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

In tidytreatment: Tidy Methods for Bayesian Treatment Effect Models

Simulate data with scenarios from Hill and Su (2013)

Description

Sample n observations with the following scheme:

1. Covariates: X_j ~ N(0,1).

2. 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).

3. 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.

4. 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
)

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

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

tidytreatment documentation built on April 4, 2025, 5:11 a.m.