ab_test_interaction_check_regression.R

sample_size <- 100000
base_rate <- 0.2
base_rpv <- 100
sd_rpv <- 40
lift <- c(0.05, 0.1)

# given treatment assigments for a user returns revenue
outcome <- function(u) {
  
  # if not converted, or revenue <0 return 0
  if (rbinom(n=1, size=1, prob=base_rate) == 0 | u['control_rpv'] <= 0) { 
    return(0) 
  }
  
  p = u['control_rpv']
  
  # if user is in variant of test 1, apply lift 1
  if (u['exp_1']) { p = p * (1+lift[1]) }
  # if user is in variant of test 2, apply lift 2
  if (u['exp_2']) { p = p * (1+lift[2]) }
  # if user is in variant of test 1 and test 2, apply interaction effect
  if (u['exp_1'] && u['exp_2']) { p = p * (1+u['interaction_effect']) }
  
  # return revenue for this user
  return(p)
}

run <- function(i) {
  # construct data frame with treatment assignments and control revenue for all users in both tests
  df = data.frame(exp_1 = rbinom(n=sample_size, size=1, prob=0.5),
                  exp_2 = rbinom(n=sample_size, size=1, prob=0.5),
                  control_rpv = rnorm(n=sample_size, mean=base_rpv, sd=sd_rpv),
                  interaction_effect = i)
  
  # add column for revenue outcome of each user
  df['revenue'] = apply(df, 1, outcome)
  
  # run regression with interaction term
  s <- summary(lm(revenue ~ exp_1*exp_2, data = df))
  
  return(s$coefficients['exp_1:exp_2',4])
}

# one run
run(0.1)

# lots of runs
# r <- sapply(rep(.1,1000), run)
# hist(r, breaks=100)