Constrained regression in Python

问题:

I have this simple regression model:

 y = a + b * x + c * z + error

with a constraint on parameters:

c = b - 1

There are similar questions posted on SO (like Constrained Linear Regression in Python). However, the constraints' type is lb <= parameter =< ub.

What are the available options to handle this specific constrained linear regression problem?

回答1:

This is how it can be done using GLM:

import statsmodels
import statsmodels.api as sm
import numpy as np

# Set the link function to identity
statsmodels.genmod.families.links.identity()

OLS_from_GLM = sm.GLM(y, sm.add_constant(np.column_stack(x, z)))

 '''Setting the restrictions on parameters in the form of (R, q), where R 
 and q are constraints' matrix and constraints' values, respectively. As
 for the restriction in the aforementioned regression model, i.e., 
 c = b - 1 or b - c = 1, R = [0, 1, -1] and q = 1.'''

res_OLS_from_GLM = OLS_from_GLM.fit_constrained(([0, 1.0, -1.0], 1))

print(res_OLS_from_GLM.summary())