在Python中,在执行OLS回归之前,需要手动声明系数。

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英文:

Declare manually the coefficients before doing an ols regression in python

问题

我想在这种类型的方程上运行OLS回归:y = b0 + b1*x1 + (1 - b1) * x2 + b2 * x3。

所以我需要手动声明系数,但我在Python中使用statsmodel包找不到如何做到这一点的方法。请问有人知道如何在方程中声明系数吗?

英文:

I want to run an ols regression on this type of equations: y = b0 + b1*x1 + (1 - b1) * x2 + b2 * x3.

So I need to declare manually the coefficients but I didn't find how to do it in python using the statsmodel package. Please anyone have an idea how to declare the coefficients in the equation?

答案1

得分: 0

如果您想要强加线性约束并估计剩余参数,有三种选项。

重新编写OLS公式

将公式:

y = b0 + b1*x1 + (1 - b1) * x2 + b2 * x3

重写为:

y - x2 = b0 + b1*(x1 - x2) + b2 * x3
y_new = b0 + b1 * x_diff + b2 *x3

然后使用后面的方程使用OLS来估计系数。缺点是:predict 返回了 y_new 的期望值。

带偏移的GLM

GLM: y ~ b0 + b1*(x1 - x2) + b2 * x3, offset=x2

这里使用了线性函数中的 offset,系数为 1。
predict 用于 y,但需要偏移项。
GLM 的默认 family 是具有线性链接的高斯分布,即与OLS相同。

带有fit_constrained的GLM

强加线性(实际上是仿射)约束,使x1和x2的系数相加等于1:

GLM.from_formula("y = x1 + x2 + x3").fit_constrained("x1 + x2 = 1")

(对于OLS不可用的 fit_constrained)。

英文:

Three options if you want to impose the linear constraint and estimate the remaining parameters

Rewrite formula for OLS

y = b0 + b1*x1 + (1 - b1) * x2 + b2 * x3

as

y - x2 = b0 + b1*(x1 - x2) + b2 * x3
y_new = b0 + b1 * x_diff + b2 *x3

and estimate coefficients with OLS using the later equation.
disadvantage: predict returns expectation for y_new.

GLM with offset

GLM: y ~ b0 + b1*(x1 - x2) + b2 * x3, offset=x2

This uses offset with coefficient 1 in the linear function.
predict is for y, but needs offset.
Default family for GLM is Gaussian with linear link, i.e. the same as OLS.

GLM with fit_constrained

impose linear (actually affine) restriction that coefficients for x1 and x2 add to 1:

GLM.from_formula("y = x1 + x2 + x3").fit_constrained("x1 + x2 = 1")

(fit_constrained is not available for OLS)

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  • 本文由 发表于 2023年6月2日 08:13:54
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