sim_two_stage_multi_actions {polle}

Simulate Two-Stage Multi-Action Data

Description

Simulate Two-Stage Multi-Action Data

Usage

sim_two_stage_multi_actions(
  n = 1000,
  par = list(gamma = 0.5, beta = 1, prob = c(0.2, 0.4, 0.4)),
  seed = NULL,
  action_model_1 = function(C_1, beta, ...) stats::rbinom(n = NROW(C_1), size = 1, prob =
    lava::expit(beta * C_1))
)

Arguments

n

Number of observations.

par

Named vector with distributional parameters.

• gamma: \gamma

• beta: \beta

• prob: p

seed

Integer.

action_model_1

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

Details

sim_two_stage_multi_actions 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)\\ P(A_1='yes'\mid C_1) = expit(\beta C_1)\\ P(A_1='no'\mid C_1) = 1 - P(A_1='yes' \mid 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)\\ P(A_2='yes') = p_1\\ P(A_2='no') = p_2\\ P(A_2='default') = p_3\\ 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.