Python中的约束回归

Question

我有这个简单的回归模型：

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

对参数有约束：

c = b - 1

在SO上也发布了类似的问题（例如Python中的约束线性回归）。但是，约束的类型为lb <= parameter =< ub。

有什么可用的选项来处理这个特定的约束线性回归问题？

Answer 1

使用GLM可以做到这一点：

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())