Lowess smoothed as defined for STATA 13.
The lowess Package
This package provides a function to perform a LOWESS on Pandas Series objects. LOWESS (locally weighted scatterplot smoothing) [1, 2] as defined by STATA . The regressions utilises some of the methods in .
Methods and Formula
Let x and y be the two variables each of length N, and assume that the data are ordered so that xi = < xi+1 for i = 1,...,N-1. For each yi, a smoothed value yis is calculated. The subset of points used in calculating yis is i- = max(1, i-k) through i+ = min(i+k, N), where
k = Floor((N × bandwidth - 0.5) / 2).
The weights for each of the observations between j = i-,...,i+ are the tricube
wj = [1 - (|xj - xi| / ∆)3]3,
where ∆ = 1.0001 max(xi+-xi, xi-xi-). The smoothed value yis is then the weighted polynomial regression prediction at xi.
NB: In this implemtation x and y should be Pandas Series objects. The series need not be sorted and x and y can be in different orders, so long as their indexes have the same elements.
Once the package has been installed it can be imported into a python script
The package provides a single module
lowess with a single function
This function has the signiture:
lowess.lowess(x, y, bandwidth=0.2, polynomialDegree=1)
where the arguments are:
- x (pandas.core.series.Series): a Pandas Series containing the x (independent/covariat) values. The indices must be unique.
- y (pandas.core.series.Series): a Pandas Series containing the y (dependent) values. It must have the same index as x (although not necessarily in the same order.)
- bandwidth (float, optional): the bandwidth for smoothing. It must be between 0 and 1. Default is 0.2
- polynomialDegree (int, optional): The degree of polynomial to use in the regression. It must be >= 0. Default is 1.
It returns a Pandas Series containing the smoothed y values, with the same index as y.
If the input is not valid or an error occurs, a
LowessError exception is raised.
Some examples are given in the directory
Via the PyPI package manager
The package can be installed with
pip via the command:
$ pip install lowess
The package can be installed from source via GitHub.
First download the repository, either via SSH
$ git clone firstname.lastname@example.org:CCGE-Cambridge/lowess.git
or via HTTPS
$ git clone https://github.com/CCGE-Cambridge/lowess.git
Then install the package via
$ cd lowess $ pip install .
Documentaion of the API is provided via Sphinx. To make the documentaion
$ cd docs $ make html $ open build/html/index.html
This may require installation of the package
Unit tests are implemented via
unittest and are in the file
To run the tests first download the source code and then run the command:
$ python tests/test_lowess.py
Copyright (c) 2020 Andrew Lee
This software is provided as is without any warranty whatsoever. Permission to use, for non-commercial purposes is granted. Permission to modify for personal or internal use is granted, provided this copyright and disclaimer are included in all copies of the software. All other rights are reserved. In particular, redistribution of the code is not allowed.
- Cleveland, W. S. 1979. Robust locally weighted regression and smoothing scatterplots. Journal of the American Statistical Association 74: 829–836. [https://www.jstor.org/stable/2286407]
- Wikipedia: Local Regression - [https://en.wikipedia.org/wiki/Local_regression] (accessed 2020-04-20)
- STATA: Lowess - [https://www.stata.com/manuals13/rlowess.pdf] (accessed 2020-04-20)
- Cappellari et al. 2013 The ATLAS3D project - XX. Mass-size and mass-σ distributions of early-type galaxies: bulge fraction drives kinematics, mass-to-light ratio, molecular gas fraction and stellar initial mass function Monthly Notices of the Royal Astronomical Society 432: 1862-1893 [https://doi.org/10.1093/mnras/stt644]
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