fabMix5.1 package

Overfitting Bayesian Mixtures of Factor Analyzers with Parsimonious Covariance and Unknown Number of Components

update_z_b

Gibbs sampling for zz

complete.log.likelihood

Complete log-likelihood function for xCx models.

complete.log.likelihood_q0

Complete log-likelihood function for xUx models and q=0q=0

complete.log.likelihood_q0_sameSigma

Complete log-likelihood function for xCx models and q=0q=0

complete.log.likelihood_Sj

Complete log-likelihood function for xUx models.

compute_A_B_G_D_and_simulate_mu_Lambda

Computation and simulations

compute_A_B_G_D_and_simulate_mu_Lambda_CCU

Computation and simulations for CCU

compute_A_B_G_D_and_simulate_mu_Lambda_CUU

Computation and simulations for CUU

compute_A_B_G_D_and_simulate_mu_Lambda_q0

Computation and simulations for q=0q = 0.

compute_A_B_G_D_and_simulate_mu_Lambda_q0_sameSigma

Computation and simulations for q=0q = 0.

compute_A_B_G_D_and_simulate_mu_Lambda_Sj

Computation and simulations

compute_sufficient_statistics

Compute sufficient statistics

compute_sufficient_statistics_given_mu

Compute sufficient statistics given mu

compute_sufficient_statistics_q0

Compute sufficient statistics for q=0q = 0

CorMat_mcmc_summary

Compute quantiles for the correlation matrix.

CovMat_mcmc_summary

Compute quantiles for the covariance matrix.

dealWithLabelSwitching

Apply label switching algorithms

fabMix-package

tools:::Rd_package_title("fabMix")

fabMix

Main function

fabMix_CxC

Function to estimate the CUC and CCC models

fabMix_CxU

Function to estimate the CCU and CUU models

fabMix_missing_values

Function to estimate the UUU or UCU models in case of missing values

fabMix_parallelModels

Function for model-level parallelization

fabMix_UxC

Function to estimate the UUC and UCC models

fabMix_UxU

Function to estimate the UUU and UCU model

getStuffForDIC

Compute information criteria

log_dirichlet_pdf

Log-density function of the Dirichlet distribution

myDirichlet

Simulate from the Dirichlet distribution

observed.log.likelihood0

Log-likelihood of the mixture model

observed.log.likelihood0_q0_sameSigma

Log-likelihood of the mixture model for q=0q=0 and same variance of err...

observed.log.likelihood0_Sj

Log-likelihood of the mixture model

observed.log.likelihood0_Sj_q0

Log-likelihood of the mixture model for q=0q=0

overfitting_q0

MCMC sampler for q=0q=0

overfitting_q0_sameSigma

MCMC sampler for q=0q=0 and same error variance parameterization

overfittingMFA

Basic MCMC sampler for the UCU model

overfittingMFA_CCC

Basic MCMC sampler for the CCC model

overfittingMFA_CCU

Basic MCMC sampler for the CCU model

overfittingMFA_CUC

Basic MCMC sampler for the CUC model

overfittingMFA_CUU

Basic MCMC sampler for the CUU model

overfittingMFA_missing_values

Basic MCMC sampler for the case of missing data

overfittingMFA_Sj

Basic MCMC sampler for the UUU model

overfittingMFA_Sj_missing_values

Basic MCMC sampler for the case of missing data and different error va...

overfittingMFA_UCC

Basic MCMC sampler for the UCC model

overfittingMFA_UUC

Basic MCMC sampler for the UUC model

plot.fabMix.object

Plot function

print.fabMix.object

Print function

readLambdaValues

Read Lambda values.

simData

Synthetic data generator

simData2

Synthetic data generator 2

summary.fabMix.object

Summary method

update_all_y

Gibbs sampling for yy in xCx model

update_all_y_Sj

Gibbs sampling for yy in xUx model

update_OmegaINV

Gibbs sampling for Ω1\Omega^{-1}

update_OmegaINV_Cxx

Gibbs sampling for Ω1\Omega^{-1} for Cxx model

update_SigmaINV_faster

Gibbs sampling for Σ1\Sigma^{-1}

update_SigmaINV_faster_q0

Gibbs sampling for Σ1\Sigma^{-1} per component for q=0q=0

update_SigmaINV_faster_q0_sameSigma

Gibbs sampling for Σ1\Sigma^{-1} per component for q=0q=0

update_SigmaINV_faster_Sj

Gibbs sampling for Σ1\Sigma^{-1} per component

update_SigmaINV_xCC

Gibbs sampling for Σ1\Sigma^{-1} for xCC models

update_SigmaINV_xUC

Gibbs sampling for Σ1\Sigma^{-1} per component for xUC models

update_z_b_Sj

Gibbs sampling for zz

update_z_q0

Gibbs sampling for zz for q=0q=0

update_z_q0_sameSigma

Gibbs sampling for zz for q=0q=0

update_z2

Collapsed Gibbs for zz using matrix inversion lemma

update_z2_Sj

Collapsed Gibbs for zz using matrix inversion lemma

update_z4

Collapsed Gibbs for zz

update_z4_Sj

Collapsed Gibbs for zz

Model-based clustering of multivariate continuous data using Bayesian mixtures of factor analyzers (Papastamoulis (2019) <DOI:10.1007/s11222-019-09891-z> (2018) <DOI:10.1016/j.csda.2018.03.007>). The number of clusters is estimated using overfitting mixture models (Rousseau and Mengersen (2011) <DOI:10.1111/j.1467-9868.2011.00781.x>): suitable prior assumptions ensure that asymptotically the extra components will have zero posterior weight, therefore, the inference is based on the ``alive'' components. A Gibbs sampler is implemented in order to (approximately) sample from the posterior distribution of the overfitting mixture. A prior parallel tempering scheme is also available, which allows to run multiple parallel chains with different prior distributions on the mixture weights. These chains run in parallel and can swap states using a Metropolis-Hastings move. Eight different parameterizations give rise to parsimonious representations of the covariance per cluster (following Mc Nicholas and Murphy (2008) <DOI:10.1007/s11222-008-9056-0>). The model parameterization and number of factors is selected according to the Bayesian Information Criterion. Identifiability issues related to label switching are dealt by post-processing the simulated output with the Equivalence Classes Representatives algorithm (Papastamoulis and Iliopoulos (2010) <DOI:10.1198/jcgs.2010.09008>, Papastamoulis (2016) <DOI:10.18637/jss.v069.c01>).