How to plot decision boundary in R for logistic regression model?

Question

I made a logistic regression model using glm in R. I have two independent variables. How can I plot the decision boundary of my model in the scatter plot of the two variables. For example, how can I plot a figure like here.

Answer 1

set.seed(1234)

x1 <- rnorm(20, 1, 2)
x2 <- rnorm(20)

y <- sign(-1 - 2 * x1 + 4 * x2 )

y[ y == -1] <- 0

df <- cbind.data.frame( y, x1, x2)

mdl <- glm( y ~ . , data = df , family=binomial)

slope <- coef(mdl)[2]/(-coef(mdl)[3])
intercept <- coef(mdl)[1]/(-coef(mdl)[3]) 

library(lattice)
xyplot( x2 ~ x1 , data = df, groups = y,
   panel=function(...){
       panel.xyplot(...)
       panel.abline(intercept , slope)
       panel.grid(...)
       })

I must remark that perfect separation occurs here, therefore the glm function gives you a warning. But that is not important here as the purpose is to illustrate how to draw the linear boundary and the observations colored according to their covariates.

Answer 2

Wanted to address the question in comment to the accepted answer above from Fernando: Can someone explain the logic behind the slope and intercept?

The hypothesis for logistics regression takes the form of:

$$h_{\theta} = g(z)$$

where, $g(z)$ is the sigmoid function and where $z$ is of the form:

$$z = \theta_{0} + \theta_{1}x_{1} + \theta_{2}x_{2}$$

Given we are classifying between 0 and 1, $y = 1$ when $h_{\theta} \geq 0.5$ which given the sigmoid function is true when:

$$\theta_{0} + \theta_{1}x_{1} + \theta_{2}x_{2} \geq 0$$

the above is the decision boundary and can be rearranged as:

$$x_{2} \geq \frac{-\theta_{0}}{\theta_{2}} + \frac{-\theta_{1}}{\theta_{2}}x_{1}$$

This is an equation in the form of $y = mx + b$ and you can see then why $m$ and $b$ are calculated the way they are in the accepted answer