约束最小二乘法 [英] Constrained least squares

问题描述

我对人均燃气使用量的R进行了简单回归.回归公式如下:

I am fitting a simple regression in R on gas usage per capita. The regression formulas looks like:

gas_b <- lm(log(gasq_pop) ~ log(gasp) + log(pcincome) + log(pn) +
            log(pd) + log(ps) + log(years), 
            data=gas)
summary(gas_b)

我想包含一个线性约束，即log(pn)+log(pd)+log(ps)=1的beta系数(总和为1).是否有一种简单的方法可以在R中实现此功能(可能在lm函数中)而无需使用constrOptim()函数?

I want to include a linear constraint that the beta coefficients of log(pn)+log(pd)+log(ps)=1 (sum to one). Is there a simple way of implementing this (possibly in the lm function) in R without having to use constrOptim() function?

推荐答案

按如下所示修改回归:

gas_b <- lm(log(gasq_pop) - log(ps) ~ log(gasp) + log(pcincome) +
  I(log(pn)-log(ps)) + I(log(pd)-log(ps)) + log(years), data=gas) 
summary(gas_b)

如果为b=coef(gas_b)，则相关系数为

log(pn): b[4]
log(pd): b[5]
log(ps): 1 - b[4] - b[5]

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