Deep interactions

deep_interactions.R

library(ggplot2)

Xs <- 10
N <- 200


d <- data.frame(matrix(rnorm(Xs * N), nrow = N))

d$prod <- apply(d, 1, function(x) prod(x[1:5]))

d$y <-  d$prod + rnorm(N, 0, 0.1)


ggplot(d, aes(y, prod)) + 
  geom_point()

ggplot(d, aes(y, X1)) + 
  geom_point()

ggplot(d, aes(y, X1 * X2)) + 
  geom_point()

testxs <- Xs
binary <- rep(list(0:1), testxs)

mods <- do.call(expand.grid, binary)
mods <- mods[rowSums(mods) > 1, ]
rsquared <- rep(NA, nrow(mods))


cand_xs <- names(d)[seq(testxs)]

for(i in seq_len(nrow(mods))){
  
  covs <- cand_xs[as.logical(unlist(mods[i, ]))]
  cov_string <- paste0(covs, collapse = ':')
  print(cov_string)
  form <- as.formula(paste0('y ~ ', cov_string))
  
  m <- lm(form, data = d)
  rsquared[i] <- summary(m)$adj.r.squared
}

plot(rsquared)