plot 如何用一个图形（例如u 形）来显示面板数据回归中的非线性关系？

Question

I am a freshman in doing regerssion and also in using python / r I am now studying the non-linear relationship between ESG performance and Financial Performance of companies, with a set of panel data and the following equation:

ROA = C(1) + C(2)*ENV + C(3)*ENV2 + C(4)*SOC + C(5)*SOC2 + C(6)*GOV + 
             C(7)*GOV2 + C(8)*LNA + C(9)*LEV + C(10)*PB + C(11)*LNOE

ENV2, SOC2 & GOV2 are the quadratic terms for ENV, SOC & GOV respectively, and C(8)-C(11) are control variables.

I would like to plot a graph to show the marginal effect of ENV/SOC/GOV on ROA, so my question is how can I do that the plot the u-shaped or inverse u-shaped fitting curve via python or r?

Many thanks!

Answer 1

You can use the plot_cap() function from the marginaleffects package for R (disclaimer: I am the author). For example, here is a model with a quadratic term:

library(marginaleffects)

# simulate
x <- rnorm(100)
y <- x + x^2 + rnorm(100)

# fit
mod <- lm(y ~ x + I(x^2), data = mtcars)

# plot
plot_cap(mod, condition = "x")