simulate_su_hill_data: Simulate data with scenarios from Hill and Su (2013)

Description

Sample \(n\) observations with the following scheme:

Covariates: \(X_j ~ N(0,1)\).
Assignment: \(Z ~ Bin(n, p)\) with \(p = logit^{-1}(a + X \gamma^L + Q \gamma^N)\) where \(a = \omega - mean(X \gamma^L + Q \gamma^N)\).
Mean response: \(E(Y(0)|X) = X \beta_0^L + Q \beta_0^N \) and \(E(Y(1)|X) = X \beta_1^L + Q \beta_1^N\).
Observation: \(Y ~ N(\mu,\sigma_y^2))\).

Superscript \(L\) denotes the linear components, whilst \(N\) denotes the non-linear components.

Usage

simulate_su_hill_data(
  n,
  treatment_linear = TRUE,
  response_parallel = TRUE,
  response_aligned = TRUE,
  y_sd = 1,
  tau = 4,
  omega = 0,
  add_categorical = FALSE,
  n_subjects = 0,
  sd_subjects = 1,
  coef_categorical_treatment = NULL,
  coef_categorical_nontreatment = NULL
)

Value

An object of class suhillsim that is a list with elements

data: Simulated data in data.frame
mean_y: The mean y values for each individual (row)
args: List of arguments passed to function
formulas: Response formulas used to generate data
coefs: Coefficients for the formulas

Arguments

n: Size of simulated sample.
treatment_linear: Treatment assignment mechanism is linear?
response_parallel: Response surface is parallel?
response_aligned: Response surface is aligned?
y_sd: Observation noise.
tau: Treatment effect for parallel response surfaces. Not applicable if surface is nonparallel.
omega: Offset to control treatment assignment ratios.
add_categorical: Should a categorical variable be added? (Not in Hill and Su)
n_subjects: How many subjects are there? For repeated observations. (Hill and Su = 0, default)
sd_subjects: Random effect intercept standard deviation for subjects. (Not in Hill and Su. Used if n_subjects > 0)
coef_categorical_treatment: What are the coefficients of the categorical variable under treatment? (Not in Hill and Su)
coef_categorical_nontreatment: What are the coefficients of the categorical variable under nontreatment? (Not in Hill and Su)

Details

Coefficients used are returned in the list this function creates. See Table 1 in Su and Hill (2013) for the table of coefficients. The \(X_j\) are in a data.frame named data in the returned list. The formula for the model matrix \([X,Q]\) is named su_hill_formula in the returned list. The coefficients used for the model matrix are contained in coefs. The Su and Hill (2013) simulations did not include categorical variables, but you can add them here using arguments: add_categorical, coef_categorical_treatment, coef_categorical_nontreatment.

Hill, Jennifer; Su, Yu-Sung. Ann. Appl. Stat. 7 (2013), no. 3, 1386--1420. doi:10.1214/13-AOAS630. https://projecteuclid.org/euclid.aoas/1380804800