gibbs_sampling function

Markov chain Monte Carlo simulation for the probit model

This function draws from the posterior distribution of the probit model via Markov chain Monte Carlo simulation-

gibbs_sampling(
  sufficient_statistics,
  prior,
  latent_classes,
  fixed_parameter,
  init,
  R,
  B,
  print_progress,
  ordered,
  ranked
)

Arguments

• sufficient_statistics: The output of sufficient_statistics.

• prior: A named list of parameters for the prior distributions. See the documentation of check_prior for details about which parameters can be specified.

• latent_classes: Either NULL (for no latent classes) or a list of parameters specifying the number of latent classes and their updating scheme:

  • C: The fixed number (greater or equal 1) of latent classes, which is set to 1 per default. If either weight_update = TRUE

    or dp_update = TRUE (i.e. if classes are updated), C

    equals the initial number of latent classes.

  • weight_update: A boolean, set to TRUE to weight-based update the latent classes. See ... for details.

  • dp_update: A boolean, set to TRUE to update the latent classes based on a Dirichlet process. See ... for details.

  • Cmax: The maximum number of latent classes.

  • buffer: The number of iterations to wait before a next weight-based update of the latent classes.

  • epsmin: The threshold weight (between 0 and 1) for removing a latent class in the weight-based updating scheme.

  • epsmax: The threshold weight (between 0 and 1) for splitting a latent class in the weight-based updating scheme.

  • distmin: The (non-negative) threshold in class mean difference for joining two latent classes in the weight-based updating scheme.

• fixed_parameter: Optionally specify a named list with fixed parameter values for alpha, C, s, b, Omega, Sigma, Sigma_full, beta, z, or d for the simulation. See the vignette on model definition

  for definitions of these variables.

• init: The output of set_initial_gibbs_values.

• R: The number of iterations of the Gibbs sampler.

• B: The length of the burn-in period, i.e. a non-negative number of samples to be discarded.

• print_progress: A boolean, determining whether to print the Gibbs sampler progress and the estimated remaining computation time.

• ordered: A boolean, FALSE per default. If TRUE, the choice set alternatives is assumed to be ordered from worst to best.

• ranked: TBA

Returns

A list of Gibbs samples for

• Sigma,
• alpha (if P_f\>0),
• s, z, b, Omega (if P_r\>0),
• d (if ordered = TRUE),

and a vector class_sequence of length R, where the rth entry is the number of latent classes after iteration r.

Details

This function is not supposed to be called directly, but rather via fit_model.