Interaction Equivalence Example

set.seed(123)

N     = 1000
p     = runif(1)
alpha = runif(1)
beta1 = runif(1)
beta2 = runif(1)
beta3 = runif(1)
X     = rnorm(N)
D     = rbinom(N,1,p)
Y     = alpha+beta1*X+beta2*D+beta3*X*D+rnorm(N)

c(alpha,beta1,beta2,beta3)
summary(lm(Y~X*D))
summary(lm(Y[D==0]~X[D==0]))
summary(lm(Y[D==1]~X[D==1]))