RTMB-based Bayesian two-sample t-test wrapper function

Performs a Bayesian two-sample t-test using RTMB. It estimates the effect size (delta) with a Cauchy prior, allowing for robust inference and calculation of Bayes factors.

Usage

rtmb_ttest(
  x,
  y = NULL,
  data = NULL,
  r = 0.707,
  y_range = NULL,
  use_weak_info = FALSE,
  prior = list(mean_sd = 10, sd_rate = 0.1),
  weak_info_prior = list(sd_ratio = 0.5),
  init = NULL,
  null = NULL,
  y1 = NULL,
  y2 = NULL
)

Arguments

x

Numeric vector of responses for group 1, or a formula (e.g., `y ~ group`).

y

Numeric vector of responses for group 2. Required if `x` is not a formula.

data

Data frame containing the variables in the formula.

r

Numeric; Cauchy prior scale for the effect size (delta). Default is 0.707.

y_range

Theoretical minimum and maximum values of the response variable as a vector c(min, max). Specifying this automatically enables weakly informative priors.

use_weak_info

Logical; whether to explicitly use weakly informative priors.

prior

List of hyperparameters for the default fixed priors.

weak_info_prior

List of hyperparameters for the weakly informative priors.

init

List of initial values.

null

Character string specifying the target parameter for the null model (e.g., "delta" or "delta ~ cauchy(0, r)").

y1

Deprecated. Use `x` instead.

y2

Deprecated. Use `y` instead.

Value

An RTMB_Model object.

Examples

if (FALSE) { # \dontrun{
  # Simulate two-sample data with a true effect size
  set.seed(123)
  y1 <- rnorm(30, mean = 0.5, sd = 1)
  y2 <- rnorm(30, mean = 0.0, sd = 1)

  # Fit the Bayesian two-sample t-test model
  # r = 0.707 is the standard scale for the Cauchy prior on the effect size
  fit_ttest <- rtmb_ttest(y1, y2, r = 0.707)

  # MCMC sampling (chains and iterations reduced for faster execution)
  mcmc_ttest <- fit_ttest$sample(sampling = 500, warmup = 500, chains = 2)
  mcmc_ttest$summary()

  # Calculate Bayes factor against the null hypothesis (effect size delta = 0)
  # Specifying "delta" automatically fixes the parameter to 0 and drops its prior
  bf_ttest <- mcmc_ttest$bayes_factor(null_model = "delta")
  print(bf_ttest)
} # }