sim_two_stage {polle}

Simulate Two-Stage Data

Description

Simulate Two-Stage Data

Usage

sim_two_stage(
  n = 10000,
  par = c(gamma = 0.5, beta = 1),
  seed = NULL,
  action_model_1 = function(C_1, beta, ...) stats::rbinom(n = NROW(C_1), size = 1, prob =
    lava::expit(beta * C_1)),
  action_model_2 = function(C_2, beta, ...) stats::rbinom(n = NROW(C_1), size = 1, prob =
    lava::expit(beta * C_2)),
  deterministic_rewards = FALSE
)

Arguments

n

Number of observations.

par

Named vector with distributional parameters.

• gamma: \gamma

• beta: \beta

seed

Integer.

action_model_1

Function used to specify the action/treatment at stage 1.

action_model_2

Function used to specify the action/treatment at stage 2.

deterministic_rewards

Logical. If TRUE, the deterministic reward contributions are returned as well (columns U_1_A0, U_1_A1, U_2_A0, U_2_A1).

Details

sim_two_stage samples n iid observation O with the following distribution: BB is a random categorical variable with levels group1, group2, and group3. Furthermore,

B \sim \mathcal{N}(0,1)\\ L_{1} \sim \mathcal{N}(0, 1)\\ C_{1} \mid L_{1} \sim \mathcal{N}(L_1, 1)\\ A_1 \mid C_1 \sim Bernoulli(expit(\beta C_1))\\ L_{2} \sim \mathcal{N} (0, 1)\\ C_{2} \mid A_1, L_1 \sim \mathcal{N}(\gamma L_1 + A_1, 1)\\ A_2 \mid C_2 \sim Bernoulli(expit(\beta C_2))\\ L_{3} \sim \mathcal{N} (0, 1)

The rewards are calculated as

U_1 = L_1\\ U_2 = A_1\cdot C_1 + L_2 \\ U_3 = A_2\cdot C_2 + L_3.

Value

data.table with n rows and columns B, BB, L_1, C_1, A_1, L_2, C_2, A_2, L_3, U_1, U_2, U_3 (,U_1_A0, U_1_A1, U_2_A0, U_2_A1).