code, manage projects, and build software together. Have a question about this project?

Sign up for a free GitHub account to open an issue and contact its maintainers and the community. Already on GitHub? Sign in to your account. Theoretically yes, but I think I never tried that, so there are likely some problems. The generic multiple spline class should take a list of individual, univariate splines.

This needs examples and unit tests to see how much it works automatically And either doc examples or a simplified API for choosing different spline bases.

**Interpolation - Cubic Splines - Basics**

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Sign up. New issue. Jump to bottom. Labels comp-gam topic-penalization type-enh. Copy link Quote reply. This needs a simpler API. This comment has been minimized.

Sign in to view. Member Author. This needs examples and unit tests to see how much it works automatically And either doc examples or a simplified API for choosing different spline bases For usage it would be nice to just use formulas for defining different spline terms.

Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment. Linked pull requests. You signed in with another tab or window. Reload to refresh your session. You signed out in another tab or window.Module code. Source code for statsmodels. If so, why do we need it? I do not know why yet. So until we understand this and decide what to do with it, I'm going to play it safe and disallow such points.

Patches accepted! It's not well documented, but basically it computes an arbitrary b-spline basis given knots and degree on some specificed points or derivatives thereof, but we do not use that functionalityand then returns some linear combination of these basis functions. To get out the basis functions themselves, we use linear combinations like [1, 0, 0], [0, 1, 0], [0, 0, 1].

NB: This probably makes it rather inefficient though I have not checked to be sure -- maybe the fortran code actually skips computing the basis function for coefficients that are zero.

Note: there are len knots - order basis functions. T plt. Parameters x : ndarray, 1-D underlying explanatory variable for smooth terms.

This avoids perfect collinearity if a constant or several components are included in the model. By default knots are selected in the same way as in patsy, however the number of knots is independent of keeping or removing the constant.

Interior knot selection is based on quantiles of the data and is the same in patsy and mgcv. Boundary points are at the limits of the data range. Wood,pp Parameters knots : ndarray The 1-d array knots used for cubic spline parametrization, must be sorted in ascending order.

Returns b, d: ndarrays arrays for mapping cyclic cubic spline values at knots to second derivatives. If 2-dimensional, then observations should be in rows and explanatory variables in columns.

Notes A constant in the spline basis function can be removed in two different ways. The first is by dropping one basis column and normalizing the remaining columns. As a consequence of the transformation, the B-spline basis functions do not have locally bounded support anymore.

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