catalytic (version 0.1.0)

cat_glm_bayes_joint_gibbs: Bayesian Estimation with Gibbs Sampling for Catalytic Generalized Linear Models (GLMs) Binomial Family for Coefficients and tau

Description

This function uses Gibbs sampling to estimate a Bayesian GLMs Binomial Family, where both the coefficients and tau parameter are jointly sampled. tau is updated via a gamma distribution, while coefficients are updated using Hamiltonian Monte Carlo (HMC) sampling. The model allows for progress updates, warm-up iterations, and initial coefficient estimation based on initial tau value.

Usage

cat_glm_bayes_joint_gibbs(
  formula,
  cat_init,
  iter = 1000,
  warmup = 500,
  coefs_iter = 5,
  tau_0 = NULL,
  tau_alpha = 2,
  tau_gamma = 1,
  refresh = TRUE
)

Value

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

gibbs_iteration_log

Matrix containing the coefficients and tau values from each Gibbs iteration.

inform_df

Summary statistics of each parameter, including mean, standard error, quantiles, and effective sample size.

tau

Mean of sampled tau values.

coefficients

Mean of sampled coefficient values.

Arguments

formula

A formula specifying the GLMs. Should at least include response variables (e.g. ~.).

cat_init

A list generated from cat_glm_initialization.

iter

Integer; the number of Gibbs sampling iterations (default = 1000).

warmup

Integer; the number of initial iterations for warm-up (default = 500).

coefs_iter

Integer; the number of iterations for the HMC step to update coefficients.

tau_0

Initial value for tau; defaults to the number of predictors / 4 if NULL.

tau_alpha

Shape parameter for the gamma distribution when updating tau. Default is 2.

tau_gamma

Scale parameter for the gamma distribution when updating tau. Default is 1.

refresh

Logical; if TRUE, displays sampling progress. Default is TRUE.

Examples

# \donttest{
binomial_data <- data.frame(
  X1 = stats::rnorm(10),
  X2 = stats::rnorm(10),
  Y = stats::rbinom(10, 1, 0.5)
)

cat_init <- cat_glm_initialization(
  formula = Y ~ 1, # formula for simple model
  data = binomial_data,
  family = binomial,
  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_gibbs(
  formula = ~.,
  cat_init = cat_init, # Only accept object generated from `cat_glm_initialization`
  iter = 10, # Number of Gibbs sampling iterations
  warmup = 5, # Number of warm-up (or burn-in) iterations for initial iterations
  coefs_iter = 2, # Number of iterations for the HMC step to update coefficients
  tau_alpha = 1, # Shape parameter for the gamma distribution when updating tau
  tau_gamma = 2, # Scale parameter for the gamma distribution when updating tau
  refresh = TRUE # Indicator for displaying sampling progress
)
cat_model
# }