multinomialLogitMix {multinomialLogitMix}

Main function

Description

The main function of the package.

Usage

multinomialLogitMix(response, design_matrix, method, 
	Kmax = 10, mcmc_parameters = NULL, em_parameters = NULL, 
	nCores, splitSmallEM = TRUE)

Arguments

response

matrix of counts.

design_matrix

design matrix (including constant term).

method

character with two possible values: "EM" or "MCMC" indicating the desired method in order to estimate the model.

Kmax

number of components of the (overfitting) mixture model.

nCores

Total number of CPU cores for parallel processing.

mcmc_parameters

List with the parameter set-up of the MCMC sampler. See details for changing the defaults.

em_parameters

List with the parameter set-up of the EM algorithm. See details for changing the defaults.

splitSmallEM

Boolean value, indicating whether the split-small EM scheme should be used to initialize the method. Default: true (suggested).

Details

The details of the parameter setup of the EM algorithm and MCMC sampler. The following specification correspond to the minimal default settings. Larger values of tsplit will result to better performance.

em_parameters <- list(maxIter = 100, emthreshold = 1e-08, maxNR = 10, tsplit = 16, msplit = 10, split = TRUE, R0 = 0.1, plotting = TRUE)

mcmc_parameters <- list(tau = 0.00035, nu2 = 100, mcmc_cycles = 2600, iter_per_cycle = 20, nChains = 8, dirPriorAlphas = c(1, 1 + 5 * exp((seq(2, 14, length = nChains - 1)))/100)/(200), warm_up = 48000, checkAR = 500, probsSave = FALSE, showGraph = 100, ar_low = 0.15, ar_up = 0.25, burn = 100, thin = 1, withRandom = TRUE)

Value

EM

List with the results of the EM algorithm.

MCMC_raw

List with the raw output of the MCMC sampler - not identifiable MCMC output.

MCMC_post_processed

Post-processed MCMC, used for the inference.

Author(s)

Panagiotis Papastamoulis

References

Papastamoulis, P. Model based clustering of multinomial count data. Advances in Data Analysis and Classification (2023). https://doi.org/10.1007/s11634-023-00547-5

Examples

#	Generate synthetic data

	K <- 2	#number of clusters
	p <- 2	#number of covariates (constant incl)
	D <- 5	#number of categories
	n <- 20 #generated number of observations
	set.seed(1)
	simData <- simulate_multinomial_data(K = K, p = p, D = D, n = n, size = 20, prob = 0.025)   


	# EM parameters
em_parameters <- list(maxIter = 100, emthreshold = 1e-08, 
    maxNR = 10, tsplit = 16, msplit = 10, split = TRUE, 
    R0 = 0.1, plotting = TRUE)

	#  MCMC parameters - just for illustration
	#	typically, set `mcmc_cycles` and `warm_up`to a larger values
	#	such as` mcmc_cycles = 2500` or more 
	#	and `warm_up = 40000` or more.
	nChains <- 2 #(set this to a larger value, such as 8 or more)
	mcmc_parameters <- list(tau = 0.00035, nu2 = 100, mcmc_cycles = 260, 
	    iter_per_cycle = 20, nChains = nChains, dirPriorAlphas = c(1, 
		1 + 5 * exp((seq(2, 14, length = nChains - 1)))/100)/(200), 
	    warm_up = 4800, checkAR = 500, probsSave = FALSE, 
	    showGraph = 100, ar_low = 0.15, ar_up = 0.25, burn = 100, 
	    thin = 1, withRandom = TRUE)

	# run EM with split-small-EM initialization, and then use the output to 
	#	initialize MCMC algorithm for an overfitting mixture with 
	#	Kmax = 5 components (max number of clusters - usually this is 
	#	set to a larger value, e.g. 10 or 20).
	#	Note: 
	#		1. the MCMC output is based on the non-empty components
	#		2. the EM algorithm clustering corresponds to the selected 
	#			number of clusters according to ICL.
	#		3. `nCores` should by adjusted according to your available cores.
	
	mlm <- multinomialLogitMix(response = simData$count_data, 
		design_matrix = simData$design_matrix, method = "MCMC", 
             Kmax = 5, nCores = 2, splitSmallEM = TRUE, 
             mcmc_parameters = mcmc_parameters, em_parameters = em_parameters)
	# retrieve clustering according to EM
	mlm$EM$estimated_clustering
	# retrieve clustering according to MCMC
	mlm$MCMC_post_processed$cluster