code to understand product terms and probit models

probit-product-term.R

# code to understand product terms and probit models

# clear workspace
rm(list = ls())

# load packages
library(tidyverse)
library(plotly)

# parameters
n_pts <- 100  # number of values of x (and z) at which we calcalte Pr(y = 1)
b_cons <- -3  # Pr(y) = Phi(b_cons + b_x*x + b_z*z + b_xz*x*z)
b_x <- 0
b_z <- -3
b_xz <- 6

# create data for surface
x_pred <- z_pred <- seq(0, 1, length.out = n_pts)  # values at which to calculate Pr(y)
df <- data.frame(x = x_pred, z = z_pred) %>%  # put values in data frame
  expand(x, z) %>%  # expand data frame to all combinations
  mutate(prob = pnorm(b_cons + b_x*x + b_z*z + b_xz*x*z))  # calculate Pr(y) for all combinations

# put Pr(y) or df$prob in a numeric matrix
X <- matrix(df$prob, nrow = n_pts, ncol = n_pts, byrow = FALSE)

# plot surface
plot_ly() %>% 
  add_surface(x = x_pred, y = z_pred, z = X) %>%
  layout(scene = list(xaxis = list(title = "x"),
                      yaxis = list(title = "z"),
                      zaxis = list(title = "Probability")))