Bayesian Model-Based Clustering with Parsimonious Gaussian Mixture Models

Carries out model-based clustering using parsimonious Gaussian mixture models. MCMC is used for parameter estimation and RJMCMC is used for model selection.

Usage

pgmm_rjmcmc(
  X,
  m_init,
  m_range,
  q_new,
  delta = 2,
  ggamma = 2,
  burn = 20,
  niter = 1000,
  constraint = c(0, 0, 0),
  d_vec = c(1, 1, 1),
  s_vec = c(1, 1, 1),
  m_step = 0,
  v_step = 0,
  split_combine = 0,
  verbose = TRUE
)

Arguments

X: the observation matrix with variables in rows and observations in columns.
m_init: the number of initial clusters.
m_range: the allowed range for the number of clusters.
q_new: the number of latent factors for a new cluster.
delta: scalar hyperparameter for the noise covariance prior
ggamma: scalar hyperparameter used in covariance-structure proposals
burn: the number of burn-in iterations
niter: the number of posterior sampling iterations
constraint: initial PGMM covariance constraint. Use a three-letter model label such as `"CCC"` or `"UUU"`, or a numeric vector of length three with binary entries. For example, `c(1, 1, 1)` is `CCC`, the fully constrained model, and `c(0, 0, 0)` is `UUU`, the fully unconstrained model.
d_vec: a vector of hyperparameters with length three, shape parameters for alpha1, alpha2 and bbeta respectively
s_vec: a vector of hyperparameters with length three, rate parameters for alpha1, alpha2 and bbeta respectively
m_step: indicator for RJMCMC model selection on the number of clusters.
v_step: indicator for RJMCMC model selection on covariance structures.
split_combine: indicator for using split/combine moves in the cluster-number RJMCMC step.
verbose: logical; if `TRUE`, print iteration progress.

Value

A list of posterior samples with snake_case fields: `tau_samples`, `psi_samples`, `mean_samples`, `lambda_samples`, `factor_score_samples`, `allocation_samples`, `constraint_samples`, `alpha1_samples`, `alpha2_samples`, `beta_samples`, and `active_cluster_samples`.

Details

The `constraint` argument follows the three-letter PGMM model notation used in Lu, Li, and Love (2021). The first entry indicates whether loading matrices are shared across clusters, the second whether noise covariance matrices are shared across clusters, and the third whether the noise covariance is isotropic within each cluster. Use [model_to_constraint()] to convert model names such as `CCC`, `CCU`, `CUC`, `CUU`, `UCC`, `UCU`, `UUC`, and `UUU` into the numeric vector used internally.