cat_glm_bayes_joint: Bayesian Estimation for Catalytic Generalized Linear Models...

In catalytic: Tools for Applying Catalytic Priors in Statistical Modeling

Bayesian Estimation for Catalytic Generalized Linear Models (GLMs) with adaptive tau

Description

This function performs Bayesian estimation for a catalytic Generalized Linear Models (GLMs) using RStan by using adaptive tau. It supports both Gaussian and Binomial family models, enabling flexibility in prior specifications and algorithm configurations.

Usage

cat_glm_bayes_joint(
  formula,
  cat_init,
  chains = 4,
  iter = 2000,
  warmup = 1000,
  algorithm = "NUTS",
  tau_alpha = 2,
  tau_gamma = 1,
  binomial_tau_lower = 0.05,
  binomial_joint_theta = FALSE,
  binomial_joint_alpha = FALSE,
  gaussian_variance_alpha = NULL,
  gaussian_variance_beta = NULL,
  ...
)

Arguments

formula	A formula specifying the GLMs. Should at least include response variables (e.g. ~.).
cat_init	A list generated from cat_glm_initialization.
chains	Number of Markov chains to run. Default is 4.
iter	Total number of iterations per chain. Default is 2000.
warmup	Number of warm-up iterations per chain (discarded from final analysis). Default is 1000.
algorithm	The sampling algorithm to use in rstan::sampling. Default is "NUTS" (No-U-Turn Sampler).
tau_alpha	Shape parameter of the prior for tau. Default is 2.
tau_gamma	Scale parameter of the prior for tau. Default is 1.
binomial_tau_lower	A numeric lower bound for tau in Binomial models. Default is 0.05.
binomial_joint_theta	Logical; if TRUE, uses joint theta (theta = 1/tau) in Binomial models. Default is FALSE.
binomial_joint_alpha	Logical; if TRUE, uses joint alpha (adaptive tau_alpha) in Binomial models. Default is FALSE. To activate this feature, both binomial_joint_theta = TRUE and binomial_joint_alpha = TRUE must be set.
gaussian_variance_alpha	The shape parameter for the inverse-gamma prior on variance if the variance is unknown in Gaussian models. Defaults to the number of predictors.
gaussian_variance_beta	The scale parameter for the inverse-gamma prior on variance if the variance is unknown in Gaussian models. Defaults to the number of predictors times variance of observation response.
...	Additional parameters to pass to rstan::sampling.

Value

A list containing the values of all the arguments and the following components:

stan_data	A data list used for fitting RStan sampling model.
stan_model	Compiled RStan model object for GLMs.
stan_sample_model	Fitted RStan sampling model containing posterior samples.
coefficients	Mean posterior estimates of model coefficients from stan_sample_model.
tau	Mean posterior of tau (or transformed theta if applicable).

Examples

gaussian_data <- data.frame(
  X1 = stats::rnorm(10),
  X2 = stats::rnorm(10),
  Y = stats::rnorm(10)
)

cat_init <- cat_glm_initialization(
  formula = Y ~ 1, # formula for simple model
  data = gaussian_data,
  syn_size = 100, # Synthetic data size
  custom_variance = NULL, # User customized variance value
  gaussian_known_variance = FALSE, # Indicating whether the data variance is unknown
  x_degree = c(1, 1), # Degrees for polynomial expansion of predictors
  resample_only = FALSE, # Whether to perform resampling only
  na_replace = stats::na.omit # How to handle NA values in data
)

cat_model <- cat_glm_bayes_joint(
  formula = ~.,
  cat_init = cat_init, # Only accept object generated from `cat_glm_initialization`
  chains = 1, # Number of Markov chains to be run in the RStan sampling
  iter = 10, # Number of iterations per chain in the RStan sampling
  warmup = 5, # Number of warm-up (or burn-in) iterations for each chain
  algorithm = "NUTS", # Sampling algorithm to use in \code{rstan::sampling}
  tau_alpha = 1, # Shape parameter of the prior for tau
  tau_gamma = 2, # Scale parameter of the prior for tau
  binomial_tau_lower = 0.05, # Lower bound for tau in Binomial models.
  binomial_joint_theta = FALSE, # Indicator for using joint theta for Binomial models
  binomial_joint_alpha = FALSE, # Indicator for using oint alpha for Binomial models
  gaussian_variance_alpha = 1, # The shape parameter for the inverse-gamma prior for variance
  gaussian_variance_beta = 2 # The scale parameter for the inverse-gamma prior for variance
)
cat_model

catalytic documentation built on April 4, 2025, 5:51 a.m.