background
this app relates to this chapter in our book https://scpoecon.github.io/ScPoEconometrics/binary.html
this should illustrate why there is no single marginal effect in a probit model. that is while in the linear model
in the nonlinear probit/logit case we have
d Pr(y_i = 1 | x) / dx_i = g(x\beta) \beta_i
where g is the pdf of the chosen cdf G (standard normal for probit, logistic for logit)
that is: the marginal effect depends not only on \beta_i but at which x you choose to evaluate that expression. In this app we assume for simplicity that \beta = 1.
Output of app
something like this plot:
library(ggplot2)
ggplot(data.frame(x = c(-5,5)), aes(x=x)) +
stat_function(fun = pnorm, aes(colour = "Probit")) +
stat_function(fun = plogis, aes(colour = "Logit")) +
theme_bw() +
scale_colour_manual(name = "Function G",values = c("red", "blue")) +
scale_y_continuous(name = "Pr(y = 1 | x)")
(but for one case at a time)
where you add a straight tangent line illustrating the slope at a certain value of x.
app input
- dropdown menu : logit vs probit
- slider: x \in [-3,3]. this value is evaluated in g(x). you draw a straight line through point (x,G(x)) (put a marker there), with slope g(x).
background
this app relates to this chapter in our book https://scpoecon.github.io/ScPoEconometrics/binary.html
this should illustrate why there is no single marginal effect in a probit model. that is while in the linear model
in the nonlinear probit/logit case we have
where
gis the pdf of the chosen cdfG(standard normal for probit, logistic for logit)that is: the marginal effect depends not only on \beta_i but at which
xyou choose to evaluate that expression. In this app we assume for simplicity that \beta = 1.Output of app
something like this plot:
(but for one case at a time)
where you add a straight tangent line illustrating the slope at a certain value of
x.app input