cjekel
commented
5 years ago I'm glad my library has been useful.
Just to be clear, in order to apply a p-value you must manually specify the break point locations. The assumption being made here is that your break point locations are the true -- or known-- break point locations.
The standard errors or p-values do not account for the error in your break point locations.
I have future plans to derive a method to approximate statistical properties when the break point locations are unknown, but this probably won't happen until there is a well documented paper for this library.
Section 2.4.2 of [1] (There are many editions of this book) defines how to calculate the p-value of individual parameters. Note that this is really a marginal test since each parameter is dependent upon the other parameters..
Essentially we have that t_j = \beta_j / se(\beta_j) where se denotes the standard error.
The p-value for t_j is the probability of having a value greater than |t_j| which follows Student's t-distribution of df=n-k-1. Where n is the number of data points, and k is the number of parameters.
And then to solve for the p-values we would do
from scipy import stats
# Get my model parameters
beta = my_pwlf.beta
# calculate the standard errors associated with each beta parameter
# not that these standard errors and p-values are only meaningful if
# you have specified the specific line segment end locations
# at least for now...
se = my_pwlf.standard_errors()
# calculate my t-value
t = beta / se
# degrees of freedom for t-distribution
n = len(x)
k = len(beta)
# calculate the p-values
pvalues = stats.t.sf(abs(t), df=n-k-1)I've just added an example here which you can use as your reference.
Ref: [1] Myers RH, Montgomery DC, Anderson-Cook CM. Response surface methodology . Hoboken. New Jersey: John Wiley & Sons, Inc. 2009;20:38-44.
Let me plan to add this to the library, but for now you'll have to add the few lines of code yourself.
adri-MASH
Hey cjekel,
Thanks a lot for your work. Is there a way I can retrieve the p-values of the coefficients of piecewise regression? Thank you.